internal heat-conduction coupling that can be approximate or just a high-enough value to force the same temperature for the two half-plates). Radiation heat rates are obtained in terms of exitances at each surface in the following way. At a Mj i, surface if there is any radiation heat-rate, , it must be equal to the net radiation input, (input radiation Aj, power minus output), which can be set in these different forms: Choosing the system interface a little bit inside the surface (when absorption and reflection of incoming radiation, have already taken place), net heat input equals absorption minus emission: Choosing the system interface a little bit outside the surface (when absorption and reflection of incoming radiation, have not yet taken place), net heat input equals irradiance minus exitance (times the area): Eliminating the irradiance from equations and : which may be interpreted from an electrical analogy as flow directly proportional to a ‘a and inversely proportional to a resistance of value It is cumbersome to extrapolate equation to the blackbody limit, since both, and tend to zero, but the blackbody case is much simpler, as explained below. Let consider now the interaction among surfaces. The net radiation heat received by surface from i surface is , where we keep to the tradition of naming (shortly ) the from to as a shorthand for j ‘heat j i’, net radiation flux received by surface from surface notice however, that with this naming, that i j’; ‘the with contrary to the definition of heat as energy flow by temperature difference). From all the Ti=Tj, ≠0 enclosure: where radiative fluxes () have been put in terms of exitances (M) and view factors (Fij), ), and the reciprocity relation applied: . Another way to get equation is: . The equations to solve to get the intermediate variables (and finally the and are the energy balance Mi Ti) at every node, , where dHi=micidTi/dt is the enthalpy change rate (equal to the internal energy change rate, dEi, in incompressible systems), and the network system can be cast as:
internal heat-conduction coupling that can be approximate or just a high-enough value to force the same temperature for the two half-plates). Radiation heat rates are obtained in terms of exitances Mj at each surface i, in the following way. At a surface Aj, if there is any radiation heat-rate, , it must be equal to the net radiation input, (input radiation power minus output), which can be set in these different forms: Choosing the system interface a little bit inside the surface (when absorption and reflection of incoming radiation, have already taken place), net heat input equals absorption minus emission: Choosing the system interface a little bit outside the surface (when absorption and reflection of incoming radiation, have not yet taken place), net heat input equals irradiance minus exitance (times the area): Eliminating the irradiance from equations and : which may be interpreted from an electrical analogy as ‘a flow directly proportional to a and inversely proportional to a resistance of value It is cumbersome to extrapolate equation to the blackbody limit, since both, and tend to zero, but the blackbody case is much simpler, as explained below. Let consider now the interaction among surfaces. The net radiation heat received by surface i from surface j is , where we keep to the tradition of naming (shortly ) the ‘heat from j to i’, as a shorthand for ‘the net radiation flux received by surface i from surface j’; notice however, that with this naming, that ≠0 with Ti=Tj, contrary to the definition of heat as energy flow by temperature difference). From all the enclosure: where radiative fluxes () have been put in terms of exitances (M) and view factors (Fij), ), and the reciprocity relation applied: . Another way to get equation is: . The equations to solve to get the intermediate variables Mi (and finally the and Ti) are the energy balance at every node, , where dHi=micidTi/dt is the enthalpy change rate (equal to the internal energy change rate, dEi, in incompressible systems), and the network system can be cast as:
Heat%20transfer%20and%20thermal%20radiation%20modelling.docx