The purpose of the research is to inquire the outcomes of viscous and ohmic dissipation on the MHD flow in porous media in the region of suction and injection. A flow model of nonlinear ODEs with assisting boundary conditions is tackled with the help of computational software by using various standard techniques. The effects of relevant parameters on the concentration, thermal, and velocity distribution are illustrated graphically; also, the skin friction coefficient and flow rates of heat and mass transfer are calculated and shown in a tabular way. An analysis of the consequences proves that the flow field is effectively appreciable by injection and suction. Comparison with the already published work is made and found to be in good agreement.

This paper presents the comparative analysis of MHD boundary layer fluid flow around a linearly stretching surface in the presence of radiative heat flux, heat generation/absorption, thermophoresis velocity, and chemical reaction effects in a permeable surface. The governing equations are highly nonlinear PDEs which are converted into coupled ODEs with the help of dimensionless variables and solved by using semianalytical techniques. The numerical and graphical outcomes are observed and presented via tables and graphs. Also, the Nusselt and Sherwood numbers and skin friction coefficient are illustrated by tables. On observation of heat and mass transfer, it was noticed that Maxwell fluid dominates the other fluids such as Newtonian, Williamson, and Casson fluid due to high rate of thermal conductivity, and hence, Maxwell fluid has better tendency for heat and mass transfer than other Newtonian and non-Newtonian fluids.

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.

Due to potential implications, boundary layer analysis of chemically reacting Carreau nanofluid has been carried out to examine flow properties of ferromagnetic fluid over a stretched sheet in the presence of magnetic dipole, for shear thinning and shear thickening fluids. Furthermore, the transportation of heat under thermal radiation, heat generation, the Brownian, and thermophoresis aspects has been evaluated. The dimensionless form of highly nonlinear coupled partial differential equations is obtained using suitable similarity transformations and then solved numerically by well-known bvp 4 c technique via MATLAB based on the shooting method. The outcomes of physical quantities are presented through graphs and numerical benchmarks. Moreover, outcomes for skin fraction, Sherwood and Nusselt numbers for velocity, concentration, and temperature are also estimated in this study. The present study reveals that the concentration and thermal boundary layer thicknesses were higher for shear thinning n < 1 fluid when compared with shear thickening n > 1 fluids, but reverse effects are to be observed for momentum boundary layer thickness.

This article addresses the numerical exploration of steady and 2D flow of MHD Carreau nanofluid filled with motile microorganisms over three different geometries, i.e., plate, wedge, and stagnation point of a flat plate. The influence of magnetic field, viscous dissipation, thermophoresis, and Brownian motion is considered for both cases, i.e., shear thinning and shear thickening. A set of relevant similarity transformations are utilized to obtain dimensionless form of governing coupled nonlinear partial differential equations (PDEs). The transformed system of ordinary differential equations (ODEs) is then numerically solved by bvp4c via MATLAB based on shooting technique and Runge–Kutta–Fehlberg (RKF) scheme via MAPLE. Also, a numerical analysis has been made for skin friction factor, heat, and mass transfer rates. Results elucidate that all the profiles except velocity show decreasing behavior for higher values of magnetic field parameter. Among all three flow geometries for both shear thinning and shear thickening cases, the flow over a plate has lesser skin friction factor. The nanoparticle concentration and density of motile microorganism decrease in both the shear thinning and shear thickening cases, for increasing values of Brownian motion (Nb), but reverse trend is observed for rising values of thermophoresis parameter (Nt). Furthermore, it is observed that, as we increase the values of suction/injection parameter (S), the velocity of fluid increases but decreases the fluid temperature, concentration of mass and density of motile organisms over a plate, wedge, and stagnation point of a flat plate. Also, we observed that shear thinning nanofluid has higher rate of heat, mass, and motile microorganisms mass transfers than shear thickening fluid. Both shear thinning and thickening nanofluid have a low rate of heat/mass and gyrotactic microorganisms mass transfer over plate among wedge and stagnation point flow.