Steady axi-symmetrical thermocapillary motion of a short melting column

This paper deals with the steady axi-symmetric thermo-capillary motion in a short meltingcolumn.with the assumptions that the Marangoni number M<<1, the Reynolds number Re<<1 andthe capillary number C<<1, at the leading order, the solutions of the problem are obtained inthe form of series. For two kinds of typical cases, symmetric and anti-symmetric distributionof air temperature, the numerical calculations are made. The results describe the effect ofendwalls on thermo-capillary flow.