## Related questions with answers

A hot surface at $120^\circ C$ is to be cooled by attaching 8 cm long, 0.8 cm in diameter aluminum pin fins $(k = 237 W/m \cdot K$ and $\alpha = 97.1 \times 10^{-6} m^2/s)$ to it with a center-to-center distance of 1.6 cm. The temperature of the surrounding medium is $15^\circ C,$ and the heat transfer coefficient. on the surfaces is $35 W/m^2 \cdot K,$ Initially, the fins are at a uniform temperature of $30^\circ,$ and at time t = 0. the temperature of the hot surface is raised to $120^\circ C.$ Assuming one-dimensional heat conduction along the fin and taking the nodal spacing to be $\Delta x=2 \mathrm{cm}$ demand a time step to be $\Delta t=0.5 \mathrm{s},$ determine the nodal temperatures after 10 min by using the explicit finite difference method. Also, determine how long it will take for steady conditions to be reached.

Solution

VerifiedThe given quantitites are:

$\begin{align*} L = 8\ \text{cm}\\ D = 0.8\ \text{cm} = 0.008\ \text{m}\\ A = \frac{\pi D^2}{4}\\ k = 237\ \frac{\text{W}}{\text{mK}}\\ \alpha = 97.1\cdot 10^{-6}\ \frac{\text{m}^2}{\text{s}}\\ T_{\infty}=15\ ^o\text{C}\\ h = 35\ \frac{\text{W}}{\text{m$^2$K}}\\ T_0=120\ ^o\text{C}\\ T_1^0 = T_2^0 = T_3^0 = T_4^0 = 30\ ^o\text{C}\\ \Delta x =2\ \text{cm}=0.02\ \text{m}\\ \Delta t=0.5\ \text{s}\\ \end{align*}$

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