HW3 solution

# HW3 solution - Homework#3 Name_solution Problem 1 A 1.5 kW...

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Homework #3 Name___ solution ____ Problem 1. A 1.5 kW resistance heater wire whose thermal conductivity is k = 10.4 BTU/h·ft 0 F has a radius of r 0 = 0.06 in. and a length of L = 15 in., and is used for space heating. Assuming constant thermal conductivity and one- dimensional heat transfer, express the mathematical formulation (the differential equation and boundary conditions) of this heat conduction problem during steady operation. The surface temperature of the rod is 220 0 F Solution: K = 10.4 BTU/h ft 0 F r 0 = 0.06 in L = 15 in kW h BTU 3412.14 1.5kW x = Q = 5,118.21 BTU/h Differential equation: 0 1 = + k g dr dT r dr d r Boundary conditions @r=0 (Thermal symmetry) 0 ) 0 ( = dr dT @r=r 0 (specified heat flux) L r A Q q h BTU r 0 2 21 . 118 , 5 0 π = = =1.303 x 10 5 BTU/(hr·ft 2 ) Also @r=r 0 (specified temperature) T(r 0 ) = 220 0 F Solve the differential equation and obtain a temperature distribution in the heater wire. What is the temperature at the center of the rod? The heat flux boundary condition at r = r 0 is not helpful, as it is redundant with the balance of . If we apply a surface temperature of T V g Q = s , then we can solve the differential equation. 1

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HW3 solution - Homework#3 Name_solution Problem 1 A 1.5 kW...

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