text:
for Evaporation from Inverted Meniscus in Porous Media
Evaporators that are capable of withstanding high-heat fluxes, for example larger than 100 W/cm2, are of great interest for electronic component cooling systems. The most promising evaporator design is the so-called "inverted meniscus" type. To predict the critical heat flux and effective heat transfer coefficients in the evaporator, a mathematical model has been developed by [[#References|Khrustalev and Faghri (1995a)]]. The model includes the following interconnected problems, which are treated simultaneously in the frames of the numerical analysis: (1) heat transfer during evaporation from a pore, (2) heat transfer and vapor flow in the dry region of a porous structure with a stable side boundary, the location of which depends on the operational conditions, and (3) heat conduction in a solid fin (or wall) with a non-uniform heat sink on the side surfaces. Heat transfer during evaporation from a pore has been presented in Section 9.6.1. Heat transfer and vapor flow in the dry region, as well as heat conduction in the solid fin, will be presented in this subsection. [[Image:NewChapter9 (9).png|thumb|400 px|alt= Schematic of the modeled elements of the inverted meniscus evaporators: | Figure 9.30 Schematic of the modeled elements of the inverted meniscus evaporators: (a) with triangular fin for low heat fluxes, (b) with triangular fin for high heat flux, and (c) with flat heated wall for high heat fluxes. ]] Schematics of two configurations for the characteristic elements of inverted meniscus evaporators are shown in Fig. 9.30. In the first configuration [Figs. 9.30 (a) and (b)], a heated triangular fin is inserted into the porous plate and sintered with it in order to provide good thermal contact. In the second configuration [Fig. 9.30 (c)], the heated wall is flat. With small heat flux, evaporation of the liquid, which saturates the porous element, can take place exclusively from the surface of the porous body into the vapor channel as shown in Fig. 9.30(a). Extremely high heat fluxes are significantly more interesting for industrial applications, and the existence of a stable vapor blanket along the heated solid surface inside the uniform porous structure was anticipated, as shown in Figs. 9.30(b) and (c). Evaporation takes place into the dry region of the porous structure at the liquid-vapor interface, the location of which shifts depending on the operational conditions. Heat from the heated surface is conducted through the porous element's dry region to the interface. The varying curvatures of the menisci along the liquid-vapor interface create a capillary pressure gradient, which in turn drives the vapor flow. While the vapor flow takes place in a comparatively narrow porous passage, the liquid with the same total mass and flow rate (steady state) is filtered perpendicularly through the entire porous element to the liquid-vapor interface. The pressure gradient in the liquid along this interface is negligible compared to that in vapor. This assumption can be justified by the case where the maximum pressure drop in liquid over the wetted region of the characteristic element under consideration is negligible compared to the pressure drop in vapor in the dry region. This assumption allows for one-dimensional approximation description of the heat transfer in the vapor blanket. The thickness of the vapor blanket, <math>{{\delta }_{v}}</math>, increases with the heat flux, which can lead to increasing thermal resistance in the element. In the situation where ''δv''|''x''=0 = 0 is of the same order of magnitude as the minimum thickness of the porous element [see Fig. 9.30 (b)], the vapor can penetrate into the liquid channels and obstruct the liquid supply of the evaporator, eventually resulting in dryout. The value of the heat flux at which the dryout takes place can be considered as critical. The operating parameters of the evaporator depend upon the heat and mass circulation in the entire system (for example in a heat pipe), with the evaporator in consideration. In the present model, the physical situation for the characteristic element is determined by three parameters: (1) the pressure in the liquid near the interface, <math>{{p}_{\ell \delta }}</math>, (2) the temperature of the solid surface, <math>{{T}_{0}}</math>, at ''x'' = 0, and (3) the liquid-vapor meniscus radius at the end of the vapor blanket (<math>x={{L}_{v\delta }}</math>), ''Rmen'',''o''. Note that the superheat of the fin exists at the following condition: {| class="wikitable" border="0" |- | width="100%" | <math>{{T}_{0}}>{{T}_{sat}}({{p}_{\ell \delta }}+2\sigma /{{R}_{men,\min }})</math> |{{EquationRef|(1)}} |} where the subscript "sat" denotes the normal saturation temperature corresponding to a pressure (<math>{{p}_{\ell \delta }}+2\sigma /{{R}_{men,\min }}</math>) and <math>{{R}_{\text{men,}\min }}={{R}_{p}}/\cos {{\theta }_{\text{men,}\min }}</math> (''Rp'' is pore radius). Inequality (1) characterizes how the value of the solid-liquid superheat, Rmen,o (curvature radius of meniscus at outlet), is related to the fluid circulation in the entire device. For the case of the evaporator with the forced liquid supply it can be set <math>{{R}_{\text{men,o}}}\gg {{R}_{\text{men,}\min }}</math>, because the pressure drop in the liquid is not due to the capillary pressure in this case. Since it can be anticipated that the temperature drops in metallic fin or wall are much smaller than those across the dry zone of the porous structure, because kw <math>\gg </math> keff, the heat conduction in the solid fin or wall is considered using a l-D approach. For the case of the flat wall [Fig. 9.30(c)] it means that dTw/dy is not included in the consideration. The heat con¬duction in the triangular metallic fin is described by the following equation [Fig. 9.30(b)], which was obtained as a result of energy balance on a differential element consideration: {| class="wikitable" border="0" |- | width="100%" | <math>\frac{{{d}^{2}}{{T}_{w}}}{d{{x}^{2}}}+\frac{d{{T}_{w}}}{dx}\frac{1}{x}+({{T}_{s}}-{{T}_{w}})\frac{{{k}_{eff}}\cos \gamma }{x{{\delta }_{v}}(x){{k}_{w}}\sin \gamma }=0</math> |{{EquationRef|(2)}} |} where ''Ts'' is the local temperature of the porous struc¬ture at the liquid-vapor interface location. Similarly, the heat conduction equation for the wall in Fig. 9.30 (c) is {| class="wikitable" border="0" |- | width="100%" | <math>\frac{{{d}^{2}}{{T}_{w}}}{d{{x}^{2}}}+({{T}_{s}}-{{T}_{w}})\frac{{{k}_{eff}}}{{{t}_{w}}{{\delta }_{v}}(x){{k}_{w}}}+\frac{{{{{q}''}}_{0}}}{{{t}_{w}}{{k}_{w}}}=0</math> |{{EquationRef|(3)}} |} The boundary conditions for equations (2) and (3) are {| class="wikitable" border="0" |- | width="100%" | <math>{{T}_{w}}={{T}_{0}},\text{ }x=0</math> |{{EquationRef|(4)}} |} {| class="wikitable" border="0" |- | width="100%" | <math>\frac{d{{T}_{w}}}{dx}=0,\text{ }x=0</math> |{{EquationRef|(5)}} |} For the second configuration, <math>{{{q}''}_{0}}</math> is the uniform heat flux at the outer surface of the heated part of the flat wall. The value of <math>{{{q}''}_{0}}</math> and the functions <math>{{\delta }_{v}}(x)</math> and <math>{{T}_{s}}(x)</math> should be given by the results of the vapor flow and heat transfer in the dry region solution considered below. The local heat flux resulting from heat conduction across the dry region of the porous structure from the solid surface to the liquid-vapor interface where evap¬oration takes place is {| class="wikitable" border="0" |- | width="100%" | <math>{{{q}''}_{loc}}={{k}_{eff}}\frac{{{T}_{w}}-{{T}_{s}}}{{{\delta }_{v}}(x)}</math> |{{EquationRef|(6)}} |} which is valid for the case <math>{{k}_{v}}\ll {{k}_{eff}}</math> and <math>{{c}_{p,v}}({{T}_{w}}-{{T}_{s}})\ll {{h}_{\ell v}}</math>. Hence, the mean velocity of the vapor flow for a given x along the solid surface is (the mass and energy conservation balances) {| class="wikitable" border="0" |- | width="100%" | <math>{{\bar{u}}_{v}}(x)=\frac{1}{{{\delta }_{v}}(x){{h}_{\ell v}}{{\rho }_{v}}}\int_{0}^{x}{{{{{q}''}}_{loc}}(x)dx}=\frac{{{k}_{eff}}}{{{\delta }_{v}}(x){{h}_{\ell v}}{{\rho }_{v}}}\int_{0}^{x}{\frac{{{T}_{w}}-{{T}_{s}}}{{{\delta }_{v}}(x)}dx}</math> |{{EquationRef|(7)}} |} where <math>{{\bar{u}}_{v}}(x)</math> is the mean vapor velocity along the x-¬coordinate. The modified Darcy's equations for the vapor flow in both directions through a porous structure where the value of 0.55 is used for a dimensionless form-drag constant are {| class="wikitable" border="0" |- | width="100%" | <math>\frac{\partial {{p}_{v}}}{\partial x}=-\frac{{{\mu }_{v}}}{K}{{u}_{v}}(x)-\frac{0.55}{\sqrt{K}}{{\rho }_{v}}u_{v}^{2}(x)</math> |{{EquationRef|(8)}} |} {| class="wikitable" border="0" |- | width="100%" | <math>\frac{\partial {{p}_{v}}}{\partial y}=-\frac{{{\mu }_{v}}}{K}{{v}_{v}}(y)-\frac{0.55}{\sqrt{K}}{{\rho }_{v}}v_{v}^{2}(y)</math> |{{EquationRef|(9)}} |} where ''uv'' and ''vv'' are the area-averaged vapor velocities. The corresponding continuity equation is {| class="wikitable" border="0" |- | width="100%" | <math>\frac{\partial {{u}_{v}}}{\partial x}+\frac{\partial {{v}_{v}}}{\partial y}=0</math> |{{EquationRef|(10)}} |} The Darcy's equation is semi¬-empirical and describes the flow with the uniform velocity profile; therefore, it is assumed in the present analysis that ''uv'' does not depend on ''y''. Taking the definitions of the mean vapor pressure (<math>{{\bar{p}}_{v}}={\int_{0}^{{{\delta }_{v}}}{{{p}_{v}}dy}}/{{{\delta }_{v}}}\;</math>) and axial vel¬ocity (<math>{{\bar{u}}_{v}}={\int_{0}^{{{\delta }_{v}}}{{{u}_{v}}dy}}/{{{\delta }_{v}}}\;</math>) for a given x into consideration and integrating eq. (8) over y, the following equation can be obtained for the gradient of the mean vapor pressure along the x-coor¬dinate {| class="wikitable" border="0" |- | width="100%" | <math>\frac{d{{{\bar{p}}}_{v}}}{dx}=-\frac{{{\mu }_{v}}}{K}{{\bar{u}}_{v}}(x)-\frac{0.55}{\sqrt{K}}{{\rho }_{v}}\bar{u}_{v}^{2}(x)</math> |{{EquationRef|(11)}} |} Since the situation when <math>{{\delta }_{v}}\ll {{L}_{vb}}</math> is considered, the vapor pressure drop across the vapor blanket is much smaller than that along the x-coordinate. At the solid fin (or wall) surface <math>{{\left. {{v}_{v}} \right|}_{y=0}}=0</math>, and at the liquid-vapor interface <math>{{\left. {{v}_{v}} \right|}_{y={{\delta }_{v}}}}={{v}_{v\delta }}\zeta </math> where <math>\zeta =\cos [\arctan (d{{\delta }_{v}}dx)]</math> is the cosine of the angle between the y coordinate and the normal to the liquid-vapor interface and <math>{{v}_{v\delta }}</math> is the blowing velocity (normal to the liquid-vapor interface) :	{| class="wikitable" border="0" |- | width="100%" | <math>{{v}_{v\delta }}={{k}_{eff}}\frac{{{T}_{w}}-{{T}_{s}}}{{{\delta }_{v}}{{h}_{\ell v}}{{\rho }_{v}}}</math> |{{EquationRef|(12)}} |} Equation (12) implies that the total amount of energy transferred from the heated solid surface to the liquid-vapor interface by the heat conduction across the dry porous zone is spent on vaporization of the liquid. Since the axial velocity profile is nearly uniform, it follows from equation (10) that <math>{{v}_{v}}={{v}_{v\delta }}\zeta y/{{\delta }_{v}}</math>. Integrating eq. (9) twice over y for a given x and implementing the definition of <math>{{\bar{p}}_{v}}</math> the difference between the vapor pressure near the liquid-vapor interface, <math>{{p}_{v\delta }}</math>, and the mean vapor pressure of the vapor flow, <math>{{\bar{p}}_{v}}</math>, for a given x can be estimated as follows {| class="wikitable" border="0" |- | width="100%" | <math>{{p}_{v\delta }}-{{\bar{p}}_{v}}={{\delta }_{v}}\left( \frac{{{v}_{v\delta }}\zeta {{\mu }_{v}}}{3K}+\frac{0.55}{4\sqrt{K}}{{\rho }_{v}}v_{v\delta }^{2}{{\zeta }^{2}} \right)</math> |{{EquationRef|(13)}} |} Combining eqs. (7) and (11), we have for the vapor filtration flow pressure gradient along the x-coordinate: {| class="wikitable" border="0" |- | width="100%" | <math>\frac{d{{{\bar{p}}}_{v}}}{dx}=-\frac{{{v}_{v}}{{k}_{eff}}}{{{\delta }_{v}}{{h}_{\ell v}}K}\int_{0}^{x}{\frac{{{T}_{w}}-{{T}_{s}}}{{{\delta }_{v}}}dx}-\frac{0.55}{{{\rho }_{v}}\sqrt{K}}{{\left[ \frac{{{k}_{eff}}}{{{\delta }_{v}}{{h}_{\ell v}}}\int_{0}^{x}{\frac{{{T}_{w}}-{{T}_{s}}}{{{\delta }_{v}}}dx} \right]}^{2}}</math> |{{EquationRef|(14)}} |} The boundary condition for eq. (14) follows from eqs. (9.248), (12) and (13) {| class="wikitable" border="0" |- | width="100%" | <math>\begin{matrix} \overline{p}_v|_{x=0} = p_{l\delta}+\frac{2\sigma}{R_{men}|_{x=0}}+\frac{\rho_v^2v_{v\delta}^2|_{x=0}}{\varepsilon^2}\left (\frac{1}{\rho_l} - \frac{1}{\rho_v} \right ) \\ -\frac{k_{eff}\mu_v \zeta (T_w-T_s)|_{x=0}}{3Kh_{lv}\rho_v}-\frac{0.55}{4\sqrt{K}}(\zeta^2v^2_{v\delta}\delta_v)|_{x=0} \end{matrix}</math> |{{EquationRef|(15)}} |} The local heat flux at the liquid-vapor interface due to the evap¬oration of the liquid is: {| class="wikitable" border="0" |- | width="100%" | <math>{{{q}''}_{loc}}=[{{T}_{s}}(x)-{{T}_{v}}(x)]{{h}_{e,p}}</math> |{{EquationRef|(16)}} |} Combining eqs. (6) and (16) because of the steady state situation, the expression for the local temperature of the porous structure at the liquid-vapor interface location is: {| class="wikitable" border="0" |- | width="100%" | <math>{{T}_{s}}(x)=\frac{{{T}_{w}}(x)+{{h}_{e,p}}(x){{T}_{v}}(x){{\delta }_{v}}(x)/{{k}_{eff}}}{1+{{h}_{e,p}}(x){{\delta }_{v}}(x)/{{k}_{eff}}}</math> |{{EquationRef|(17)}} |} Substituting eqs. (12) and (13) into eq. (9.248) and differentiating it, the following equation for the radius of the meniscus curvature can be obtained {| class="wikitable" border="0" |- | width="100%" | <math>\begin{align} & \frac{d}{dx}\left( \frac{2\sigma }{{{R}_{men}}} \right)=\frac{d{{{\bar{p}}}_{v}}}{dx}-\frac{2{{\rho }_{v}}{{v}_{v\delta }}}{{{\varepsilon }^{2}}}\left( \frac{1}{{{\rho }_{\ell }}}-\frac{1}{{{\rho }_{v}}} \right)\frac{{{k}_{eff}}{{\mu }_{v}}}{{{h}_{\ell v}}\delta _{v}^{2}}\left[ \left( \frac{d{{T}_{w}}}{dx}-\frac{d{{T}_{s}}}{dx} \right){{\delta }_{v}} \right. \\ & \left. -({{T}_{w}}-{{T}_{s}})\frac{d{{\delta }_{v}}}{dx} \right]+\frac{{{k}_{eff}}{{\mu }_{v}}}{3K{{h}_{\ell v}}{{\rho }_{v}}}\left[ \zeta \left( \frac{d{{T}_{w}}}{dx}-\frac{d{{T}_{s}}}{dx} \right)+({{T}_{w}}-{{T}_{s}})\frac{d\zeta }{dx} \right] \\ & +\frac{0.55{{\rho }_{v}}}{4\sqrt{K}}{{\left( \frac{{{k}_{eff}}}{{{h}_{\ell v}}{{\rho }_{v}}{{\delta }_{v}}} \right)}^{2}}\left\{ {{\zeta }^{2}}\left[ 2({{T}_{w}}-{{T}_{s}})\left( \frac{d{{T}_{w}}}{dx}-\frac{d{{T}_{s}}}{dx} \right){{\delta }_{v}}-{{({{T}_{w}}-{{T}_{s}})}^{2}}\frac{d{{\delta }_{v}}}{dx} \right] \right. \\ & \left. +2\zeta {{\delta }_{v}}{{({{T}_{w}}-{{T}_{s}})}^{2}}\frac{d\zeta }{dx} \right\} \\ \end{align}</math> |{{EquationRef|(18)}} |} with the boundary condition {| class="wikitable" border="0" |- | width="100%" | <math>{{\left. {{R}_{men}} \right|}_{x=0}}={{C}_{0}}</math> |{{EquationRef|(19)}} |} where ''C0'' should be chosen from the constitutive con¬dition for the minimum value of the meniscus radius along the liquid-vapor interface {| class="wikitable" border="0" |- | width="100%" | <math>\min \left\{ {{R}_{men}}(x) \right\}={{R}_{p}}/\cos {{\theta }_{men,\min }}</math> |{{EquationRef|(20)}} |} Now, the condition of the liquid-vapor interface mechanical equilibrium should be considered in order to find its location or <math>{{\delta }_{v}}(x)</math>. In the analysis by [[#References|Solov'ev and Kovalev (1987)]] it was assumed that <math>{{\delta }_{v}}(x)=\text{const}\cdot {{x}^{0.33}},</math> which is not quite satisfactory for several reasons. For example, in a hypothetical situation in which the definite start point along the x-coordinate is ''x1'', and there is no evaporation from the liquid-vapor interface, <math>{{\left. {{\delta }_{v}} \right|}_{x>{{x}_{1}}}}=\text{const}</math>, a condition which is not satisfied by the discussed expression. [[#References|Wulz and Embacher (1990)]] have modeled the vapor flow in the uniform zone of the dry porous structure. The thickness of the vapor zone was determined as 0.1 mm at <math>{{{q}''}_{\max }}=</math>17500 W/m2 by comparing the calculated temperature difference between the fin top and the phase boundary with the value determined by the experiment using the simpler vapor zone model. [[#References|Chung and Catton (1993)]] have con-sidered the problem of steam injection into a slow water flow through porous media, where the interface location was also unknown. They have found "…that the interface can be idealized as a stream line as far as the momentum equations are concerned." Here the concept of a streamline is used indirectly as explained below. For the asymptotic case, <math>K\to \infty ,\text{ }{{\mu }_{v}}\to 0,</math>integrating Euler's equation along a streamline gives {| class="wikitable" border="0" |- | width="100%" | <math>{{p}_{v}}+\frac{{{\rho }_{v}}u_{v}^{2}}{2}+\frac{{{\rho }_{v}}v_{v}^{2}}{2}={{\left. {{p}_{v}} \right|}_{x=0}}</math> |{{EquationRef|(21)}} |} where the terms containing <math>u_{v}^{2}\text{ and }v_{v}^{2}</math> correspond to the inertia effects due to acceleration of fluid. In the present analysis, the vapor flow through a porous medium is described by Darcy's momentum equation. However, it is assumed that since the velocity profile of the vapor flow along the x-coordinate, <math>{{u}_{v}},</math> is nearly uniform, eq. (21) can be used for the description of the inertia effects at the liquid-vapor interface due to acceleration of the vapor. The liquid-vapor interface can be stable provided it has the shape that eliminates the influence of the inertia effects due to acceleration of the vapor flow on the vapor pressure near this interface. While the steady-state situation is analyzed, the liquid pressure along the interface is constant, and the pressure losses in the vapor flow in both directions due to friction and solid obstacles are compensated by the capillary pressure, the vapor pressure gradient along the stable interface due to these inertia effects should be equal to zero. Since the velocity profile of the vapor flow along the x-coordinate is nearly uniform, it follows from eq. (21) that {| class="wikitable" border="0" |- | width="100%" | <math>\frac{{{\rho }_{v}}u_{v}^{2}}{2}+\frac{{{\rho }_{v}}v_{v}^{2}}{2}=\text{const}</math> |{{EquationRef|(22)}} |} Note that eq. (22) is not used for the fluid flow in the porous medium but describes the inertia effects at the adjustable liquid-vapor interface in which the momentum equations for the vapor flow in the porous medium are concerned. Equation (22) is necessary in order to find the equilibrium location of the liquid-vapor boundary. Substituting eqs. (7) and (12) into eq. (22) and differentiating it after some rearrangements gives the equation for the vapor blanket thickness, <math>{{\delta }_{v}}</math> {| class="wikitable" border="0" |- | width="100%" | <math>\begin{align} & \frac{d\delta _{v}^{2}}{d{{x}^{2}}}\left\{ {{\delta }_{v}}{{({{T}_{w}}-{{T}_{s}})}^{2}}\zeta \sin \left( \arctan \frac{d{{\delta }_{v}}}{dx} \right){{\left[ 1+{{\left( \frac{d{{\delta }_{v}}}{dx} \right)}^{2}} \right]}^{-1}} \right\} \\ & =({{T}_{w}}-{{T}_{s}})\left[ \int_{0}^{x}{\frac{{{T}_{w}}-{{T}_{s}}}{{{\delta }_{v}}}dx}+{{\delta }_{v}}{{\zeta }^{2}}\left( \frac{d{{T}_{w}}}{dx}-\frac{d{{T}_{s}}}{dx} \right) \right] \\ & -\frac{d{{\delta }_{v}}}{dx}\left[ {{\left( \int_{0}^{{{\delta }_{v}}}{\frac{{{T}_{w}}-{{T}_{s}}}{{{\delta }_{v}}}dx} \right)}^{2}}+{{\zeta }^{2}}{{({{T}_{w}}-{{T}_{s}})}^{2}} \right] \\ \end{align}</math> |{{EquationRef|(23)}} |} where all of the terms containing <math>({{T}_{w}}-{{T}_{s}})</math> can be calculated in the numerical procedure using the func¬tions ''Tw''(x) and ''Ts''(x) determined at the previous iter¬ation. The second-order differential equation (9.331) should be solved with the two boundary conditions for the variables <math>{{\delta }_{v}}</math> and <math>d{{\delta }_{v}}/dx</math>. The first boundary condition is {| class="wikitable" border="0" |- | width="100%" | <math>{{\left. {{\delta }_{v}} \right|}_{x=0}}={{C}_{1}}</math> |{{EquationRef|(24)}} |} where ''C1'' should be chosen from the constitutive condition as the value of <math>{{\left. {{\delta }_{v}} \right|}_{x=0}},</math> which satisfies the following boundary condition {| class="wikitable" border="0" |- | width="100%" | <math>{{\left. {{R}_{men}} \right|}_{x={{L}_{vb}}}}={{R}_{men,o}}</math> |{{EquationRef|(25)}} |} The second boundary condition is due to the sym¬metry of the considered element (Fig. 9.29). Since at the point x = 0, dTw/dx = 0, dTs/dx = 0, and <math>d{{v}_{v\delta }}/dx=0</math> due to the physical reasons, it follows from equation (12) {| class="wikitable" border="0" |- | width="100%" | <math>{{\left. \frac{d{{\delta }_{v}}}{dx} \right|}_{x=0}}=0</math> |{{EquationRef|(26)}} |} Thus we have six main variables (or unknown func¬tions): <math>{{p}_{v\delta }},</math> <math>{{\bar{p}}_{v}},</math> Rmen, 'Ts'', ''vvδ'' and ''δv'' which should be found from the six equations: (9.248), (12), (14), (17), (18), and (23). These six equations should be solved along with those presented in the previous sections for variables <math>{{h}_{e,p}}(x)</math> and Tw(x). Note that the value <math>{{{q}''}_{0}}</math>which is needed for eq. (9.311) can now be found as: {| class="wikitable" border="0" |- | width="100%" | <math>{{{q}''}_{0}}=\frac{1}{W}\int_{0}^{{{L}_{vb}}}{{{k}_{eff}}\frac{{{T}_{w}}(x)-{{T}_{s}}(x)}{{{\delta }_{v}}(x)}dx}</math> |{{EquationRef|(27)}} |} [[Image:NewChapter9 (10).png|thumb|400 px|alt= Performance characteristics of the modeled evaporator element along the heated fin surface. | Figure 9.31 Performance characteristics of the modeled evaporator element along the heated fin surface: (a) temperatures of the fin surface and of the porous structure at the liquid-vapor interface and (b) local heat flux across the vapor blanket. ]] For the first configuration, <math>{{{q}''}_{0}}</math> is the heat flux in the solid fin corresponding to the porous structure-vapor channel plane. The heat flux on the outer surface of the evaporator (and the corresponding effective heat transfer coefficient) can be recalculated taking the geometry of the evaporator into consideration. Although the vapor leaving the dry zone of the porous structure is superheated, it is convenient to relate the local effective heat transfer coefficient to the vapor saturation temperature, because <math>{{c}_{p,v}}({{T}_{w}}-{{T}_{s}})\ll {{h}_{\ell v}}</math>. Thus, the local effective heat transfer coefficient cor¬responding to the point x = ''Lvb'' (outlet of the vapor flow) is defined as: {| class="wikitable" border="0" |- | width="100%" | <math>{{h}_{eff}}=\frac{1}{W{{({{T}_{w}}-{{T}_{v}})}_{o}}}\int_{0}^{{{L}_{vb}}}{{{k}_{eff}}\frac{{{T}_{w}}(x)-{{T}_{s}}(x)}{{{\delta }_{v}}(x)}dx}</math> |{{EquationRef|(28)}} |} [[#References|Khrustalev and Faghri (1995a)]] modeled heat transfer during evaporation from a pore (see Section 9.6.2), heat conduction in the solid fin or wall, vapor flow and heat transfer in the dry region of the porous structure. Numerical solution was performed and the results were obtained with constant thermal physical properties corresponding to the saturation temperature <math>{{T}_{sat}}({{p}_{\ell \delta }})=100\text{ }{}^{\text{o}}\text{C}</math>. The numerical results were obtained for the first configuration [Fig. 9.30(b)] for the case of a miniature evaporator: <math>\gamma ={{30}^{\circ }},</math> <math>{{t}_{pen}}=0.2\text{ mm,}</math> <math>{{R}_{p}}=20\text{ }\!\!\mu\!\!\text{ m,}</math> <math>{{\theta }_{\text{men,}\min }}={{33}^{\circ }},</math> <math>\alpha =0.05,</math><math>{{k}_{eff}}=10\text{ W/m-K,}</math> <math>{{k}_{w}}=438</math> W/m-K, <math>\varepsilon =0.5,</math><math>{{\varepsilon }_{s}}=0.5,</math><math>K=0.5\times {{10}^{-12}}\text{ }{{\text{m}}^{\text{2}}},</math>and<math>{{p}_{\ell \delta }}=</math> <math>1.013\times {{10}^{5}}\text{ Pa}\text{.}</math> Since the longitudinal circulation of the fluid in the heat pipe was not considered, the numerical results were obtained for several fixed Rmen,o. The temperatures of the fin surface and the porous structure at the liquid-vapor interface, as well as local heat flux across the vapor blanket, are shown in Fig. 9.31. It can be seen that the temperature drops at the solid heated surface were significantly smaller than those corresponding to the porous skeleton at the liquid-vapor interface. The real superheat of the liquid, <math>{{T}_{s}}-{{T}_{v}}</math>, which could initiate the boiling, was significantly smaller than the superheat of the heated solid surface: <math>{{T}_{s}}-{{T}_{v}}<{{T}_{w}}-{{T}_{v}}</math>. The local heat fluxes across the dry zone had their maximums at the point ''x'' = 0, as can be seen in Fig. 9.31(b). For extremely high heat fluxes, <math>{{{q}''}_{loc}}</math>, when the temperature drop (<math>{{T}_{s}}-{{T}_{v}}</math>) is large, boiling of the liquid at the liquid-vapor interface can occur. This can cause instabilities at the liquid-vapor interface. However, boiling of the liquid does not necessarily result in dryout for an evaporator of this type. Since <math>{{{q}''}_{o}}>{{{q}''}_{loc}}</math> due to <math>{{L}_{vb}}>W</math>, the triangular geometry of the solid fin helps to postpone boiling; this may make the fin more desirable than the flat wall in the second configuration shown in Fig. 9.30 (c). In other words, the triangular geometry of the fin provides a higher value for the heat flux on the outer surface of the evaporator, which corresponds to the beginning of liquid boiling at the liquid-vapor interface. ==References== Chung, M., and Catton, I., 1993, "Steam Injection into a Slow Water Flow through Porous Media," ASME Journal of Heat Transfer, Vol. 115, pp. 734-743 Khrustalev, D. and Faghri, A., 1995a, "Heat Transfer in the Inverted Meniscus Type Evaporator at High Heat Fluxes," International Journal of Heat and Mass Transfer, Vol. 38, pp. 3091-3101. Wulz, H., and Embacher, E., 1990, "Capillary Pumped Loops for Space Applications Experimental and Theoretical Studies on the Performance of Capillary Evaporator Designs," Proceedings of the AIAA/ASME 5th Joint Thermophysics and Heat Transfer Conference, Seattle, WA, AIAA Paper No. 90-1739.
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text:
People God Can Count On
Scripture: 1 Timothy 6:17-19
Track 3 of 52 in the Sermons from 2003 series
Sermon for Sunday, May 18, 2003
(1 Timothy 6:17-19)
C. Sackett
I don't own anything worth dying for. I made that discovery in December of 1985. My daughter woke up about 2 o'clock in the morning and started hacking and coughing and Gail went in to find out what was wrong, only to find her room full of smoke and our house was on fire. I discovered in a hurry what I really valued, my children and my wife and my life and out the door we went. Now it wasn't a horrid fire. We didn't lose a lot. I look back at that and it wasn't as traumatic as it could have been for many people, but I did make this amazing discovery. I just don't own anything worth dying for. I was not tempted to go back in the house for any of that stuff. It's just "STUFF". Not everybody has felt that way, in fact, I didn't always feel that way. I was absolutely certain there were things I would go back for until it actually happened.
In the 1950's Jacques Lowes became the Kennedy photographer. Over the years, after starting with Joseph Kennedy's family and working up through the John Kennedy family, he took somewhere in the neighborhood of 40,000 pictures of the Kennedy's. Only about three or four hundred of those ever got printed, but he guarded those with his life. They were his, in fact, livelihood. They were everything about him. He would personally print all of the pictures himself and then take the negatives back and put them in the vault.
They were actually stored in the vault at the J. P. Morgan Bank in downtown Manhattan, supposedly a fireproof vault. The word supposedly should be the dead giveaway here. There was this funny thing that happened (well I don't mean funny, as in humorous, I mean this ironic thing that happened) on September 11. Number 5 World Trade Center was one of the buildings in the cluster that was damaged when the other two buildings fell. It included the J. P. Morgan Bank, and when they went to the vault, all of those negatives were destroyed.
It's that sense ya know, that you can try as hard as you want to protect "stuff". In the end, it doesn't matter much, does it? It's that contrasting set of values that we all bring to the table in one form or another.
