Flow driven by a hot wire immersed in a horizontal liquid layer

The thermocapillary or buoyancy-driven flow induced by a hot wire placed beneath the free surface of an horizontal liquid layer is determined. The temperature distribution induced by the wire is obtained in a conductive state by the method of images. The upper surface is assumed adiabatic, whereas the lower surface is taken either conductive or adiabatic. Then, the flow driven by the horizontal thermal gradient and the associated deformation of the free surface are determined, considering the action of either thermocapillary or buoyancy effects. In the latter case, a simplified expression of the temperature distribution is used in order to obtain analytical results. Depending on whether thermocapillary or buoyancy effects are considered, the deflection of the free surface above the wire is found to be either concave or convex.