  The steady thermocapillary droplet migration in a uniform temperature
gradient combined with a radiation energy source at large Reynolds and
Marangoni numbers is studied. To reach a terminal quasi-steady process, the
magnitude of the radiation energy source is required to preserve the
conservative integral thermal flux across the surface. Under the quasi-steady
state assumption, an analytical result for the steady thermocapillary migration
of a droplet at large Reynolds and Marangoni numbers is derived by using the
method of matched asymptotic expansions. It is shown that the thermocapillary
droplet migration speed increases as Marangoni number increases, while the
radiation energy source with the sine square dependence is provided.