I'm sure this is a fanciful story, I don't know, maybe it's true, but, it seems a little far fetched. It's about the little boy that went to the soda fountain. The lady came up to wait on him. She was busy! Had other things to do. He's just this little boy. He wants to know how much it costs to buy an ice cream sundae. She told him 50� (that tells ya how long ago it was). He's counting out his coins. Pretty soon he says, well - how much would just a dish of ice cream be? Of course, she's growing impatient at how long this is taking and she says 35� and he recounts his money one more time and she's growing more impatient all the time. And he finally says, I'll take the ice cream but not the sundae. So she rather hurriedly gets him his ice cream. She slips it over there in front of him and she goes about to do her business. When she comes back to clean up the spot where the little boy was, a little indignant about the whole waste of time, she picked up the cup where the ice cream was and found the reason he didn't eat the sundae was so that he could leave her a 15� tip. He had enough, but he wanted to be generous.
It's that contrasting set of values between the little boy and the J. P. Morgan Bank. It's that sense of understanding where our values are and what really is important to us and maybe more importantly, what's important to the Lord.
I want to cluster three texts together before we land on the one in 1Timothy 6:17. We're going to start in 1Timothy 6 however, because it has this rather famous passage; 1Timothy 6:6-10. I want to just hold that for a second while we look at a second text over in Philippians 4, then we'll come back to this primary text in 1Timothy 6 again.
1Timothy 6, Verse 6 - After having talked about godliness and some people thinking that they can be godly and that will lead to some kind of financial gain, he says in Verse 6.
But godliness with contentment is great gain. For we brought nothing into the world, and we can take nothing out of it. But if we have food and clothing, we will be content with that. People who want to get rich fall into temptation and a trap and into many foolish and harmful desires that plunge men into ruin and destruction. For the love of money is a root of all kinds of evil. Some people, eager for money, have wandered from the faith and pierced themselves with many griefs.
Now hold that and just slide back a couple of chapters to Philippians Chapter 4 - Paul in writing to the church, this church that so faithfully supported him in his missionary endeavors - in the last chapter where he's saying thank you for all the things that the Philippians have done for him - says in Chapter 4, Verse 10 these things.
I rejoice greatly in the Lord that at last you have renewed your concern for me. Indeed, you have been concerned, but you had no opportunity to show it. I am not saying this because I am in need, for I have learned to be content whatever the circumstances. I know what it is to be in need, and I know what it is to have plenty. I have learned the secret of being content in any and every situation, whether well fed or hungry, whether living in plenty or in want. I can do everything through him who gives me strength.
I love the context in which that verse occurs. I remember as a brand new Christian, having Philippians 4:13 as one of those early memory verses. I can do everything through him who gives me strength. And having it placed in this kind of broad context of that applies to absolutely everything, except that in the context in Philippians 4, it's very clearly tied to a person's contentment. I can learn, he says, to be content in any set of circumstances because of what Christ can do for me.
Well, back to 1Timothy 6 - the text I want for us to spend some time with this morning. Starting in Verse 17 he says -
Command those who are rich in this present world not to be arrogant nor to put their hope in wealth, which is so uncertain, but to put their hope in God, who richly provides us with everything for our enjoyment. Command them to do good, to be rich in good deeds, and to be generous and willing to share. In this way they will lay up treasure for themselves as a firm foundation for the coming age, so that they may take hold of the life that is truly life.
I'd like to park for a minute here in this text and just spend some time. We're gonna wander to a couple other places but this will be the primary place of our focus and what I want to suggest to you this morning is that the people that God counts on possess a healthy perspective on their possessions. That the people that God can really rely on in this life, to be the people that he needs for us to be, are people who have learned to view what they have in a way that is healthy. It starts like this in Verse 17. We know the source of our supply. You notice that in Verse Number 17 - put their hope in God, who richly provides us with everything for our enjoyment. One of the main things that you and I come to learn in our relationship with the Father is that he's the one who is the provider. It isn't about us! It isn't about what we can do! It's about what he has already given us and that includes he says, absolutely every arena of our life, that we've learned to understand where our "stuff" comes from. I want to just hold this text and ask you to look back at Deuteronomy Chapter 8.
This, I think, needs such little elaboration. I don't intend to say a lot about it. It just strikes me as one of the fundamental principles of all of Christian experiences that we recognize where it is that God fits in us and with us. And that he is the one who supplies everything and yet the temptation is in life, especially when life is good, when life is at least reasonably comfortable, the temptation is to forget where it comes from. We don't forget when times are hard, because when times are hard, we're constantly talking to God about making them not so hard. But when they're comfortable, when they're easy, like they are for many of us on an every day basis, we sometimes lapse into forgetfulness.
Deuteronomy 8, not to sound terribly trite, comes after Deuteronomy 5. Deuteronomy 5 is the giving of the ten words - The Ten Commandments. We're ready to talk about a relationship with God. And having laid out all of the things that God has in mind in the covenant relationship, you come to Chapter 8 and Verse 10. He says, in light of going into the land and inheriting the land and having God as their guide he says,
When you have eaten and are satisfied, praise the Lord your God for the good land he has given you. Be careful that you do not forget the Lord your God, failing to observe his commands, his laws and decrees that I am giving you this day.
Otherwise, when you eat and are satisfied, when you build fine houses and settle down, and when your herds and your flocks grow large and your silver and gold increase and all you have is multiplied,, then your heart will become proud and you will forget the Lord your God, who brought you out of Egypt, out of the land of slavery. He led you through the vast and dreadful desert, that thirsty and waterless land, with its venomous snakes and scorpions. He brought you water out of hard rock. He gave you manna to eat in the desert, something your fathers had never known, to humble and to test you so that in the end it might go well with you.
Now I've underlined Verses 17 and 18 in my Bible. You don't have to do that. They just struck me as being so profound.
You may say to yourself, "My power and the strength of my hands have produced this wealth for me." But remember the Lord your God, for it is he who gives you the ability to produce wealth, and so confirms his covenant, which he swore to your forefathers, as it is today.
See. The people that God counts on understand this one fundamental principle. God is the source of my supply. He not only gives me the "Stuff" that I have, this text reminds me that the very abilities that I have to produce that wealth, whether it be working with my hands, or my feet, or my mouth, or my mind, or my heart, or whatever it is, those all come from HIM. And the reminder is - don't forget the source. Don't go get so enamored with what you're able to do that you forget that all of that comes from HIM and belongs to HIM - and it's a gift to you! See. The people that God counts on possess a healthy perspective about their own possessions and they understand that God is the source of that. God is the supply.
Verse 18 tells us this, that we know the purpose of our possessions. Back in 1Timothy 6, Verse 18.
Command them to do good, to be rich in good deeds, and to be generous and willing to share. Do you hear the reason behind what you have? See. The people that God counts on understand - they - they understand the purpose for why God gave them the "Stuff" that he gave and that's so that it can be useful - so that something good can come out of it.
I'm not a huge basketball fan - I suppose I'm not a huge sports fan, but one of my favorite characters in professional basketball has been David Robinson, because he is a professed Christian and has, I think, demonstrated that kind of Christian character. Here's a comment that he made.
By the way, he has established a foundation called "Feed My Sheep" that takes care of the homeless. He gets needy families diapers and baby food through a charity that he's started called the "Ruth Project" and here's what he says.
"These aren't sacrifices. If I'm clutching onto my money with both hands, how am I gonna be free to hug my wife and my kids." I just love the perspective, that he understands that what he has, he has not to be held on to but to be turned loose, so that it can accomplish that for which God gave it in the first place.
