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Chapter 10
Heat Transfer in a Pipe with Uniform Heat Generation in Its Walls

Excerpt

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]):

d2TdR2+(1R)dTdR+Qk=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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