hwk3 - 2 Consider heat transfer across a slab of thickness...

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ME 410 Spring 2008 Homework 3 Due: January 22, 2008 1. Consider a large plane wall of thickness L = 0.25 m. The wall surface at x = 0 is insulated while the surface at x = L is maintained at a temperature of 30 ° C. The thermal conductivity of the wall is k = 26 W/m ° C, and heat is generated in the wall at a rate of 3 5 . 0 / m W e q q L x o - = where 3 5 / 10 10 . 1 m W x q o = . Assuming steady one-dimensional heat transfer (a) express the differential equation and the boundary conditions for the heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation and (c) determine the temperature of the insulated surface of the wall.
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Unformatted text preview: 2. Consider heat transfer across a slab of thickness L and thermal conductivity k that has internal heat generation, q . Heat flows in x = 0 at a flux of in q ′ ′ , the other surface, x=L, is exposed to convection at T ∞ with a convective heat transfer coefficient h ∞ . Solve for the temperature distribution in the slab (a general solution). Graph the temperature distribution in the slab for five values of q (0, 25000, 50000, 100000, 250000) for a uranium slab of thickness 0.1-meter with a T ∞ of 290 K, h ∞ of 250 W/(m 2 K), and in q ′ ′ of 25,000 W/m 2 ....
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