You see, we've been given in order to give.
Back in the days of the Wesley's, in some of Wesley's writings, in his rules of conduct, John Wesley made this comment: "Do all the good you can, by all the means you can, in all the ways you can, in all the places you can, to all the people you can as long as you ever can." It's a perspective isn't it? - that understands that we have what we have for a reason.
Jesus would put it this way in Luke 12 - Whatever you do, don't fail to be rich toward God. Did you hear that contrast? Here's the contrast between Verse 17 - those who are rich in this world and Verse 18 - those who are rich in good deeds.
We're going to give you that opportunity, by the way, to do that - ah, those of you who can. Tomorrow - there will be a gathering here at the church building to go over to the Westoffs (??) on the Missouri side of the river and take some trucks and some gloves and some bags and just walk the field and see if you can figure out where all that farm went. 'Cause it's just missing, and they need to clean things up. It's an opportunity, simply to demonstrate that you are rich in good deeds. If you have the time and are capable, you are invited to come. There will be more information available to you just a bit later.
To be rich toward God - just the practical things that we can do with the things that we have.
The book that you're reading - at least I trust that you're reading. You were to have read the third chapter for this week where Kregg Hood talks about some, just really practical advice and here's what I would say is a summary of what I consider to be very good, very practical advice. He says, for example; Give to the Lord now - just don't put it off. If you sit around and wait, you're never going to get there. You just have to start somewhere and he says, start NOW.
You know, that's just plain ole good advice about life. My daughter wants to run a marathon. You know what she's going to have to start doing if she's ever gonna get there? What we did Saturday - she's gonna have to put her shoes on and we're gonna have to go run. 'Cause you just don't wake up one day - well, some of you might - but I just cannot wake up on Saturday morning and say I think I wanna run 26 miles - you gotta start somewhere - AND if you're ever going to do it, you've got to start NOW!
So Hood says, be intentional. Make up your mind that you're gonna start TODAY! Then he says it this way - Give regularly - just make it a habit to give consistently with regularity. His suggestion is that you give every week. We give you - if you want them - offering envelopes that are weekly envelopes. Some of you don't give weekly because you get paid once a month or twice a month. And if that's how you do it, that's certainly okay as long as you can keep that all in order. Personally, it's very helpful for me to give every week, and so, that's what we do. We try to use all 52 of those offering envelopes and every once in awhile - I hate to confess it in front of God and everybody - but once in awhile I go to that offering envelope and I realize - oops! - somehow in the busy week I forgot! Well, that's pretty easy to do. So he just says, do it systematically. Do it regularly. Just get in the habit of every, well whatever, every week, every other week, every month - whatever it is that you do, but do it with consistency. He says that's how you develop what you're going to do.
So, my daughter says, now, can I just keep running three miles every day? Yep! As long as you do it every day - well - within reason.
The third thing that Hood says is, Give to the Lord abundantly, be generous, stretch yourself.
See. We did this long five mile run on Saturday. That's the longest my daughter has ever run. But if we run five miles every other Saturday from now until kingdom come, we will never get 26 miles. See. In two weeks it will be six and then two weeks later it will be seven and two weeks later it will be eight and two weeks later it will be ten and then twelve - because if you don't ever stretch yourself, you'll never get any further. That's true in our giving as well. It's one thing to give now and intentionally and it's another thing to give regularly, but it's also another thing to stretch yourself to give abundantly, generously. That requires a little work.
Well, the people that God counts on possess this healthy perspective about their possessions. They know the source of their supply and they know the purpose of their possessions. Verse 19 says that we also know the result of our response. See. All of us make some kind of response. Verse 19 says, In this way they will lay up treasure for themselves as a firm foundation for the coming age, so that they may take hold of the life that is truly life. Paul understands that there are consequences to all of the decisions that we make in our life and that includes stewardship decisions. And what people understand, who are healthy in their perspective, is that there are consequences and that there is an impact to their decisions and it affects their life.
I ran into this story this week - it just struck me - maybe in part because it's so - well the end of the story is just too true. Mark Buchanan is a preacher who had the opportunity to go to Uganda, Africa. He says it was about seven years ago. . . . . by rock something, something - can't make it out!!
Every Sunday evening about a hundred Christians from the neighboring area gather to worship. They meet under a tin roof lean-to that was set up at the edge of the corn field. They sit, he says, when they do sit, on rough wooden benches. The floor is dirt. The instruments are old. Some of the guitars don't have all the strings but could they worship! They made HELL run for shelter when they got loose! I love that line! That is just a great line. There was one guy with us, a real stiff-backed, button-down white boy who liked his worship stayed and orderly and brief. And even he couldn't stand still! He was jumping and clapping and yelling out his hallelujah's. One Sunday evening the preacher asked us if anyone had anything to share. A tall willowy woman came to the front. She was plain, but beautiful. Oh brothers and sisters, I love Jesus so much. Tell us, sister, tell us they shouted back. Oh I love him so much, I don't know where to begin to tell you how good he is. Well begin there, sister, begin right there. He's so good to me, I praise him all the time for how good he is to me. For three months I prayed to the Lord for shoes and look - the woman held up one foot and we could see one very ordinary shoe. He gave me shoes! Hallelujah, he's so good and all these Ugandans clapped and yelled back their hallelujahs. I didn't! I was devastated! I sat there, hollowed out, hammered down. In all my life I had not once prayed for shoes and in all of my life I had never once thanked him for the many, many pairs I already have.
See. There's a consequence to the decisions that we make about the things that we have. It impacts even the very way that we worship, whether or not we come with this perspective that God is the source of our supply and they've been given to us for a good reason. So the challenge becomes then - is it going to be greed or generosity? Is our focus going to be on the present life or is our focus going to be on the coming age? That's 17 and 19. 17 is the rich in this world. 19 is they're laying up treasures in heaven. Chapter 6 in Matthew. You remember what Jesus says. Don't collect stuff down here where rust and moss corrupt, but lay up treasure in heaven. I don't know how all that works but I have a pretty clear understanding that it has something to do with being generous with what I have and not trying to hoard it in this life, because frankly, it's not going with me. And he says, what the end result will be is you will have REAL life.
The end of Verse 19 is a powerful verse. To take hold of life that is really life. See, if you don't own anything that's worth dying for, then you're not going to worry too much about what's in the back seat of your car while you're off at the store.
And if you're like my friend, sitting in the - well the equivalent of a Wal-Mart parking lot, when a guy walked up and stuck a gun in his face and said give me your wallet, you're going to come to the same realization he did. I don't have anything worth dying for and so he just handed it over.
I don't! I don't own a single thing that's worth dying for. But I am owned by one who is worth giving to. And the reason is because he saw me as valuable enough that he would die for me. Now - he owns things worth dying for. They are all in this room and out there on those streets. And that one who owns you is worth giving to. What's stewardship about? It's really simple. It's just having a very healthy perspective on the stuff that he's already given you. Remembering where it's from and what it's for and that there are consequences to the way you use it.
We're inviting you to this one who loves you enough that he can't live without you. He just can't live without you, and so, he was willing to die so he could live with you and if you don't know Jesus, this ONE - we invite you to get to know him. To place your confidence and your trust in HIM, to obey HIM, to walk with HIM - if you're ready to do that today, this is a great time to make that choice. If you don't know what to do, I'll tell you one more time, come and ask. Don't go out of here not knowing how to walk with Jesus.
Let's stand. Let this song voice your heart.

