Well-posedness of an instationary non-Newtonian flows under conduction heat term with numerical applications

The current work deals with visco-plastic flows with thermal effects. The fluid motion is governed by the quasistatic Norton-Hoff operator coupled with the instationary heat equation involving the conduction term. The fluid׳s viscosity is modeled by the exponential non-linear Arrhenius law. The main novelties of this contribution are to establish the well-posedness of the coupled system using an adequate fixed point and to supply some numerical examples to illustrate the influence of the conductivity on the evolution of the flow.