Thermodynamics HW Solutions 94

Thermodynamics HW Solutions 94 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-48 Water flows through a pipe whose outer surface is wrapped with a thin electric heater that consumes 300 W per m length of the pipe. The exposed surface of the heater is heavily insulated so that the entire heat generated in the heater is transferred to the pipe. Heat is transferred from the inner surface of the pipe to the water by convection. Assuming constant thermal conductivity and one-dimensional heat transfer, the mathematical formulation (the differential equation and the boundary conditions) of the heat conduction in the pipe is to be obtained for steady operation. Assumptions 1 Heat transfer is given to be steady and one-dimensional. 2 Thermal conductivity is given to be constant. 3 There is no heat generation in the medium. 4 The outer surface at r = r 2 is subjected to uniform heat flux and the inner surface at r = r 1 is subjected to convection. Analysis The heat flux at the outer surface of the pipe is & && (.
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