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In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

This paper aims to incorporate a numerical investigation of unsteady flow of nano-fluid near the boundary wall and heat transmission over a flat sheet in porous media under the assumption that sheet is continuously stretching. A comprehensive study is accomplished to probe the impacts of different physical parameters on heat transmission and fluid flow.

The problem is designed mathematically by using Navier–Stokes equations and corresponding equations are transmuted into non-dimensional form, which are reduced to local non-similarity equations. Implicit finite difference scheme is used to attain a non-similar solution for values of similarity variable ranging in [0,1]

The reduced Nusselt number is a decreasing function of each dimensionless number, while the reduced Sherwood number is an increasing function of each considered value of parameters Pr, Sc, Nb and Nt.

Motivated by the industrial, technological and scientific importance, the objective of this study is to discuss the unsteady flow generated by linear stretching of the surface in Nano-fluid in a porous medium. However, the investigation of unsteady boundary layer flow and heat transfer of a Nano-fluid past a stretching surface immersed in a porous medium has not been discussed yet. Furthermore, finite difference scheme is used to solve the problem, and authenticate results are achieved which are in good agreement with published work.

The purpose of this paper is to investigate the steady 2D buoyancy effects on MHD flow over a permeable stretching sheet through porous medium in the presence of suction/injection.

Similarity transformations are employed to transform the governing partial differential equations into ordinary differential equations. The transformed equations are then solved numerically by a shooting technique.

The working fluid is examined for several sundry parameters graphically and in tabular form. It is observed that with an increase in magnetic field and permeability of porous parameter, velocity profile decreases while temperature and concentration enhances. Stretching sheet parameter reduces velocity, temperature and concentration, whereas it increases skin friction factor, Nusselt number and Sherwood number.

Till now no numerical studies are reported on the effects of heat source and thermal radiation on MHD flow over a permeable stretching sheet embedded in porous medium in the presence of chemical reaction.

The purpose of this paper is to study the comparative analysis between three hybrid nanofluids flow past a permeable stretching surface in a porous medium with thermal radiation. Uniform magnetic field is applied together with heat source and sink. Three set of different hybrid nanofluids with water as a base fluid having suspension of Copper-Aluminum Oxide (Cu−Al2O3), Silver-Aluminum Oxide (Ag−Al2O3) and Copper-Silver (Cu−Ag) nanoparticles are considered. The Marangoni boundary condition is applied.

The governing model of the flow is solved by Runga–Kutta fourth-order method with shooting technique, using appropriate similarity transformations. Temperature and velocity field are explained by the figures for many flow pertinent parameters.

Almost same behavior is observed for all the parameters presented in this analysis for the three set of hybrid nanofluids. For increased mass transfer wall parameter ( fw) and Prandtl Number (Pr), heat transfer rate cuts down for all three sets of hybrid nanofluids, and reverse effect is seen for radiation parameter (R), and heat source/sink parameter ( δ).

The thermal conductivity of hybrid nanofluids is much larger than the conventional fluids; thus, heat transfer efficiency can be improved with these fluids and its implications can be seen in the fields of biomedical, microelectronics, thin-film stretching, lubrication, refrigeration, etc.

The current analysis is to optimize heat transfer of three different radiative hybrid nanofluids ( Cu−Al2O3/H2O, Ag−Al2O3/H2O and Cu−Ag/H2O) over stretching surface after applying heat source/sink with Marangoni convection. To the best of the authors’ knowledge, this work is new and never published before.

The purpose of this paper is to study the Soret and Dufour effects in three-dimensional flow induced by an exponential stretching surface in a porous medium.

Series solutions are developed.

The authors observed that the temperature profile and thermal boundary layer thickness are enhanced when the authors increase the values of Dufour number. It is also examined that the concentration field and its associated boundary layer thickness are higher for the larger values of Soret number.

Such investigation is not available in the literature.

This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of suction/blowing, volumetric heat source/sink and velocity ratio parameter will be studied in this analysis.

