Thermodynamics HW Solutions 109

Thermodynamics HW Solutions 109 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-66E A large plate is subjected to convection, radiation, and specified temperature on the top surface and no conditions on the bottom surface. The mathematical formulation, the variation of temperature in the plate, and the bottom surface temperature are to be determined for steady one-dimensional heat transfer. Assumptions 1 Heat conduction is steady and one-dimensional since the plate is large relative to its thickness, and the thermal conditions on both sides of the plate are uniform. 2 Thermal conductivity is constant. 3 There is no heat generation in the plate. Properties The thermal conductivity and emissivity are given to be k =7.2 Btu/h ft °F and ε = 0.6. Analysis ( a ) Taking the direction normal to the surface of the plate to be the x direction with x = 0 at the bottom surface, and the mathematical formulation of this problem can be expressed as dT dx 2 2 0 = and ] ) 460 [( ] [ ] ) ( [ ] ) ( [ ) ( 4 sky 4 2 2 4 sky 4 T T T T h T L T T L T h dx L dT k + + = + = εσ TL T () ==° 2 75 F ( b ) Integrating the differential equation twice with respect to
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