Unsteady Heat Transfer to a Semi-Infinite Solid with Arbitrary Surface Temperature History and Variable Thermal Properties

摘要

Methods are presented that incorporate the variation of thermal properties with temperature into the determination of the heat flux to and the total heat absorbed by a semi-infinite isotropic solid initially at uniform temperature with arbitrary surface temperature variation with time. Two different numerical procedures are developed. A relatively simple procedure is presented that permits evaluation of heat flux and the total heat transfered when thermal properties other than diffusivity vary. A second method based on a well-known finite difference approximation of the governing equations accounts for variation in all thermal properties. The accuracy of each method is demonstrated by comparison with exact solutions for special cases. Results obtained by application of the methods in three representative cases confirm that significant errors may be introduced into the calculation of heat transfer quantities if variation in thermal properties is ignored. The techniques presented are particularly suited to the determination of heat transfer rates from measurements of surface temperature made with thin-film resistance thermometers and similar instruments. (Author)