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

Abstract

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