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Consider an engine cover that is made with two layers of metal plates. The inner layer is stainless steel (k1 = 14 W/m*k) with a thickness of 10 mm, and the outer layer is aluminum (k2 = 237 W/m*K) with a thickness of 5 mm. Both metal plates have a surface roughness of about 23 micrometers. The aluminum plate is attached on the stainless steel plate by screws that exert an average pressure of 20 MPa at the interface. The inside stainless steel surface of the cover is exposed to heat from the engine with a convection heat transfer coefficient of 10 W/m^2*K at an ambient temperature of150 degrees C. The outside aluminum surface is exposed to a convection heat transfer coefficient of 25 W/m^2*K at an ambient temperature of 40 degrees C. Determine the heat flux through the engine cover.
Construct the homogeneous solution in terms of four constant that could be determined from initial conditions and show the equations of motion
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