Heat Generation and Conduction through Composite Walls

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Temperature profiles are calculated for steady-state conduction through a series of three walls with different thermal conductivity. There is also a contact resistance between each pair of walls. Heat is generated at a constant rate in either wall or (select using buttons). Set the rate of heat generation and the contact resistance between the walls with sliders. The distance between the walls is exaggerated so that the temperature profile is more easily seen. The left side of wall is insulated, and heat is transferred from the right side of wall to the flowing air, which is at 20 °C.

Contributed by: Adam J. Johnston (October 2016)
Additional contributions by: Rachael L. Baumann and John L. Falconer
University of Colorado Boulder, Department of Chemical and Biological Engineering
Open content licensed under CC BY-NC-SA


Snapshots


Details

The heat flux from the wall with generation is uniform and directed toward the right:

,

where is in , is the thickness of the wall with generation (m) and is the volumetric heat generation rate ().

A thermal circuit is considered from the right side of the wall with generation to the air with forced convection. If is the wall with generation, then the heat flux can be written as:

,

where is contact resistance (), is the right surface of wall and is the right side of wall (°C). However, if wall is the wall with generation, then the thermal circuit can only be used to solve up to , the right side of wall .

The temperature profile for heat generation in either wall or is calculated using:

,

where is the thermal conductivity of the wall with generation.

The boundary conditions are:

,

;

the left side () is well insulated so the flux is zero. The temperature of the right side of the wall with generation is determined from the thermal circuit.

Reference

[1] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken: John Wiley and Sons, 2011.



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