redpajama_set_name: RedPajamaCommonCrawl


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Therefore this is actually the level wherever equipment understanding for big information analytics comes into play. In unit learning process, more the data you offer to the machine, more the machine can learn from it, and returning all the info you're looking and ergo make your research successful. So we can claim that big information has a significant role in unit learning.
Previously, the equipment learning calculations were presented more appropriate data relatively. So the results were also accurate at that time. But in these days, there's an ambiguity in the info because the information is produced from various resources which are uncertain and imperfect too. So, it is a big challenge for device learning in huge data analytics. Exemplory instance of uncertain data is the information which can be produced in instant systems due to noise, shadowing, fading etc.
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Q: Error: couldn't open display [IP ADDRESS] on WSL 2 with Ubuntu 20.04 I am having issues displaying glxgears or any other GUI application, like Gazebo or rviz.
I have VcXsrv as my windows X server for WSL2 with Ubuntu 20.04.
I followed this link for instructions: https://lifesaver.codes/answer/ros-gazebo-black-screen-3368, but this is the end result:
Error: couldn't open display

Any Ideas?

redpajama_set_name: RedPajamaStackExchange


She Is, is the women's ministry of Dwelling Place Church, gathering the women of our church and our city.
She can be a voice calling out to those around her to be who they are destined to be.
To exchange the labels forced on her and embrace who her heavenly Father says she is!


Description According to Japanese legend, earthquakes were caused by the movements of a monster catfish that lived under the island of Japan. Immediately following the great Ansei earthquake of October 2, 1855, woodblock prints called Namazu-e ("catfish pictures") appeared in Edo (now Tokyo), the most affected area. These imaginative and sometimes brutal depictions served as a unique source of information and reassurance to the local population. In this picture, the sly Namazu tries to beguile unwary children.


Did you know…the Local Laws and Customs?
Did you take the time to research the local laws and customs of your destination before your most recent trip abroad? The Foreign and Commonwealth Office (or FCO) are assuming you probably didn't, judging from the results of their recent research.
A big part of the FCO's job is to advise travellers and help them if they need assistance outside of the UK, however many Brits are apparently causing themselves an unnecessary amount of holiday hassle by not following the rules.
The FCO's survey found that, although 70% of people admitted that researching local laws and customs before their trip would probably make their holiday more enjoyable, less than half had actually made this part of their pre-travel research or preparations.
In fact, from 2013-2014 the FCO recorded over 5,000 British arrests abroad (according to their 'British Behaviour Abroad Report'), many of which could have been avoided if the travellers had been aware of the local regulations of their destination.
This means that many travellers don't actually realise they are breaking the law until they are approach by Police, as the rules can be very different to those in the UK. To help anyone planning a trip abroad, the FCO have created this a handy info-graphic to alert travellers to some of the strange rules which must be abided by to avoid a holiday encounter of the legal kind.
For more information on the laws in specific destinations, please visit the FCO's Travel Advice Directory.