The modeled governing equations for the assumed problem are dimensional nonlinear partial differential equations in nature. To reduce these equations, non-similar transformations are used to get the dimensionless nonlinear partial differential equations. Then, quasi-linearization technique is used to linearize these non-dimensional nonlinear partial differential equations. Finally, an implicit finite difference scheme is used to discretize the resulting equations.

The physical explanations are provided for the variations of various non-dimensional governing parameters over the velocity and temperature profiles. Also, the effects of these dimensionless parameters on skin friction coefficient and heat transfer rate are scrutinized in a manner which highlights their physical interpretation. The detailed discussion exhibits the fact that the streamwise co-ordinate velocity ratio parameter, partial slip parameter and the thermal jump parameter have significant influence over the flow and thermal fields.

This work has not been reported in the literature to the authors’ best of knowledge.

The purpose of this paper is to analyze hydromagnetic flow between two horizontal plates in a rotating system. The bottom plate is a stretching sheet and the top one is a solid porous plate. Heat transfer in an electrically conducting fluid bounded by two parallel plates is also studied in the presence of viscous dissipation.

Differential Transformation Method (DTM) is used to obtain a complete analytic solution for the velocity and temperature fields and the effects of different governing parameters on these fields are discussed through the graphs.

The obtained results showed that by adding a magnetic field to this system, transverse velocity component reduces between the two plates. Also as the Prandtl number increases, in presence of viscous dissipation, the temperature between the two plates enhances while an opposite behavior is observed when the viscous dissipation is negligible.

The equations of conservation of mass, momentum and energy are reduced to a non‐linear ordinary differential equations system. Differential Transformation Method is utilized to approximate the solution for velocity and temperature profiles.

The purpose of this paper is to investigate the Newtonian heating and slip effect on mixed convective flow near a stagnation point in a porous medium with thermal radiation in the presence of magnetohydrodynamic (MHD), heat generation/absorption and chemical reaction.

The governing nonlinear coupled equations are converted into ordinary differential equations by similarity transformation. These equations are solved numerically using a Runge–Kutta–Fehlberg method with shooting technique and analytically using the homotopy analysis method (HAM).

The effects of different parameters on the fluid flow and heat transfer are investigated. It is found that the velocity and temperature profiles increase on an increase in the Biot number. The velocity and concentration profiles increase on decreasing the chemical reaction parameter.

This paper is helpful to the engineers and scientists in the field of thermal and manufacturing engineering.

The two-dimensional boundary layer flow over a vertical plate with slip and convective boundary conditions near the stagnation-point is analysed in the presence of magnetic field, radiation and heat generation/absorption. This paper is helpful to the engineers and scientists in the field of thermal and manufacturing engineering.

The purpose of this paper is to examine the influence of magnetic field on Williamson nanofluid embedded in a porous medium in the presence of non-uniform heat source/sink, chemical reaction and thermal radiation effects.

The governing physical problem is presented using the traditional Navier–Stokes theory. Consequential system of equations is transformed into a set of non-linear ordinary differential equations by means of scaling group of transformation, which are solved using the Runge–Kutta–Fehlberg method.

The working fluid is examined for several sundry parameters graphically and in a tabular form. It is noticed that with an increase in Eckert number, there is an increase in velocity and temperature along with a decrease in shear stress and heat transfer rate.

A good agreement of the present results has been observed by comparing with the existing literature results.

The purpose of this paper, is to study the MHD double-diffusive natural convection of a nanofluid over a linearly stretching sheet using the Buongiorno model.

The transport equations are transformed into coupled similarity equations. The numerical self-similar solutions are compared with the literature for the special case of pure fluid flow and found to be in good agreement. Graphical results are presented to illustrate the effects of various fluid flow, heat transfer and nano concentration parameters for both assisting and opposing flows.

It is found that the heat transfer rate increases as nanoparticles and salt are suspended in water. It is also found that dual solutions exist for the stretching parameter.

First paper on this model for stretching sheet.