Chapter 2 Heat Conduction Equation2-91A long homogeneous resistance heater wire with specified surface temperature is used to boil water. The temperature of the wire 2 mm from the center is to be determined in steady operation. Assumptions 1Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the center line and no change in the axial direction.3 Thermal conductivity is constant.4 Heat generation in the wire is uniform. PropertiesThe thermal conductivity is given to be k= 8 W/m⋅°C. Analysis Noting that heat transfer is steady and one-dimensional in the radial r direction, the mathematical formulation of this problem can be expressed as 01=+⎟⎠⎞⎜⎝⎛kgdrdTrdrdr&and 180°C (specified surface temperature) TrTs()0==dTdr00=(thermal symmetry about the centerline) Multiplying both sides of the differential equation by r and rearranging gives g 180°CResistance wire rrorkgdrdT
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