a (100 points) A square-shaped piece of solid has a size of Im x 1m, which is shown in the following figure. The thermal
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a (100 points) A square-shaped piece of solid has a size of Im x 1m, which is shown in the following figure. The thermal conductivity k= 100 W/ mK. The top side of the solid is kept with a constant temperature T, = 300K, while all other sides are kept with another constant temperature T 150K T2=300K L=1m B T=150K L=1m T2=150K L=1m D с T2=150K L=1m
(f) Use the boundary conditions for the problem in HW3, in which the left side (AD) is subjected to a constant temperature T3 = 200K, the bottom side (DC) is subjected to an incoming heat flux q"=5000 W/m², and the right side (CB) is subjected to the convection that T.=150K and h=200 W/m².
K, and the top side (AB) is adiabatic. Repeat (b) for this new set of boundary conditions. Does this problem have an exact/analytic solution? • If yes, please use the analytic/exact solution as a benchmark to quantify the error in your FD solution. • If not, how do you know your solution is correct or not? How can you quantify the error?
(g) Bonus question (20 points). Use the boundary conditions in (t) and consider a uniform internal heat generation g = 8500 W/m², solve this new problem in Matlab with the iterative finite difference method. Show the results and discuss how you would know whether your solution is correct or not.