Abstract
The problem of Marangoni convection in a horizontal fluid layer with internal heat generation is solved using the sequential gradient-restoration algorithm (SGRA) developed for optimal control problems. A general discussion of the method is given. The effects of the temperature-dependent surface tension and viscosity are studied by examining the critical Marangoni numbers and wave numbers. The validity of the method is established by comparison with the work in the literature for the case of a linear temperature profile across the fluid layer.
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