Asymptotic behavior of solutions for a non-isothermal coupled problem with nonlinear boundary conditions in a thin domain

Abstract

This manuscript analyzes the asymptotic behavior of a non-isothermal, incompressible Herschel–Bulkley fluid in a thin domain governed by a steady nonlinear system with Tresca friction. We study the limit as the domain thickness tends to zero, prove strong convergence of velocity, temperature, and pressure, and derive the corresponding Reynolds equation.