THE FLOW PATTERN IN A LIQUID LAYER AND THE SPECTRUM OF THE BOUNDARY-VALUE PROBLEM WHEN THE SURFACE-TENSION DEPENDS NONLINEARLY ON THE TEMPERATURE

The flow of a liquid in a plane channel on the bottom of which a speci fied temperature distribution is maintained while the free surface is thermally isolated is considered. The surface tension of the liquid de pends quadratically on the temperature. The system of Navier-Stokes an d heat conduction equations possess a self-similar solution which lead s to the non-linear eigenvalue problem of finding the flow temperature fields in the channel. The spectrum of this problem is investigated a nalytically for low Marangoni numbers (the second approximation) and n umerically in the limiting case of an ideally heat conducting liquid f or any Marangoni number. The pattern of the thermocapillary flow in th e layer is analysed as a function of the parameter values. The non-uni queness of the solution, which is typical for problems of this kind, i s established. The results are compared with those obtained previously in the first approximation with respect to the Marangoni number. (C) 1997 Elsevier Science Ltd.