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Edinburgh Cookery School Launches New Patisserie Diploma
The Edinburgh School of Food and Wine (ESFW), Scotland's award winning and oldest independent cookery school, has announced the launch of an innovative new course – a Diploma in Professional Patisserie, the first course to specialise in the discipline of patisserie in the country.
Starting in October 2016, the intensive three month course aims to teach students a range of practical skills over a Monday to Friday working week timetable. with creativity being highly encouraged to fit into the mould that modern patisserie now sits. Applications are now being accepted for the course, with anyone from aspiring chefs to those who simply have a passion for pastry welcome.
Ian Pirrie, Principal at the Edinburgh School of Food and Wine, told online publication The Scotsman: "We are very proud to offer this new diploma, the first of its kind in Scotland, to aspiring patisserie chefs and food enthusiasts across the country.
"Scotland has an incredible culinary culture, and many talented chefs with great passion for food and a desire for excellence. This new course will prepare up-and-coming chefs with the fundamental skills and techniques they need to master their craft and succeed in the industry."
There is currently a high demand in the catering industry for professionally trained pastry chefs. The skills required from a Chef de Patisserie range from making delightful dough and fabulous filo pastries, to the fine art of classic patisserie, where precision techniques are put into practice to create intricate desserts that capture the eye as well as the taste buds.
The course is led by Chris Stewart, formally the Head Pastry Chef at the internationally acclaimed Waldorf Astoria, and alumni will receive continued support after completion of the course.
Based in central Scotland in the grounds of Newliston Estate, the Edinburgh School of Food and Wine has fostered a reputation for excellence since it was established in 1986. It offers a wide range of courses, from six-month diplomas to one-off specialised evening classes. The school aims to make the educated appreciation of food and wine accessible to everyone, with each course designed by experienced professional chefs to be practical, hands-on and fun.
Find out more on the ESFW
Whopper To The Future


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A lot of tradesmen prefer air tools for their workshop, because of their greater power, lighter weight and good long-term value for money. Whether you're thinking about making the switch, or just adding to your existing range, quality tools are important.
You just can't afford the lack of reliabailitybudget products give you and the extra cost of a longer production time. And then there's the quality of the finish – cheap air tools give you a poor quality finish, it's as simple as that.
Budget compressors also don't pump up to the same high pressure of quality trade compressors, so your tools won't work to their optimum. Your work will take longer and some tools may not even work at all.
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Click on the categories below to find the items you're looking for and if you're unsure about anything, jump on the chat button and get some expert advice.


hey guys, turkey day is close and i wanted to open asks for it!
ask the derp pone silvy, his cousin lulu , twix or nerdy scoots and her roommates stuffs!
and has silvy or any of his friends ever recieved a "naugty" christmas present?
Silvy - What other things do you do with the turkey besides eating it?
To whoever can give the best/naughtiest answer. what do you do while the turkey is cooking?


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Nicole Letourneau
Principal Investigator and Director
Email: nicole.letourneau@ucalgary.ca
Nicole Letourneau RN BN MN PhD FCAHS
Education. She attained her BN (1991) from University of New Brunswick (UNB), Master's (1994) and PhD (1998) degrees in Nursing from University of Alberta (UofA), focusing on pediatrics and community health. She completed post-doctoral training with Dr. Miriam Stewart at UofA and Dr. Doug Willms at Canadian Research Institute for Social Policy, focusing on social support in vulnerable childbearing families (1999-2003; Canadian Institutes of Health Research (CIHR) and Alberta Heritage Fund for Medical Research funding).
Positions. She was appointed Assistant Professor at UofA (1999), then she moved to UNB and was appointed Associate Professor (2003), all in Faculties of Nursing. She became Canada Research Chair in Healthy Child Development, attained tenure and was promoted to Full Professor (2007). She relocated to University of Calgary (UofC) to assume the Alberta Children's Foundation Chair in Parent-Infant Mental Health (2011-current). Primarily appointed in UofC Faculty of Nursing, additional appointments are in Cumming School of Medicine in Depts. of Pediatrics, Psychiatry & Community Health Sciences. She volunteers extensively in regional (Discovery House Board), provincial (College & Association of Registered Nurses of Alberta-CARNA), national (CIHR Governing Council) and international (International Association for Study of Attachment) venues. She was recently elected to President-Elect of CARNA.
Research. She is Principal Investigator of the CHILD (Child Health Intervention and Longitudinal Development) Studies Program examining parenting, attachment and child development in the context of maternal depression, family violence, low income and other risks. She is Director of RESOLVE (Research & Education for Solutions to Violence). Her research is consistently community-based to guide best practice in parent-child support and intervention. Of the 10 studies she currently leads, key projects include:
APrON (Alberta Pregnancy Outcomes and Nutrition) cohort study of 2200 Alberta families, examining parental mental health influences on infants/children. Recent studies include the influence of mothers' adverse childhood experiences and perinatal mental health on epigenetic expression of their three-month old infants, both explorations of intergenerational trauma mechanisms.
Harvard Center on the Developing Child-funded ATTACH (Attachment and Child Health) study, testing an innovative intervention to promote reflective function of high-risk mothers in order to promote secure maternal-infant attachment and child development.
CIHR-funded VID-KIDS (Video Feedback Intervention for Depressed Mothers and Infants), a nurse-delivered intervention for mothers with postpartum depression to support healthy maternal-child relationships and child development.
Honours. She regularly receives honours including:
CIHR's Canada's Premier Young Researcher (2006),
Canada's Top 40 Under 40TM (2007),
Excellence in Research Awards from New Brunswick Nurses Association (2011) and College and Association of RNs of Alberta (2015),
Fellow of Canadian Academy of Health Sciences (2014),
Excellence in Research Award from Canadian Association of Schools of Nursing (2017),
Centre for Addiction and Mental Health--Difference Maker Award (2017).
Productivity. She has attained $55+ million in research funding, with $18+ million as lead investigator. She has ~20K Twitter followers (@DrNLetourneau), 150+ peer-reviewed papers (https://scholar.google.ca/scholar?hl=en&as_sdt=0%2C5&q=nicole+letourneau&oq=ni), 14+ book chapters, 100+ opinion editorials in print and online Canadian news outlets, and authored;
Scientific Parenting: What Science Reveals About Parental Influence (2013) https://www.amazon.ca/Scientific-Parenting-Science-Parental-Influence/dp/1459710088
What Kind of Parent Am I? (2018) https://www.amazon.ca/s/ref=nb_sb_noss?url=search-alias%3Dstripbooks&field-keywords=what+kind+of+parent+am+i
both published by Dundurn.


These days, Lolla is far from Chicago's only music festival, what with another Riot Fest or Wavefront popping up every five minutes. But it is certainly the biggest. When this year's Lolla tickets sold out in less than two hours after going on sale, I automatically assumed it was because scalpers had bought them all up with plans to sell them back to Chicago's "true" music fans at ridiculous prices. Not so. I was paying attention at Lolla this year, and it became clear that there really are more than 300,000 people in the world who want to attend the festival.
Lolla is so big that though the lineup boasts hundreds of acts, dozens of whom are pretty high-profile, even the most determined three-day festivalgoers will have a hard time catching more than four or five of the ones they want. The abundance of good acts often leads to unfortunate overlap (seriously, how is a modern indie-rock fan supposed to choose between Vampire Weekend, Beach House and Grizzly Bear?) and the spaces between stages are too gigantic to cross quickly.
Lolla is so big that the experience is now beyond summary or quantification. For example, it's sometimes too easy to stereotype the attendee at Pitchfork, where every other person has either a tattoo, an intricate hipster moustache and/or an intimate familiarity with Pavement's catalogue. By contrast, at this year's Lolla you might have passed both a Cure fan clad in black makeup and a muddy Perry's bro with glazed eyes on your way to see dozens of passionate young Alt-J fans throw up triangle finger formations.
No doubt some people see Lolla's bigness as a flaw. If you identify yourself as a passionate music fan, you're probably annoyed with the suburban teenagers who see Lolla as their chance to go on a three-day bender and miss headlining acts because they're too busy puking in a Port-a-Potty.
But Lolla's bigness is also its greatest strength, and makes for some pretty amazing experiences. Huge crowds forced my friends and me to observe The Killers' Friday set from a side hill, but when that same crowd united to loudly sing along to set opener "Mr. Brightside," my eighth-grade self dramatically reemerged to remind me I like The Killers more than I realized. And it might be cool to hate on Mumford & Sons, but it's hard not to be overcome by emotion when thousands of people around you are jumping, singing and crying together because of a shared musical experience.
There were a lot of great acts this weekend. Eric Church demonstrated how country can be just as badass as rock in the right hands, and Icona Pop's catchy jams powered the crowd through the weekend's only real bout of rain. But for me, the biggest moment of this year's Lolla came at the end of Vampire Weekend's Sunday set. I had taken turns this weekend hanging out with different groups of old high school friends, and somehow they all came together in time for "Walcott," the epic ode to leaving home that serves as the finale for every Vampire Weekend show. Watching everyone unanimously screaming "out of Cape Cod tonight!" together was a reminder that sometimes, big is better.


