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Computer programs have been developed for solving cumbersome heat-transfer equations relating to moving heat sources encountered in welding operations. The objective is to provide the welding engineer and designer with a reference that will guide them in making practical use of heat-transfer equations that describe the thermal history at weld heat-affected zones. Solutions for four types of problems are now available: ( 1 ) thermal mapping to determine the temperature hill enveloping the welding heat source on a semiinfinite plate; ( 2 ) determining peak temperatures at some distance from the weld centerline or from the bond line; ( 3 ) determining the surface peak temperature at an edge of a plate parallel to the weld; ( 4 ) determining the peak temperature on the bottom side of plates having partial-penetration welds. ( auth )