The transient temperature field (as seen by a moving observer) due to a moving heat source, such as the process zone near a dynamically propagating crack tip or an external agent as in the case of welding, is analyzed by a moving-mesh finite element procedure. The effects of the temperature-dependent material properties, and of the loss of heat to the surrounding medium through convection and radiation, are studied. Situations under which conditions in the process zone may be labeled as “isothermal” or “adiabatic” are explored. Estimates of temperature rise near the tip of a crack propagating at realistic speeds in structural steels are made.

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