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Thermodynamics HW Solutions 154

# Thermodynamics HW Solutions 154 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-133 A cylindrical shell with variable conductivity is subjected to specified temperatures on both sides. The rate of heat transfer through the shell is to be determined. Assumptions 1 Heat transfer is given to be steady and one- dimensional. 2 Thermal conductivity varies quadratically. 3 There is no heat generation. Properties The thermal conductivity is given to be . kT k T () ( ) =+ 0 2 1 β Analysis When the variation of thermal conductivity with temperature k ( T ) is known, the average value of the thermal conductivity in the temperature range between TT is determined from 12 and r 2 T 2 r r 1 T 1 k ( T ) + + + = + = + = + = = 2 1 2 1 2 2 0 1 2 3 1 3 2 1 2 0 1 2 3 0 1 2 2 0 1 2 ave 3 1 3 3 ) 1 ( ) ( 2 1 2 1 2 1 T T T T k T T T T T T k T T T T k T T dT T k T T dT T k k T T T T T T This relation is based on the requirement that the rate of heat transfer through a medium with constant
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