Justify that we can assume t is only a function of x ttx

Question

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 = 200^oC. The fin is losing heat to the surrounding medium at T = 25^oC 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).