A Simplified Numerical Solution of Unsteady Heat Conduction Problems with an Application to a Short Cylinder

Abstract

A simple numerical approach is introduced, for solving transient one-dimensional heat conduction problems, in both a plate and a long cylinder with or without internal heat generation, using spreadsheets. Details of developing the nodal equations and writing them in spreadsheet format are presented. Then, the formulated problems are used to solve transient multi-dimensional heat conduction in a short cylinder applying the principle of the separation of variables. This reduces the two-dimensional nature of the problem into a couple of one-dimensional problems that are easily solved using spreadsheets. Temperature at any location and time is obtained by combining both solutions. The method allows the easy change in time increment and Biot number in a way that make it general for solving transient heat conduction in a short cylinder. It is believed that this method is appropriate for teaching transient conduction numerically to undergraduate heat transfer students.