Estimating equilibration times and heating/cooling rates in heat treatment of workpieces with arbitrary geometry

Estimation of both equilibration times and heating/cooling rates is very important in heat treatment practices. An improved, practical virtual sphere method recently developed by two of the authors, Gao and Reid, based on the theory of heat conduction in solids, is further examined and evaluated in this article. The method is capable of estimating equilibration times for any workpiece with arbitrary geometry. The requirement of input data for this method is kept to a minimum. The method is simple and cost effective to use and offers much better accuracy than those methods based on rules of thumb. The engineering approach of applying the virtual sphere method for determining both equilibration times and heating/cooling rates at the center is provided in this article. It can be easily implemented in a computer program, and hand calculations are also possible. The test cases presented in this article for evaluating the method include a long cylinder, an infinite plate, and a short cylinder with exact analytical solutions and a H13 die with experimentally measured temperature history for a heat treatment cycle. The method is recommended for engineering applications.