Chapter 5: Problem 47
Consider an aluminum alloy fin \((k=180 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) of triangular cross section whose length is \(L=5 \mathrm{~cm}\), base thickness is \(b=1 \mathrm{~cm}\), and width \(w\) in the direction normal to the plane of paper is very large. The base of the fin is maintained at a temperature of \(T_{0}=180^{\circ} \mathrm{C}\). The fin is losing heat by convection to the ambient air at \(T_{\infty}=25^{\circ} \mathrm{C}\) with a heat transfer coefficient of \(h=25 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and by radiation to the surrounding surfaces at an average temperature of \(T_{\text {surr }}=290 \mathrm{~K}\). Using the finite difference method with six equally spaced nodes along the fin in the \(x\)-direction, determine \((a)\) the temperatures at the nodes and \((b)\) the rate of heat transfer from the fin for \(w=1 \mathrm{~m}\). Take the emissivity of the fin surface to be \(0.9\) and assume steady one-dimensional heat transfer in the fin.
Short Answer
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Key Concepts
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