Bingham viscoplastic flow over a stretching sheet with second-order velocity slip and inclined magnetic effects

Purpose The study aims to investigate a steady, two-dimensional, laminar, and incompressible flow of a bi-viscous Bingham hybrid nanofluid past a porous surface in the presence of an inclined magnetic field, thermal radiation and Xue thermal effect with first- and second-order velocity slips. Design/methodology/approach An effective and higher-order numerical scheme spectral quasi-linearisation method has been used to solve the resulting system of dimensionless non-linear differential equations with various forms of Dirichlet and Robin-type boundary conditions. Findings A rise in the bi-viscous Bingham parameter decreased the velocity of the fluid, while it increased with the impact of the secondary slip parameter (λ2). The temperature profile increased with an increase in the magnetic parameter (M) and with the primary slip parameter (λ1). The convergence range for the normed residuals of flow profiles was of the order of 10−2 to 10−8. The increase in radiation parameter (Rd) resulted in an increase of Nusselt number, while the heat transfer rates followed the following order: regular fluid < nanofluid<hybrid nanofluid. Strong wall adherences resulted in early separation at low λ1 values, while with stronger slip, the separation gets suppressed in the solid–fluid interface. It was observed that the contours flatten and smoothens with the absence of distinct separation regions with increasing M values. Entropy increased with Rd and Schmidt number (Sc) parameters. Originality/value The present study analyses the first- and second-order velocity slip effects for the bi-viscous Bingham fluid flow with variable thermal diffusion coefficient in the presence of the Xue model of thermal conductivity and using a spectral approach to obtain the numerical solutions of the governing dimensionless equations, which have not been addressed in the literature. This attests to the novelty of the study.