Thermodynamics HW Solutions 128

Thermodynamics HW Solutions 128 - 1 Heat transfer is steady...

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Chapter 2 Heat Conduction Equation Assumptions 1 Heat transfer is steady since there is no 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 heater is uniform. Properties The thermal conductivity is given to be k = 5.8 Btu/h ft °F. Analysis The resistance heater converts electric energy into heat at a rate of 3 kW. The rate of heat generation per unit length of the wire is 3 8 2 2 wire Btu/h.ft 10 933 . 2 ft) (1 ft) 12 / 04 . 0 ( Btu/h) 14 . 3412 3 ( × = × = = = π L r Q V Q g o gen gen Then the temperature difference between the centerline and the surface becomes F 140.4 ° = ° × = = Δ F) Btu/h.ft. 8 . 5 ( 4 ft) 12 / 04 . 0 )( Btu/h.ft 10 933 . 2 ( 4 2 3 8 2 max k r g T o 2-88E Heat is generated uniformly in a resistance heater wire. The temperature difference between the center and the surface of the wire is to be determined. r T s r o Heater 0 Assumptions
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Unformatted text preview: 1 Heat transfer is steady since there is no 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 heater is uniform. Properties The thermal conductivity is given to be k = 4.5 Btu/h ft F. Analysis The resistance heater converts electric energy into heat at a rate of 3 kW. The rate of heat generation per unit volume of the wire is 3 8 2 2 wire Btu/h.ft 10 933 . 2 ft) (1 ft) 12 / 04 . ( Btu/h) 14 . 3412 3 ( = = = = L r Q V Q g o gen gen & & & Then the temperature difference between the centerline and the surface becomes F 181.0 = = = F) Btu/h.ft. 5 . 4 ( 4 ft) 12 / 04 . )( Btu/h.ft 10 933 . 2 ( 4 2 3 8 2 max k r g T o & 2-51...
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