Asymptotic Behavior of Weak Solutions of Nonisothermal Flow of Herschel–Bulkley Fluid to Free Boundary

Abstract

In this manuscript, the behavior of a Herschel–Bulkley fluid has been discussed in a thin layer in ${ℝ}^3$ associated with a nonlinear stationary, nonisothermal, and incompressible model. Furthermore, the limit problem has been considered, and the studied problem in ${\mathrm{\Omega }}^{\epsilon }$ is transformed into another problem defined in ${\mathrm{\Omega }}^{\epsilon }$ without the parameter ${\mathrm{\Omega }}^{\epsilon }$ ( $\epsilon$ is the parameter representing the thickness of the layer tend to zero is studied). We also investigated the convergence of the unknowns which are the velocity, pressure, and the temperature of the fluid. In addition, we established the limit problem and the specific Reynolds equation.