Thermodynamics HW Solutions 133

Thermodynamics HW Solutions 133 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-92 Heat is generated in a large plane wall whose one side is insulated while the other side is maintained at a specified temperature. The mathematical formulation, the variation of temperature in the wall, and the temperature of the insulated surface are to be determined for steady one-dimensional heat transfer. Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since the wall is large relative to its thickness, and there is thermal symmetry about the center plane. 3 Thermal conductivity is constant. 4 Heat generation varies with location in the x direction. Properties The thermal conductivity is given to be k = 30 W/m °C. Analysis ( a ) Noting that heat transfer is steady and one-dimensional in x direction, the mathematical formulation of this problem can be expressed as T 2 =30°C x k g Insulated L dT dx gx k 2 2 0 += & () where and = 8 × 10 && ./ gg e xL = 0 05 & g 0 6 W/m 3 and dT dx 0 0 = (insulated surface at x
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