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Continuous heating of a thick slurry. Thick slurries and pastes flow mostly as a plug in pipes, i . e . with an approximately constant
Continuous heating of a thick slurry. Thick slurries and pastes flow mostly as a plug in pipes, ie with an approximately constant velocity profile across the radial dimension. Interestingly, heat transfer to this type of flow in pipes is usually omitted in most books of heat transfer. Fortunately, the governing PDE is fairly easy to solve, and some important results can be derived from the general series solution obtained by separation of variables.
a Assuming show by a shell balance that the steadystate heating process is described by the following PDE for a hot pipe with constant wall temperature,
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b Note that the BCs on axis are not homogeneous. Nondimensionalize the PDE and the BCs so that you obtain the following:
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where What are the definitions of and
c Solve the PDE and show that the solution is :
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