Welding, Glazing, and Heat Treating —A dimensional analysis of heat flow

Abstract

Through a rigorous mathematic demonstration and the application of general enthalpy equations, the key dimensionless variables that characterize heat flow during welding, glazing, and heat treating of a workpiece were systematically presented. Both the 2-dimensional and the 3-dimensional heat flows due to a moving heat source were considered. The 2-dimensional heat flow during the welding of thin plates with a stationary, instantaneous heat source was also analyzed. While the primary dimensionless variables such as the dimensionless temperature, the Fourier number, and the dimensionless distances were sufficient to describe the heat flow during heat treating, additional primary dimensionless variables such as the dimensionless heat input, the Stephan number, the dimensionless thermal conductivity, and the dimensionless specific heat were found necessary to define the heat flow during welding and glazing. The validity of such a dimensional analysis was verified by existing analytical solutions. Due to the additional heat flow variables such as the size of the heat source, the size of the workpiece, the surface heat loss, and the freezing range of alloy systems, secondary dimensionless variables including the dimensionless size of the heat source, the dimensionless width and thickness of the workpiece, the Biot number, and the dimensionless liquidus temperature were presented and discussed. The results of heat flow calculations involving both the surface heat treating of a substrate with a square laser beam and the gas tungsten-arc full-penetration welding of 5052 and 2014 aluminum alloys were presented using the dimensionless variables introduced in the present study.