## Related questions with answers

Question

Air at $20^\circ C$ with a convection heat transfer coefficient of $25 W/m^2 \cdot K$ blows over a horizontal steel hot plate $(k = 43 W/m \cdot K).$ The surface area of the plate is $0.38 m^2$ with a thickness of 2 cm. The plate surface is maintained at a constant temperature of $T_s = 250^\circ C$ and the plate loses 300 W from its surface by radiation. Calculate the inside plate temperature $(T_i).$

Solution

VerifiedStep 1

1 of 2Applying the energy balance for the plate

$\begin{align*} \dot{Q}_\text{cond}&=\dot{Q}_\text{conv}+\dot{Q}_\text{rad}\\ kA\dfrac{T_i-T_s}{L}&=hA\left(T_s-T_\infty \right)+\dot{Q}_\text{rad}\\ 43*0.38*\dfrac{T_i-250}{0.02}&=25*0.38*\left(250-20 \right)+300 \end{align*}$

```
Hence, the inside plate temperature is
```

$\color{#c34632}{T_i=253.04\ ^o\text{C}}$

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