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This article reviews the classical models for the pseudo-steady-state temperature distribution of the thermal field around moving point and line sources. These include thick- and thin-plate models and the medium-thick-plate model. The analytical solutions to the differential heat flow equation under conditions applicable to fusion welding are provided. The article also provides an overview of the factors affecting heat flow in a real welding situation using the analytical modeling approach because this makes it possible to derive relatively simple equations that provide the required background for an understanding of the temperature-time pattern.

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Ole Runar Myhr, Øystein Grong, Factors Influencing Heat Flow in Fusion Welding, Welding Fundamentals and Processes, Vol 6A, ASM Handbook, Edited By T. Lienert, T. Siewert, S. Babu, V. Acoff, ASM International, 2011, p 67–81,

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