Chapter 2 Heat Conduction EquationAssumptions 1Heat conduction is steady and one-dimensional since there is no change with time and there is thermal symmetry about the mid point. 2Thermal conductivity is constant. 3 There is no heat generation in the container. PropertiesThe thermal conductivity is given to be k= 1.5 W/m⋅°C. The specific heat of water at the average temperature of (100+20)/2 = 60°C is 4.185 kJ/kg⋅°C (Table A-9). Analysis (a) Noting that the 90% of the 500 W generated by the strip heater is transferred to the container, the heat flux through the outer surface is determined to be 22222W/m0.213m)(0.414W50090.04=×===ππrQAQqsss&&&Noting that heat transfer is one-dimensional in the radial r direction and heat flux is in the negative r direction, the mathematical formulation of this problem can be expressed as 02=⎟⎠⎞⎜⎝⎛drdTrdrdand TrT()11100== °CkdT rdrqs&2=(b) Integrating the differential equation once with respect to r gives rdTdrC21=r1r2T1k
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