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Daniel Alejandro Torres
This article uses Spanish naming customs: the first or paternal family name is Torres and the second or maternal family name is Rojas.
Daniel Alejandro "Dani" Torres Rojas (born 15 November 1989) is a Colombian professional footballer who plays as a defensive midfielder for Spanish club Deportivo Alavés.
Dani Torres
Daniel Alejandro Torres Rojas
(1989-11-15) 15 November 1989 (age 29)
Cáqueza, Colombia
Defensive midfielder
Youth career
Sporting de Cáqueza
Senior career*
Team Apps (Gls)
Independiente Santa Fe 158 (1)
→ Atlético Nacional (loan) 12 (0)
Independiente Medellín 39 (3)
Alavés 42 (0)
→ Albacete (loan) 16 (0)
National team‡
Colombia 14 (0)
Copa América Centenario
2016 United States
* Senior club appearances and goals counted for the domestic league only and correct as of 8 June 2019
‡ National team caps and goals correct as of 13 June 2017
Club careerEdit
Santa FeEdit
Born in Cáqueza, Cundinamarca, Torres joined Independiente Santa Fe's youth setup in 2005 at the age of 15. He made his senior debut on 8 June 2008, starting in a 0–3 away loss against América de Cali.[1]
On 8 July 2011, Torres was loaned to fellow league team Atlético Nacional until the end of the year, with a buyout clause.[2] However, he only appeared sparingly for the club, being released in the end of the year mainly due to disciplinary problems (some of them related to alcoholism).[3]
Upon returning to Santa Fe, Torres established himself as a regular starter and helped the side in their 2012 and 2014 successful campaigns. He scored his first professional goal on 9 August of the latter year, netting the second in a 2–1 home win against Independiente Medellín.
Independiente MedellínEdit
On 5 July 2015, Torres and fellow Santa Fe teammate Luis Carlos Arias were transferred to Independiente Medellín.[4] He featured regularly for the side during his spell, scoring two goals in the 2015 season.
AlavésEdit
On 19 July 2016, Torres signed a four-year contract with Deportivo Alavés, newly promoted to La Liga.[5] He made his debut in the category on 21 August, starting in a 1–1 away draw against Atlético Madrid.[6]
On 31 January 2019, after featuring rarely during the first half of the campaign, Torres was loaned to Segunda División side Albacete Balompié, for six months.[7]
International careerEdit
On 6 November 2015, Torres was called up by Colombia national team manager José Pékerman for two 2018 FIFA World Cup qualifying matches against Chile and Argentina. He made his full international debut six days later, playing the full 90 minutes in a 1–1 draw against the former.
Torres was also included in Pékerman's final 23-man list for the Copa América Centenario, featuring regularly as his side finished third.
In October 2016, Torres produced a video urging Colombians against supporting the peace deal with FARC.[8] Torres is a devout Christian, who cited his opposition to then president Juan Manuel Santos as that Santos did not put Jesus at the center of his politics.[9]
Career statisticsEdit
ClubEdit
As of 5 December 2018[10][11]
Club performance
Cup[n 1]
Santa Fe 2008 Categoría Primera A 5 0 0 0 0 0 5 0
2009 16 0 0 0 0 0 16 0
2014 36 1 11 0 12 0 59 1
Atlético Nacional (loan) 2011 Categoría Primera A 12 0 4 0 0 0 16 0
Independiente Medellín 2015 Categoría Primera A 23 2 6 0 8 0 37 2
Alavés 2016–17 La Liga 21 0 5 0 0 0 26 0
2018–19 2 0 1 0 0 0 3 0
^ Includes Copa Colombia and Superliga Colombiana.
HonoursEdit
Categoría Primera A: 2012-I, 2014-II
Copa Colombia: 2009
Superliga Colombiana: 2013, 2015
InternationalEdit
Copa América: Third place 2016
^ "Daniel Torres, pidiendo pista en la Selección" [Daniel Torres, asking for a place in the National Team] (in Spanish). En Directo Sabana. 7 November 2014. Archived from the original on 19 September 2016. Retrieved 10 September 2016.
^ "El volante Daniel Torres es nuevo jugador de Atlético Nacional" [Defensive midfielder Daniel Torres is the new player of Atlético Nacional] (in Spanish). Caracol Radio. 8 July 2011. Retrieved 10 September 2016.
^ "Daniel Torres, jugador del Santa Fe, venció el alcoholismo" [Daniel Torres, player of Santa Fe, defeated the alcoholism] (in Spanish). Noticias RCN. 20 January 2014. Retrieved 10 September 2016.
^ "Daniel Torres y Luis Carlos Arias fueron transferidos al Medellín" [Daniel Torres and Luís Carlos Arias were transferred to Medellín] (in Spanish). Caracol Televisión. 5 July 2015. Retrieved 10 September 2016.
^ "Daniel Torres, juego, contención y liderazgo en el centro del campo" [Daniel Torres, break-up play and leadership in the centre of the midfield] (in Spanish). Deportivo Alavés. 19 July 2016. Retrieved 10 September 2016.
^ "Al Atleti le sobra el final" [To Atleti the ending is too much] (in Spanish). Marca. 21 August 2016. Retrieved 10 September 2016.
^ "Dani Torres jugará cedido en el Albacete" [Dani Torres will play on loan at Albacete] (in Spanish). Deportivo Alavés. 31 January 2019. Retrieved 31 January 2019.
^ "Colombian Opposition to Peace Deal Feeds Off Gay Rights Backlash". New York Times. 8 October 2016. Retrieved 10 October 2016.
^ ""Señor presidente, el centro de esta negociación no es Jesucristo"". Semana (in Spanish). September 27, 2016. Retrieved October 2, 2016.
^ Daniel Torres at Soccerway. Retrieved 10 September 2016.
^ Daniel Torres at ESPN FC
Dani Torres at BDFutbol
Dani Torres at National-Football-Teams.com
Retrieved from "https://en.wikipedia.org/w/index.php?title=Daniel_Alejandro_Torres&oldid=904770603"


Mogadishu:- Today, HE The President Hassan Sheikh Mohamud, signed the Convention for the Rights of the Child. Attending the ceremony at Hamar Jab Jab School were Mr Nicholas Kay, Special Representative of the UN Secretary General for Somalia, Mr Steven Lauwerier, UNICEF Representative for Somalia, Interim Minister for Justice Hon Farah Sheikh Abdulkadir, Interim Minister for Women and Human Rights Hon Khadijo Mohamed Diriye, Interim Minister for Information Hon Mustaf Sheikh Ali Dhuhulow, Interim Minister for Agriculture, Abdi Mohamed Bafo and several serving Members of Parliament.
The Convention of the Rights of the Child was ratified by the Federal Parliament of Somalia on 13 December 2014. The Convention outlines the rights of and means to protect children and provides the basis for the Federal Government of Somalia to realise the rights of all Somali children. It is the most widely ratified human rights treaty in the world. South Sudan and the United States of America have still to sign the Convention.
The Federal Government will now work on drafting and adopting child friendly policies and systems, and implement measures to target child survival, development, participation and protection, and provide regular reports on its progress to The Committee on the Rights of the Child.
The President concluded his speech saying, "Any agreement has two sides. With rights come responsibilities. I want to remind you of your responsibilities. You are Somali. This is the first thing and it is the most important thing. You are part of one people, one nation, and together we are creating one future.


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Tilamuta is a town in Sulawesi in Indonesia and is the seat of the Regency of Boalemo

Populated places in Sulawesi
Regency seats of Gorontalo

redpajama_set_name: RedPajamaWikipedia


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Q: Plotting a time series of positions on a map Is there a good way of displaying a series of timestamps on a map, in a way that highlights the temporal aspect, as the points are in order of appearance?
Basically I am trying to track an object throughout the city. I have the respective coordinates of the current point and the point, where the object was previously spotted, and the respective timestamps along with some other related features.
Ideally in python, but I can see myself picking up a more cartography specific tool for it.
What I have tried: I created n (tested with 3 and 5) points in addition to current and previous position and plotted a heatmap with those points, but that doesn't really capture the "Ordered", time-series, aspect of it all.

A: I have solved it with the movingpandas package, as Kadir suggested:
import pandas as pd
import geopandas as gpd
import movingpandas as mpd
import matplotlib.pyplot as plt
import contextily as ctx
import geoplot

fig, ax = plt.subplots(figsize = (25, 25), dpi = 200)

df = pd.read_csv("/path/to/csv").set_index('snapshot_timestamp')

gdf = gpd.GeoDataFrame(df, geometry = gpd.points_from_xy(df['lng'], df['lat']), crs = 'EPSG:4326')

traj = mpd.Trajectory(gdf, 1)

traj.plot(ax = ax)
ctx.add_basemap(ax, crs = 'EPSG:4326')

plt.show()


Low-profile design for use as magazine dump pouch, evidence bag, flex cuff pouch, etc. Hook & loop attachment. Belt-mounted folding/roll-up dump pouch. Mounts to belt. Dimensions: 11″ (H) x 8″ (W) x 5″ (D). Dump Pouch Color: Coyote Tan. Low profile design.


We exist to ECHO God's love across our city and beyond. The messages below are designed to help you encounter, respond to and grow in God's love. You're welcome to engage these messages and to share them with others. Please let us know how we can help you take next steps!