Numerical and Machine Solutions of Transient Heat-Conduction Problems Involving Melting or Freezing: Part I—Method of Analysis and Sample Solutions

Previously published methods for the solution of one-dimensional heat-conduction problems with melting or freezing are briefly reviewed and weaknesses of previous analytic and numerical methods are outlined. Two new and more generally applicable numerical methods, applicable to digital and analog computation, are developed in the paper. Sample problems using these new techniques are solved and compared with the results of a widely used conventional method. An evaluation of the various methods and recommendations on areas of application are included.