Scaling Analysis of a Moving Point Heat Source in Steady State on a Semi-Infinite Solid

[+] Author and Article Information
Patricio F. Mendez

Professor, Member of ASME, Chemical and Materials Engineering, University of Alberta, Donadeo ICE 12-332, 9211 116St, Edmonton, AB T6G 2V4

Yi Lu

MSc Student, Chemical and Materials Engineering, University of Alberta

Ying Wang

MSc Student, Chemical and Materials Engineering, University of Alberta

1Corresponding author.

ASME doi:10.1115/1.4039353 History: Received December 01, 2017; Revised February 01, 2018


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.

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