General solutions for stationary/moving plane heat source problems in manufacturing and tribology

General solutions (both transient and steady state) for the temperature ris e at any point due to stationary/moving plane heat sources of different sha pes (elliptical, circular, rectangular, and square) and heat intensity dist ributions (uniform, parabolic, and normal) are presented using the Jaeger's classical heat source method (J.C. Jaeger, Moving sources of heat and the temperature at sliding contacts, Proc. Royal Society of NSW 76 (1942) 203-2 24). Starting from an instantaneous point heat source solution, an elliptic al moving heat source with different heat intensity distributions, namely, uniform, parabolic and normal, was used as the basic plane heat source and its solution for the temperature rise at any point was derived. This analys is was then extended to other plane heat sources, such as circular, rectang ular, and square heat sources to cover a range of manufacturing processes a nd tribological problems experienced in engineering practice. In addition, the analysis presented here is valid for both transient and steady state co nditions while most analyses to date are strictly for quasi-steady state co nditions. The solutions for the stationary heat sources are obtained from t he moving heat source solution by simply equating the velocity of sliding t o zero. Further, the analysis can be used to determine the temperature dist ribution net only at the surface but also with respective to the depth whic h again is a very important consideration in most manufacturing and tribolo gical applications since it effects the subsurface deformation, metallurgic al changes, hardness variation, and residual stresses. It can also be used to determine the maximum and average temperatures within the area of the he at source. Thus, the analysis presented here is believed to be comprehensiv e. (C) 2000 Elsevier Science Ltd. All rights reserved.