Chapter 2 Heat Conduction Equation2-56 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. Assumptions1Heat conduction is steady and one-dimensional. 2Thermal conductivity is constant. 3 There is no heat generation. PropertiesThe 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 dTdx220=xT∞=15°C h=24 W/m2.°CT1=80°C A=20 m2L=0.4 mk and TT()0801==°C−=−∞kdT LdxhT L T[()] (b) Integrating the differential equation twice with respect to x yields dTdxC=1TxCx C=+12where Cand C12are arbitrary constants.
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