Thermodynamics HW Solutions 151

Thermodynamics HW Solutions 151 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-130 The base plate of an iron is subjected to specified heat flux on the left surface and convection and radiation on the right surface. The mathematical formulation, and an expression for the outer surface temperature and its value 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. 4 Heat loss through the upper part of the iron is negligible. Properties The thermal conductivity and emissivity are given to be k = 2.3 W/m °C and ε = 0.7. Analysis ( a ) Noting that the upper part of the iron is well insulated and thus the entire heat generated in the resistance wires is transferred to the base plate, the heat flux through the inner surface is determined to be 2 2 4 base 0 0 W/m 000 , 100 m 10 150 W 1500 = × = = A Q q & & 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 = and −= = k dT dx q () & , 0 80 000
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