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Thermodynamics HW Solutions 97

Thermodynamics HW Solutions 97 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-56 A large plane wall is subjected to specified temperature on the left surface and convection on the right surface. The mathematical formulation, the variation of temperature, and the rate of heat transfer are to be determined for steady one-dimensional heat transfer. Assumptions 1 Heat conduction is steady and one-dimensional. 2 Thermal conductivity is constant. 3 There is no heat generation. Properties The thermal conductivity is given to be k = 2.3 W/m °C. Analysis ( a ) Taking the direction normal to the surface of the wall to be the x direction with x = 0 at the left surface, the mathematical formulation of this problem can be expressed as dT dx 2 2 0 = x T =15°C h= 24 W/m 2 .°C T 1 =80°C A= 20 m 2 L= 0.4 m k and TT () 08 0 1 ==° C −= k dT L dx hT L T [() ] ( b ) Integrating the differential equation twice with respect to x yields dT dx C = 1 Tx Cx C =+ 12 where C and C 1 2 are arbitrary constants.
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