Thermocapillary evacuation of liquid leaking from a porous wall (Q1317673)

Without deforming the free boundary, the thermocapillary force can result in fluid motion with rotation of the streamlines through \(90^ \circ\), outwardly recalling Hiemenz flow. This corresponds to heating of the surface in accordance with a parabolic law and is described by the exact solution of the system of Navier-Stokes and energy equations. We consider the thermocapillary flow of a liquid on a horizontal porous wall -- the extension of the preceding problem to the case of a layer of finite thickness. The liquid leaks through a permeable base, and the temperature distribution at the free boundary is assumed to be symmetric. Under certain conditions this problem can serve as a model of the uniform motion of the fusion front when the surface of a body is nonuniformly heated.