(Solved): A fin used in car radiator system is shown in Figure. 2 the fin consists of composition of differe ...

A fin used in car radiator system is shown in Figure. 2 the fin consists of composition of different martials. Your role is to simplify the problem and make use of FEA techniques to critically analyze the temperature distribution through the fin. Figure.2: Thick plate used as a fin in car radiator system The following information have been provided: - The thickness to the fin, $z=3\mathrm{mm}$ - The Hight of the fin, $y=60\mathrm{cm}$ - The width of the fin, $x=20\mathrm{cm}$ 1. Based on the given geometry information, provide justified explanation and recommendations to simplify the problem from three-dimensional (3D) to one-dimensional (1D), consider the ratio $z/x$ and $y/x$ 2. Given that the problem can be modeled by the following differential equation: $D\frac{d^{2}T}{d{x}^2}=0$ here $D$ is thermal conductivity for each element. - Make use of the 1D layout that is demonstrated in Figure.3, perform the following: a. Construct one-dimensional elements line (i.e., grid/mesh line), make the correct numbering and labeling of nodes and elements. b. Construct grid/mesh information table 3. Write the shapes function, $N_i$ and $N_j$ for each element (e) and plot the shape function diagram 4. Construct the weight functions for the one-dimensional elements' line/mesh. 5. Calculate the nodal temperature values and the distribution through each element using element matrices-Galerkin method. 6. Find the heat flow rate, $q$ for each element., If $q$ is given by: $q=?D\frac{dT}{dx}$ 7. Would you increase (refine) the number of nodes/elements for this problem, explain your answer? 8. Justify your mesh/grid divisions for this problem in terms of complication of geometry or materials compositions. Figure.3: Thick plate simplified as 1D- heat transfer problem