change 1 1 1 1 2 Increasing the specific heat capacity: no changes in temperature gradient, area, energy flux density and energy flux; increase in time to reach steady-state. = 1 m = 0.01 m = 2 W.m-1.oC-1 = 1 J.kg-1.oC-1 = 1 kg.m-3 L r k c dT/dx A J dQ/dt 5 [oC.m-1] [m2] [W.m-2] [W] [s] -100 3.1410-4 100 3.1410-2 1.066 change 1 1 1 1 2 Increasing the density: no changes in temperature gradient, area, energy flux density and energy flux; increase in time to reach steady-state. Simulation 2 Conduction through a composite slab tp_rod_12.m Consider a rod consisting of two different materials connected in series. The temperature at the ends of the rod are kept constant at and The rod’s TA TB. temperature will evolve with time from its initial temperature to a steady-state situation when the energy flux density is uniform along the length of the rod, that is, the rate of energy transfer through the two materials must be equal. Therefore, we can write (10) We can model a rod of length = 0.2 m and radius = 0.01 m made of copper and L R iron in which the temperatures at the end of the rod are = 100 oC and = 0 oC. TA TB The junction between the cooper and the iron is at the centre of the rod. Copper Iron = 400 W.m-1.K-1 = 50 W.m-1.K-1 k1 k2 = 380 J.kg-1.K-1 = 450 J.kg-1.K-1 c1 c2 1 = 8900 kg.m-3 2 = 7900 kg.m-3 We can calculate the theoretical temperature at the centre of the rod from equation TC (10) Using equation (10), the theoretical steady-state energy flux density is Jcond
change 1 1 1 1 2 Increasing the specific heat capacity: no changes in temperature gradient, area, energy flux density and energy flux; increase in time to reach steady-state. L = 1 m r = 0.01 m k = 2 W.m-1.oC-1 c = 1 J.kg-1.oC-1 = 1 kg.m-3 dT/dx [oC.m-1] -100 A [m2] 3.1410-4 J [W.m-2] 100 dQ/dt [W] 3.1410-2 5 [s] 1.066 change 1 1 1 1 2 Increasing the density: no changes in temperature gradient, area, energy flux density and energy flux; increase in time to reach steady-state. Simulation 2 Conduction through a composite slab tp_rod_12.m Consider a rod consisting of two different materials connected in series. The temperature at the ends of the rod are kept constant at TA and TB. The rod’s temperature will evolve with time from its initial temperature to a steady-state situation when the energy flux density is uniform along the length of the rod, that is, the rate of energy transfer through the two materials must be equal. Therefore, we can write (10) We can model a rod of length L = 0.2 m and radius R = 0.01 m made of copper and iron in which the temperatures at the end of the rod are TA = 100 oC and TB = 0 oC. The junction between the cooper and the iron is at the centre of the rod. Copper Iron k1 = 400 W.m-1.K-1 k2 = 50 W.m-1.K-1 c1 = 380 J.kg-1.K-1 c2 = 450 J.kg-1.K-1 1 = 8900 kg.m-3 2 = 7900 kg.m-3 We can calculate the theoretical temperature TC at the centre of the rod from equation (10) Using equation (10), the theoretical steady-state energy flux density Jcond is
tp_conduction.docx