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Problem - Consider an aluminum alloy fin (k =180 W/m·oC) of triangular cross section with length L= 150 cm, base thickness b = 1 cm, and w = 1 m in the direction normal to the plane of paper, as shown in Figure. The base of the fin is maintained at a temperature of T0 = 200oC. The fin is losing heat to the surrounding medium at T = 25oC with a heat transfer coefficient of h = 15 W/m2·oC. The half top surface (from middle to right end) absorbs solar radiation with heat flus q" = 100 W/m2.
Please using the finite difference method starting with six equally spaced nodes along the fin in the x-direction to compute T(x). You may refine your grids to the point till the temperature profile is not affected.
(a) Justify that we can assume T is only a function of x, T=T(x);
(b) Clearly show how you define your grid and write down the detailed energy balance for each node.
(c) Plot T(x).
The solution has to be step by step and good quality. Please using the finite difference method starting with six equally spaced nodes along the fin in the x-direction to compute T(x). You may refine your grids to the point till the temperature profile is not affected.
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