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The purpose of this paper is to present both an analytical and a numerical analysis of the unsteady magnetohydrodynamic (MHD) rear stagnation-point flow over off-centred deformable surfaces.

The numerical MATLAB solver bvp4c suitable for routine boundary value problem is used for the set of ordinary differential equations reduced from the governing partial differential equations.

Multiple solutions are found for particular eigenvalues. The physical solution is computed by the help of a linear stability analysis. The authors have succeeded in discovering the second solutions, and it is suggested that these solutions are unstable and not physically realisable in practice. The current findings add to a growing body of literature on MHD stagnation-point flow problems. It is also found that the governing parameters have different effects on the flow characteristics.

Even though problems of steady MHD flows have been extensively studied for stagnation-point flows, limited findings can be found on the unsteady MHD rear stagnation-point flow over off-centred deformable surfaces.

The originality of this work is the application of a magnetic field on a time-dependent MHD rear stagnation-point flow over off-centred deformable surfaces.

To explore the fusion of dust particles and of polymers in a viscous liquid is the main purpose of this article. Newtonian fluid as a base fluid is considered and the mutual presence of polymers and dusty bodies is investigated. It discusses the steady laminar flow and heat transportation of a polymeric dusty liquid induced by a uniformly heated, penetrable and stretchable surface inside the boundary layer.

The mathematical system incorporates separate equations of energy and momentum for dusty bodies and for fluid. The classical Oldroyd-B model is chosen for exploring polymer presence. For the fluid phase, this model adds another stress to the conservation law of momentum. Appropriate similarity variables are introduced to transform the system of partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs). The problem is solved by introducing a numerical iterative procedure which turned out to be fastly converging.

Expeditious changes inside the boundary layer cause polymers to deform. No changes outside the boundary layer are noticed on account of polymer stretching. The dependence of heat transfer rate and skin friction on the parameter of polymer concentration and Weissenberg number is analyzed and displayed graphically against interaction parameters for temperature and velocity, dust particles’ mass concentration, Eckert and Prandtl numbers. Combining effects of polymers and dust particles cause skin friction to decrease and heat transfer rate to increase. Increasing values of interaction parameter for velocity, dust particles’ mass concentration and Eckert number reduces the drag coefficient and local Nusselt number. On the other hand, the Prandtl number and interaction parameter of temperature magnify the heat flux at the wall.

This article studies the infinite extensibility of polymers. FENE and FENE-P models can be used to investigate the polymer presence in dusty fluids in the future.

In this article, the authors’ aim is to study the combined presence of polymers and dusty bodies. Keeping the existing literature in view, this type of fusion is not studied yet. Polymer inclusion in a viscous dusty fluid is studied and the behavior of fluid flow and heat transportation is investigated within the boundary layer over a permeable linearly stretching sheet.