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The problem of moving heat sources is central to a wide range of fields including welding, heat treatment, tribology, grinding, machining, and manufacturing of microfluidic channels. This problem has been approached numerically and analytically but the solutions are often difficult to apply in engineering practice.

Numerical solutions are often difficult to implement for practitioners without specialized software or not versed in computational modelling. The solutions published are valid for the particular values of parameters considered in each publication, and it was been difficult to generalize the results to a large number of practical cases with different parameters. Analytical solutions are also diffi cult for practitioners to implement because they often involve series summations that typically have inconvenient expressions for addressing practical questions. For example, the question of 鈥渨hat is the weld width" is difficult to answer, even as a rough approximation, using the simplest of models, the one proposed by Rosenthal and Rykalyn independently. Textbooks often omit a treatment of moving heat sources, or introduce the foundations for mathematical or numerical analysis, but do not present practical expressions amenable to use by practitioners.

This presentation will introduce current work using a modern methodology to obtain useful engineering expressions for identifying moving heat source features of interest to practitioners, such as isotherm width, cooling rate and melting efficiency. The methodology is based on the concepts of characteristic values like isotherm width and cooling rate, dimensional analysis, asymptotic analysis, and blending techniques. A specific example of how to calculate such characteristic values with the equations directly simplified from analytical solutions will also be presented.