hw11 - S09 - temperature of the steel plate is 300 K. a)...

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Chemical Engineering 150A Spring Semester, 2009 Homework 10: Heat Transfer, Conservation of Energy, 1D problems Problem 1 Consider heat transfer in half a solid cylindrical shell as indicated in the figure. a) Starting with equation 16-13 in WWWR (see handout under “Heat Transfer”), simplify this equation to the most general one that will describe heat transfer in the solid cylindrical shell if the thermal conductivity is constant and there are no source terms. b) Reduce the eqation from part a to the form applicable for steady state heat transfer in the θ direction. c) For the conditions depicted in the figure, that is, T = T o at θ = 0, and T = T π at θ = π , and the radial surfaces insulated, solve for the temperature profile. d) Generate an expression for the heat flow rate, q θ , using the result of part c. Problem 2 A composite solid is made up of an aluminum plate of thickness 0.09 m and steel plate of thickness 0.22 m. The surface temperature of the aluminum plate is 450 K, while the surface
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Unformatted text preview: temperature of the steel plate is 300 K. a) Assuming the thermal conductivity is independent of temperature, solve for the temperature at the interface of the aluminum and steel plates. Calculate the heat flux conducted through the composite solid. k Al = 205.9 W/mK (averaged value over 300 to 450 K) k steel = 45.1 W/mK (averaged value over 300 to 450 K) b) Assuming the thermal conductivity varies linearly with temperature, solve for the temperature at the interface of the aluminum and steel plates. Calculate the heat flux conducted through the composite solid. k Al (T) = (0.464 W/mK 2 ) T + 32 W/mK k steel (T) = (-0.021 W/mK 2 ) T + 53 W/mK Problem 3 A plane wall (infinite in the y and z directions), has internal heat generation per unit volume which varies according to L x e q q / -= & & . The boundary conditions which apply are T = T at x = 0 and T = T L at x = L . Solve for the temperature distribution in the wall. Assume steady state and no viscous dissipation....
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hw11 - S09 - temperature of the steel plate is 300 K. a)...

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