Thermodynamics HW Solutions 120

Thermodynamics HW Solutions 120 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-80E A long homogeneous resistance heater wire with specified convection conditions at the surface is used to boil water. The mathematical formulation, the variation of temperature in the wire, and the temperature at the centerline of the wire are to be determined. Assumptions 1 Heat 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. Properties The thermal conductivity is given to be k = 8.6 Btu/h ft °F. 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 0 1 = + k g dr dT r dr d r & and −= k dT r dr hTr T () [() ] 0 0 (convection at the outer surface) dT dr 0 0 = (thermal symmetry about the centerline)
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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