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

The sphere heats and cools by exchanging thermal energy with the surrounding fluid by convection and this energy exchange is proportional to the difference between the sphere's surface temperature Ts and the temperature of the fluid Tf.  Inside the sphere the thermal energy is transported by diffusion.   The temperature inside is uniform if thermal energy transfer within the sphere 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 Sphere model allows users to select copper, aluminum, and iron material properties and to set the sphere's radius and its heat transfer coefficient to observe these effects.

The Heating and Cooling a Sphere 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_HeatingAndCoolingSphere.jar file will run the program if Java is installed.

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