# Everyday Heat Transfer Problems: Sensitivities to Governing Variables

By
M. Kemal Atesmen
M. Kemal Atesmen
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ISBN:
9780791802830
No. of Pages:
238
Publisher:
ASME Press
Publication date:
2009
Under steady-state conditions, constant thermophysical properties and uniform heat generation in the walls, the one-dimensional conduction heat transfer equation in radial direction of a pipe can be written as (see Reference by Carslaw, H. S. and J. C. Jaeger [17]):
$d2T∕dR2+(1∕R)dT∕dR+Q∕k=0$
where the radial heat flux is positive in the negative radial direction (towards the center of the pipe), Q is uniform heat generation in the pipe walls in W∕m3, and k is pipe wall thermal conductivity in W∕m-C. This differential Eq. (10-1) can be solved for the radial temperature distribution in the pipe wall by specifying the pipe wall temperatures with the inner and outer wall radii as boundary conditions.
$T=TiatR=Ri$
and
$T=ToatR=Ro$
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