Free Boundary Problemin Norton-Hoff Steady Flow with Thermal Effects

We consider the free boundary identification problem in a steady viscoplastic flow. The fluid motion is governed by the incompressible Norton-Hoff model coupled with the heat equation. The viscosity of the fluid is modeled by the Arrhenius law .Our point of view is to treat the problem as a shape sensitivity of a cost functional formulated on the free boundary and governed by the Norton-Hoff state. One of the main results of this paper is to provide a shape sensitivity result to the considered cost functional.