Question

MEGR 3116 Heat Transfer Summer 2019 NAME Please show all of your work. Open book and open notes. 1) A flat/planar window of thickness, L, having a thermal conductivity, k, is exposed on its inner face to a room at temperature, T。, and on its outer surface to outside air having temperature, T-(far from the window surface). Define an x-axis having origin at the window's inner surface and directed towards the outer surface, and assume that the inner surface temperature is Ta. In addition, assume that convection heat transfer takes place at the window's outer surface, and that the convective heat transfer coefficient, he, is known. Finally, assume that the room temperature, T, is higher than the bu'k air temperature, T a) (4 pts) Sketch the heat transfer problem. Include the x-coordinate axis. b) (3 pts) In which direction does heat flow? You can sketch this on your sketch above. c) (5 pts) Write down the differential equation governing heat conduction within the window

Answer 1

Room Oulside Given: To >Too air Windon Too Thermal =D-Heat Hansfe r takes place from Room to outside air he Conductivity Direction of via windono. heat transfer Derivation of govering equation Considering a slab element of thickness dz at a distance χ from point(X ) Applying Energyconservation asthere is no heat generation Egen AE )cvso : Gteady stat e 0 dt dt dt qx-fut 2x.gx.) de} e dt. Cat dt Using Fourier Law xKAOT anc .2.1 -KADT rdz - 9A-4χ@dT dt ax. dt a22 202 K dt an of- thermal diffusivity PCp