Non-Quasi-Steady Analysis of Heat Conduction From a Moving Heat Source

Abstract

The problem of heat conduction resulting from a moving heat source applies to many fields of engineering such as arc welding, surface hardening, continuous casting, metal material treatment, moving friction between mechanical parts, laser machining, and even in nucleate boiling theory. Many investigations of this problem have been performed. Earlier work is based on the principle of a quasi-steady state, that is, if the heat source with constant power moves with a constant velocity in a medium of sufficiently large dimensions, then the temperature field appears to be at steady state with respect to the moving coordinate system after quite a long time. Although the quasi-steady solution has been widely used in engineering, there are some rigid limits to it. First, the power in the moving heat source must be constant, otherwise the quasi-steady state cannot appear even if the medium is large. Next, the medium itself must be large, so that the quasi-steady state can be reached. Both of these conditions must be simultaneously satisfied. In developing high technologies such as laser, plasma, and others, greater importance is given to research into heat conduction in bodies with finite size resulting from a moving heat source. For these bodies, themore » temperature distribution is non-quasi-steady, not only for the moving heat source with variable power, but also for those with constant power. The present note considers heat conduction in a finite medium or a thin rod with heat loss from the rod surface resulting from a moving plane source through the use of a heat source method and presents the appropriate exact analytical solutions.« less