Modified Darcy law-based MHD simulation of reactive viscoelastic nanofluids on an inclined plane using a single-phase model subject to an exothermic reaction

The flow of fluids (including viscoelastic fluids) down an incline finds vast application, say, in geophysical flows, manufacturing and industrial processes, food and chemical processing and rheometry. The current study presents a detailed numerical investigation of the flow of viscoelastic fluid-based nanofluids (VFBN) down an inclined plane. The Giesekus constitutive model is employed to describe the fluid viscoelasticity. The flow of the VFBN is considered under various conditions. A transverse magnetic field of constant strength is applied to the flow field. The flow is assumed to be non-isothermal and subject to exothermic reactions. The non-isothermal nature of the flow entails the use of temperature-dependent viscosity and thermal conductivity as well as convective cooling at the free surface. The VFBN flows through a porous medium, which is uniformly distributed down the inclined plane. The flow is described by a coupled system of nonlinear partial differential equations derived from the conservation laws of mass, momentum and energy as well as from the Giesekus viscoelastic constitutive model. The governing equations are reduced to non-dimensional forms and solved using robust and efficient semi-implicit finite difference methods (SIFDM). A comprehensive qualitative study examines the influence of key dimensionless parameters on the flow velocity and fluid temperature. Key findings show that VFBN are less susceptible to thermal runaway phenomena than corresponding Newtonian fluid-based nanofluids (NFBN). We also find that the porous media strength (as with the magnetic field strength) is associated with flow retardation.