Chemical Engineering
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Consider a solid slab of thickness $2L$ and uniform cross section $A$. The volumetric rate of heat generation within the slab is $\dot{g} \: (W \: m^{-3})$. The slab loses heat by convection at both the ends to air with heat transfer coefficient $h$. Assuming steady state, one-dimensional heat transfer, the temperature profile within the slab along the thickness is given by: $$T(x)= \dfrac{\dot{g}L^2}{2k} \left[ 1- \left ( \dfrac{x}{L} \right) ^2 \right ] + T_s \text{ for } -L \leq x \leq L$$ where $k$ is the thermal conductivity of the slab and $T_s$ is the surface temperature. If $T_s = 350 \: K$, ambient air temperature $T_{\infty} = 300 \: K$, and Biot number (based on $L$ as the characteristic length) is $0.5$, the maximum temperature in the slab is _______ $K$ (round off to nearest integer).
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