Question

Consider the system with uniform heat generation shown in the figure below the text. \text { qgen }=2 \times 10^{7} \mathrm{~W} / \mathrm{m}^{3} \text { metal thickness }=3 \mathrm{~mm} \mathrm{k}_{\text

{fuel }}=60 \mathrm{~W} /(\mathrm{m} \mathrm{K}) \mathrm{k}_{\text {metal }}=18 \mathrm{~W} /(\mathrm{m} \mathrm{K}) \mathrm{h}=10,000 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K} \mathrm{T}_{\text {inf }}=200^{\circ} \mathrm{C} Inner compartment thickness = 2 L where L = 15 mm a. Derive the equation for the temperature distribution T(x) in the fuel compartment. Express your equation in terms of the above variables. (3 points) b. Calculate the maximum and minimum temperatures in the fuel compartment. (2 points) c. Repeat the calculations in part b if the insulation is removed and replaced with the same convection conditions present on the other side. (2 points) d. Write a MATLAB program that plots the temperature profile for the conditions depicted in part b.(9 points) e. Write a MATLAB program that plots the temperature profile for the conditions depicted in part c. (9 points) Note that both MATLAB programs must be m-files containing the necessary coding to generate the plots.You must submit your plots, code and calculations. This assignment must be uploaded to Blackboard by Wednesday morning no later than 10am.

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