The Heating and Cooling a Cylinder model computes the radial temperature distribution within a long cylinder as it is heated and cooled by a surrounding fluid.  The cylinder is broken into shells and the temperature of each shell is computed using a finite difference approximation to the radial heat equation in cylindrical coordinates.  It is a supplemental simulation for an article by William Dittrich in The Physics Teacher (TPT).  

The cylinder heats and cools by exchanging thermal energy with the surrounding fluid by convection and this energy exchange is proportional to the difference between the cylinder's surface temperature Ts and the temperature of the fluid Tf.  Inside the cylinder the thermal energy is transported by diffusion.   The temperature inside is uniform if thermal energy transfer within the cylinder is faster than thermal energy transfer at the surface.

The simulation shows how a temperature gradient appears if the heat transfer coefficient or the transfer coefficient are large.  The Heating and Cooling a Cylinder model allows users to select copper, aluminum, and iron material properties and to set the cylinder's radius and its heat transfer coefficient to observe these effects.

The Heating and Cooling a Cylinder model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_heat_HeatingAndCoolingCylinder.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java.