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We study a problem describing the motion of an incompressible, nonisothermaland non-Newtonian uid, taking into account the heat convection term. Thenovelty here is that uid viscosity depends on the temperature, the velocity ofthe uid, and also of the deformation tensor, but not explicitly. The boundaryconditions take into account the slip phenomenon on a part of the boundary ofthe domain. By using the notion of pseudo-monotone operators and xed pointTheorem we prove an existence result of its weak solution.

Existence result for a strongly coupled problem with heat convection term and Tresca's law