Study of multilayer flow of a bi-viscous Bingham fluid sandwiched between hybrid nanofluid in a vertical slab with nonlinear Boussinesq approximation

Bi-viscosity Bingham plastic fluids are used to understand the rheological characteristics of pigment–oil suspensions, polymeric gels, emulsions, heavy oil, etc. In many industrial and engineering problems involving high-temperature situation, a linear density-temperature variation is inadequate describe convective heat transport. Therefore, nonlinear flow bi-viscous fluid (BVBF) through three layers in vertical slab studied. The two outer oil-based hybrid nanofluid intermediate layer BVBF considered. thermal buoyancy force governed by Boussinesq approximation. Continuity flux, velocity, shear stress, temperature imposed on interfaces. governing equations derived from Navier–Stokes equation, conservation energy, mass for layers. multi-point (four-point) boundary value problem solved using differential transform method (DTM). Converging DTM solutions obtained, they validated. entropy equation Bejan number were also analyzed. It established that density–temperature leads significant improvement magnitude velocity profiles due increased force, as result, drag walls gets reduced. reduced decreasing volume fraction nanoparticles. Furthermore, convection mixed give rise an advanced rate transport thereby enhanced situation.