Thermodynamics HW Solutions 127

Thermodynamics HW Solutions 127 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-86 A long resistance heater wire is subjected to convection at its outer surface. The surface temperature of the wire is to be determined using the applicable relations directly and by solving the applicable differential equation. 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 = 15.1 W/m °C. T h r k g T h r o 0 Analysis ( a ) The heat generation per unit volume of the wire is & && (. . g Q V Q rL gen gen o == = = × wire 2 3 W m) (6 m) W/m π 2 8 2000 0 001 1061 10 The surface temperature of the wire is then (Eq. 2-68) TT gr h s o =+ = ° + × ° & ) ( 2 30 1061 10 0 001 2 140 8 C m) W/m . C) 3 2 409 C ( b ) The mathematical formulation of this problem can be expressed as 0 1 = + k g dr dT r dr
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