A speculative investigation has been presented to explore the salient features of magnetohydrodynamic (MHD) Prandtl-Eyring nanofluid over stretching surface. Effects of Navier slip and convective boundary conditions are included in flow configuration. The effects of higher order chemical reactions along with Nield conditions are assumed in the concentration of nanoparticles. The mathematical modelling of the said flow problem accomplished the nonlinear partial differential equations along with appropriate boundary conditions. The nondimensional form of governing problem is yielded with the aid of similarity variables. The pivotal physical quantities, ie, velocity, temperature, and concentration (in nondimensional form), within boundary layer region are computed with shooting technique. The physical significance of flow controlling parameters on velocity, temperature, and concentration is illustrated through graphs. Additionally, thermophysical aspects of fluid near stretching surface (wall friction factor, wall heat flux, and wall mass flux) are instantiated graphically. A comparison of the current solution with reported data is established to validate the accuracy of adapted procedure. It is observed that the current findings agree with existing data. This led to confidence on adapted numerical procedure.

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In this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes elementQ~1/Q0is utilized which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. The discretized systems of nonlinear equations are treated by using the Newton method and the inner linear subproablems are solved by the direct solver UMFPACK. A qualitative comparison is done with the results reported in the literature. In addition to these comparisons, some new reference data for the kinetic energy is generated. All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.

Solution of non-similarity boundary-layer flows over a porous wedge is studied. The free stream velocity U w (x) ∼ a x m and the injection velocity V w (x) ∼ b x n at the surface are considered, which result in the corresponding non-similarity boundary-layer flows governed by a nonlinear partial differential equation. An analytic technique for strongly nonlinear problems, namely, the homotopy analysis method (HAM), is employed to obtain the series solutions of the non-similarity boundary-layer flows over a porous wedge. An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of the physical parameters on the skin friction coefficient and displacement thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.