Thermodynamics HW Solutions 149

Thermodynamics HW Solutions 149 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-128 A large plane wall is subjected to convection, radiation, and specified temperature on the right surface and no conditions on the left surface. The mathematical formulation, the variation of temperature in the wall, and the left surface temperature are to be determined for steady one-dimensional heat transfer. Assumptions 1 Heat conduction is steady and one-dimensional since the wall is large relative to its thickness, and the thermal conditions on both sides of the wall are uniform. 2 Thermal conductivity is constant. 3 There is no heat generation in the wall. Properties The thermal conductivity and emissivity are given to be k = 8.4 W/m °C and ε = 0.7. Analysis ( a ) Taking the direction normal to the surface of the wall to be the x direction with x = 0 at the left surface, and the mathematical formulation of this problem can be expressed as dT dx 2 2 0 = and = −+ = + ∞∞ k dT L dx hT L T T L T hT T T T () [ ( )][ ( ) ] [ ][ ( ) εσ 4 22 4 273 surr 4 surr 4 ] TL T ==° 2 45 C ( b ) Integrating the differential equation twice with respect to
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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