Fundamentals of Heat and Mass Transfer
Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2, Problem 2.49P

Two-dimensional. steady-state conduction occurs in a hollow cylindrical solid of thermal conductivity k = 16 W/m K , outer radius r o = 1 m and overall length 2 z o = 5 m , where the origin of the coordinate system is located at the midpoint of the center line. The inner surface of the cylinder is insulated, and the temperature distribution within the cylinder has the form T ( r , z ) = a + b r 2 + c ln r + d z 2 , where a = 20 ° C, b = 150 ° C/m 2 , c = 12 ° C, d = 300 ° C/m 2 and r and zare in meters.

  1. Determine the inner radius r i of the cylinder.
  2. Obtain an expression for the volumetric rate of heat generation, q . ( W/m 3 ) .
  3. Determine the axial distribution of the heat flux at the outer surface, q r n ( r o , z ) . What is the heat rate at the outer surface? Is it into or out of the cylinder?
  4. Determine the radial distribution of the heat flux at the end faces of the cylinder, q r n ( r , + z o ) and q r n ( r , z o ) . What are the corresponding heat rates? Are they into or out of the cylinder?
  5. Verify that your results are consistent with an over-all energy balance on the cylinder.

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Chapter 2 Solutions

Fundamentals of Heat and Mass Transfer

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