P. Ehrhard et al., TEMPERATURE AND PENETRATION DEPTH PREDICTION FOR A 3-DIMENSIONAL FIELD BELOW A MOVING HEAT-SOURCE, International journal of heat and mass transfer, 36(16), 1993, pp. 3997-4008
Predictions for both penetration depth of a specific isotherm and for
peak temperatures achieved during processing of brick-type workpieces
are inferred. A rectangular heated area is thereby travelled at consta
nt speed across the top surface of the workpiece. The model accounts f
or the finite cross-track extents of the workpiece as well as for a re
alistic heat transfer towards an underlying table. The model is strict
ly valid for conduction-dominated processes. New results are obtained
for cases where, due to geometry of workpiece and heated area, truly t
hree-dimensional heat flow situations are present. This is particularl
y relevant, when the bottom plane's heat losses or the limiting side p
lanes have a considerable influence on the heat flow. Moreover, it is
explored which parameter ranges allow reasonable predictions by using
simplified models, as given by several previous studies.