Scaling expressions of characteristic values for a moving point heat source in steady state on a semi-infinite solid

Engineering expressions for characteristic values of a moving point heat source on a semi-infinite solid are presented. Related characteristic values are: maximum isotherm width and its location, leading and trailing lengths of isotherm, centerline heating rate and cooling rate, maximum temperature and its gradient at maximum width, aspect ratio of isotherms, melting efficiency, cooling time from 800 degrees C to 500 degrees C (often used for studying steels), solidification time, the thickness of zone affected by the heat source, and modification criteria to account for the effect of joint preparation. All engineering expressions proposed are accurate to within 7% of the exact analytical solutions, and are obtained with a systematic approach. Dimensional analysis indicates that the expressions developed depend on a single dimensionless parameter that captures all possible cases. This dimensionless number is typically the Rykalin number (Ry), which characterizes three dimensional heat flow induced by a moving point heat source. The obtained engineering equations are of great practical value for very diverse fields where moving heat sources are involved, and are simple enough to be calculated with a calculator or spreadsheet. (C) 2019 Elsevier Ltd. All rights reserved.