This paper presents a systematic scaling analysis of the point heat source in steady-state on a semi-infinite solid. It is shown that all characteristic values related to an isotherm can be reduced to a dimensionless expression dependent only on the Rykalin number (Ry). The maximum width of an isotherm and its location are determined for the first time in explicit form for the whole range of Ry, with an error below 2% from the exact solution. The methodology employed involves normalization, dimensional analysis, asymptotic analysis, and blending techniques. The expressions developed can be calculated using a handheld calculator or a basic spreadsheet to estimate, for example, the width of a weld or the size of zone affected by the heat source in a number of processes. These expressions are also useful to verify numerical models.
Scaling Analysis of a Moving Point Heat Source in Steady-State on a Semi-Infinite Solid
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 1, 2017; final manuscript received February 1, 2018; published online April 11, 2018. Assoc. Editor: Alan McGaughey.
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Mendez, P. F., Lu, Y., and Wang, Y. (April 11, 2018). "Scaling Analysis of a Moving Point Heat Source in Steady-State on a Semi-Infinite Solid." ASME. J. Heat Transfer. August 2018; 140(8): 081301. https://doi.org/10.1115/1.4039353
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