Thermodynamics HW Solutions 136

Thermodynamics HW Solutions 136 - Chapter 2 Heat Conduction...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 2 Heat Conduction Equation 2-100 A cylindrical shell with variable conductivity is subjected to specified temperatures on both sides. The variation of temperature and the rate of heat transfer through the shell are to be determined. Assumptions 1 Heat transfer is given to be steady and one-dimensional. 2 Thermal conductivity varies linearly. 3 There is no heat generation. Properties The thermal conductivity is given to be kT k T () ( ) = + 0 1 β . Solution ( a ) The rate of heat transfer through the shell is expressed as & ln( / ) Qk L TT rr cylinder ave = 2 12 21 π where L is the length of the cylinder, r 1 is the inner radius, and r 2 is the outer radius, and + + = = 2 1 ) ( 1 2 0 ave ave T T k T k k r 2 T 2 r r 1 T 1 k ( T ) is the average thermal conductivity. ( b ) To determine the temperature distribution in the shell, we begin with the Fourier’s law of heat conduction expressed as & T A dT dr =− where the rate of conduction heat transfer is constant and the heat conduction area A = 2 π rL is variable. Separating the variables in the above equation and integrating from
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

Ask a homework question - tutors are online