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 Ω ε is transformed into another problem defined in Ω ε without the parameter Ω ε ( ε 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.

Modelling, Control Methods and Applications of Chaotic Oscillators

“…Yazid et al [25] studied the asymptotic behavior of weak solutions of non-isothermal fow of Herschel-Bulkley fuid in a layer in associated with a nonlinear stationary, nonisothermal, and incompressible model. After formulating the problem statement and variational formulation, the authors derive the estimates for the velocity feld and the pressure independently of the parameter.…”