A plane wall, under steady conditions and with no internal heat generation, is subjected to a constant heat flux on one side and convection on the other as shown below. The heater is perfectly insulated on the backside, has a negligible thickness, and creates a uniform heat flux of q''h . The wall has a thickness L and thermal conductivity k. The right face is exposed to convection with an ambient fluid temperature of Tamb and heat transfer coefficient h. a) Derive an expression for the maximum temperature in the wall in terms of constant parameters q''h, L, k, Tamb, h, and/or any other necessary parameters. b) Derive an expression for the surface temperature of the wall (at x = L) in terms of appropriately defined parameters. c) For conditions where q''h=2200 W/m^2, L = 5 cm, k=15.1 W/(mK), Tamb=20C, h=100 W/(m^2K) Calculate the maximum temperature of the wall and thesurface temperature at x = L.
A plane wall, under steady conditions and with no internal heat generation, is subjected to a constant heat flux on one side and convection on the other as shown below. The heater is perfectly insulated on the backside, has a negligible thickness, and creates a uniform heat flux of q''h . The wall has a thickness L and thermal conductivity k. The right face is exposed to convection with an ambient fluid temperature of Tamb and heat transfer coefficient h.
a) Derive an expression for the maximum temperature in the wall in terms of constant
parameters q''h, L, k, Tamb, h, and/or any other necessary parameters.
b) Derive an expression for the surface temperature of the wall (at x = L) in terms of
appropriately defined parameters.
c) For conditions where q''h=2200 W/m^2, L = 5 cm, k=15.1 W/(mK), Tamb=20C, h=100 W/(m^2K)
Calculate the maximum temperature of the wall and thesurface temperature at x = L.
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