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The study investigates the unsteady free convective two-dimensional MHD flow past a vertical porous plate with convective surface boundary condition in porous medium in slip flow regime under the action of variable suction velocity. Analytical solutions are obtained for the system using perturbation technique that converts non-linear coupled governing partial differential equations into non-dimensional form of ordinary differential equations. Effects of variable suction velocity, rarefactions parameter and heat change parameter are analysed and discussed graphically for various values of effective physical parameter such as Grasshof number, Magnetic field parameter, Prandtl number, Permeability parameter on fluid velocity and temperature, skin friction, and heat transfer.

The paper investigates two-dimensional, steady, nonlinear laminar boundary layer heat and mass transfer MHD flow past a stretching porous surface embedded in a porous medium under the action of internal heat generation with the consideration of viscous and joules heat dissipation in the presence of a transverse magnetic field. The two-dimensional governing equations are solved by using MATLAB built in bvp4c solver technique for different values of physical parameters. The numerical values of various flow parameters such as velocity, temperature, concentration are calculated numerically and analysed graphically for various values of the non-dimensional physical parameters of the problem followed by conclusions. The study concludes opposite behaviour of transverse and longitudinal velocity under the action of suction velocity in addition to the effects of heat source on fluid velocities, temperature and concentration.

The paper examines solution for a two-dimensional steady, viscous, heat dissipation, incompressible hydro-magnetic free convective flow past a uniformly moving vertical porous plate immersed in a porous material in the presence of the Soret effect, Dofour effect and Chemical reaction. A constant magnetic field is directed into the fluid area perpendicular to the plate. The MATLAB built-in bvp4c solver approach is used to solve the governing non-dimensional equations. The discussion of the current issue focuses mostly on the impacts of thermal diffusion, magnetic field, thermal radiation, Grashof number, Soret number, Dufour number, and chemical reaction. It is observed that the Soret number improves fluid temperature. In addition, the fluid's temperature, concentration, and velocity all drop as the magnetic field parameter rises. Although the heat dissipation caused by the medium's porosity is usually disregarded in convective MHD flow simulations, it is considered in this work.

An analysis is carried out to study laminar MHD convection flow of a second order dusty viscoelastic fluid in porous medium through an inclined parallel plate channel in the presence of molecular diffusivity. The plates are maintained at two different temperatures that decay with time. The study is done under the consideration that viscosity and density of the fluid are variable to the extent that it causes stratification and joule heating effect in the process of the flow. The purpose of the study is to examine how stratification and joule heating affect the flow in relation to the physical quantities namely, Stratification factor, Hartmann number, Viscoelastic coefficient, Joule heating parameter, Prandtl number, Eckert number, Schmidt number and Porosity of the medium etc. The non-dimensional governing equations are solved analytically by using regular perturbation technique, and the graphs are plotted using MATLAB programming language. The mathematical expressions for fluid and particle velocity, fluid temperature, fluid concentration, skin friction for fluid and particle, flow flux for fluid and particle, Nusselt number, Sherwood number at the plates are evaluated and their nature of variations for different numerical values of physical parameters are shown graphically, discussed and conclusions are drawn.

The paper studies effect of induced magnetic field on laminar convection flow of a viscous electrically conducting incompressible fluid between two parallel porous plates at constant temperature gradient in presence of a uniform inclined magnetic field. An angle (θ) is formed with the vertical line by applying a magnetic field in that direction and field is strong enough to induce another field along the line of flow. Using the proper similarity transformations, the flow equations are converted into ordinary differential equations, which are then numerically solved by using MATLAB's bvp4c solver. Plotting of the graphs allows one to examine the effects of several critical parameters such as Hartmann number, Darcy number, Magnetic Reynolds number, Prandtl number, and Field inclination on velocity field, induced magnetic field, temperature field at the plates. The acquired results demonstrate that the flow system is effectively influenced by the field inclination, the magnetic parameter, and the plate porosity. The rise in field inclination leads to an increase in magnetic drag force.

The paper examines heat and mass transfer in MHD convective flow across a vertical porous plate in presence of radiation, heat sink, and dissipation of heat. A strong magnetic field is applied perpendicular to the plate and directed into the fluid area. The governing non-dimensional equations are solved using MATLAB built-in bvp4c solver technique. With the use of mathematical software, the findings are computed, and the effect of the various non-dimensional parameters entering into the problem on the velocity, temperature and concentration profiles are displayed in graphical formats. It has been noted that the application of the magnetic field slows down fluid velocity. Additionally, both the thermal radiation effect and the Prandtl number are fully applicable to the fluid temperature. It is significant to notice that the heat sink dramatically reduces fluid temperature and fluid velocity. The current work is utilized in many real life applications, such as chemical engineering, industrial processes, a system may contain multiple components, each of whose concentrations varies from one point to the next in a number of different circumstances.

A numerical study of the heat and mass transfer of a micropolar nanofluid flow over a stretching sheet embedded in a porous medium is carried out in this investigation. The main objective of this work is to investigate the influence of Arrhenius activation energy, heat source and viscous dissipation on the fluid velocity, microrotation, temperature, and concentration distribution. The equations governing the flow are transformed into ordinary differential equations using appropriate similarity transformations and solved numerically using bvp4c solver in MATLAB. Graphs are plotted to study the influences of important parameters such as magnetic parameter, porosity parameter, thermophoresis parameter, Brownian motion parameter, activation energy parameter and Lewis number on velocity, microrotation, temperature and concentration distribution. The graphical representation explores that the velocity of the liquid diminishes for increasing values of magnetic parameter, whereas the angular velocity increases with it. This study also reports that an enhancement of temperature and concentration distribution is observed for the higher values of activation energy parameter, whereas the Lewis number shows the opposite behavior. The effects of various pertinent parameters are exposed realistically on skin friction coefficient, Nusselt and Sherwood numbers via tables. A comparison with previous work is conducted, and the results show good agreement.