Study of the stationary solution of non-isothermal Bingham flow with nonlinear boundary conditions in a thin domain

We study in this manuscript the asymptotic behavior of an incompressible Bingham fluid in a three-dimensional thin domain with Tresca friction law coupled with A nonlinear stationary, non-isothermal and incompressible model, Firstly, we demonstrate the results for the existence and uniqueness of the weak solution. Then we reformulate the problem in fixed domain, and we also then we show the estimates for the velocity field , the pressure and the temperature. Finally we obtain the limit problem with the specific Reynolds equation and prove the uniqueness of the limit.