## Related questions with answers

Hot air at $80^{\circ} \mathrm{C}$ is blown over a $2-m \times 4-m$ flat surface at $30^{\circ} \mathrm{C}.$ If the average convection heat transfer coefficient is $55 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K},$ determine the rate of heat transfer from the air to the plate, in kW.

Solution

VerifiedEquation for the $\textbf{rate of heat transfer}$ between a solid and a fluid is:

$\begin{equation*} \dot{Q}=h A_s \left ( T_s-T_{\infty} \right ) \end{equation*}$

From given dimensions of the plate we can calculate the needed area $A_s$:

$\begin{align*} A_s&=a \cdot b \\ A_s&=2 \mathrm{m} \cdot 4 \mathrm{m} \\ A_s&= \color{#4257b2}{8 \mathrm{m^2}} \end{align*}$

We are also given the $\textbf{surface temperature}$ $T_s=30\mathrm{^o C}$, $\textbf{air temperature}$

$T_{\infty} =80\mathrm{^o C}$ and the $\textbf{average heat transfer coefficient}$ $h=55 \mathrm{\frac{W}{m^2 K}}$.

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