Chapter 2 Heat Conduction Equation2-92Heat 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 1Heat 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. PropertiesThe 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 T2=30°Cxk g InsulatedL dTdxgxk220+=&()where and = 8×10&&./ggexL=−005&g06W/m3and dTdx00=(insulated surface at x
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