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A 40 mm stainless steel block has a uniform volumetric heat generation of q = 5*
10<sup>6</sup> W/m<sup>3</sup>. The plate is exposed to a 1-dimensional cooling taking place on two of its opposite
surfaces. See the figure below.
a. Determine the heat flux through one of the sides of the block. (5 pts)
Externally
cooled
x=-0.02
x=0.02
Externally
cooled
b. As a result of the cooling, both surfaces are kept at constant temperature of T<sub>s</sub> = 20 °C.
If the thermal conductivity of the steel block is k = 40 W/m. K, determine the equation
for the temperature distribution within the block and plot. (5 pts)
Hint: at x = 0,
$\frac{dT}{dx}$ = 0
