Analytical solutions for transient temperature of semi-infinite body subjected to 3-D moving heat sources

The analytical solution for a double-ellipsoidal power density moving heal source in a semi-infinite body with conduction-only consideration has been derived. The solution has been obtained by integrating the instant point he at source throughout the volume of the ellipsoidal one. Very good agreement between the predicted transient temperatures and the measured ones at vari ous points in bead-on-plate specimens has been obtained. The predicted geom etry of the weld pool is also in good agreement with the measured one. This may pave the way for the future applications of this solution in the probl ems such as microstructure modeling, thermal stress analysis, residual stre ss/distortions and welding process simulation.