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Steady-Conduction in an Insulated, Volumetrically Heated Cylinder

UPDATED: 09/16/2022
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This workbook evaluates and plots the temperature profile from the analytical solution for steady-state conduction in an insulated, volumetrically heated cylinder and plots it.  The volumetric heating could come from nuclear fission, radioactive decay or Ohmic heating.   The left boundary is adiabatic (no heat flow) by symmetry; the outer (right) boundary is subject to convection (Newton’s Law of cooling).

Temperature Distribution in a cylinder as function of radius. The inner section (red) has uniform volumetric heat generation; the outer section (blue) is insulation and has no volumetric generation. The right hand boundary (green) is in contact with a fluid and the heat transfer there is given by Newton's Law of Cooling.. The red section is concave up, the blue section is convex up.
Steady temperature distribution as function of radius.  The inner section (red) has uniform volumetric heat generation; the outer section (blue) is insulation and has no volumetric generation.  Note that in the volumetrically heated section the temperature profile is concave down, while in the unheated section to the right, the temperature is concave up due to the area increasing with r.

 

This workbook is fairly similar to the workbook for volumetric heating in nuclear fuel rod, but with fewer complications.

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