Asymptotic analysis of 3D Bingham flows with Tresca slip and thermal effects

We investigate the asymptotic behavior of incompressible thermally coupled Bingham flows in a three-dimensional thin domain Ωε, subject to Tresca slip conditions on part of the boundary and Dirichlet conditions elsewhere. Using a variational inequality framework and a rescaling of the thin domain onto a fixed reference domain, we establish the existence and uniqueness of weak solutions together with uniform ε-independent estimates. By combining compactness arguments and asymptotic analysis as ε→0, we derive the effective limiting model and identify the asymptotic form of the Tresca slip condition. In particular, we prove that the pressure becomes independent of the transverse variable and obtain a Reynolds-type equation governing the limit flow.