A square aluminum plate has a temperature distribution given as T(x,y)=30 + 10x

Question

A square aluminum plate has a temperature distribution given as T(x,y)=30 + 10x +10y, where x and y range from 0 to 1 m, and T is given in C. The thickness of the plate is 1cm, so we assume it is isothermal in the z direction.

a) What is the temperature at the center of the plate?

b) Calculate the heat flux vector at a few points on the plate and draw the heat flux vectors on a schematic of the plate (in the x-y plane)

c) What is the rate of heat transfer in the y-direction along the top edge of the plate?

Explanation / Answer

a)Temp at (0.5,0.5) = 30+5+5 = 40 degree C b) dT/dx = 10 dT/dy = 10 so flux vector is at 45 degree with the axis. c) Along top edge, y = 1 m also dT/dy = 10 so heat transfer = 10*1*0.01 = 0.1 Watt

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