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The purpose of this paper is to examine the unsteady pressure-driven flow of a reactive third-grade non-Newtonian fluid in a channel filled with a porous medium. The flow is subjected to buoyancy, suction/injection asymmetrical and convective boundary conditions.

The authors assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The authors also assume unidirectional suction injection flow of uniform strength across the channel. The flow system is modeled via coupled non-linear partial differential equations derived from conservation laws of physics. The flow velocity and temperature are obtained by solving the governing equations numerically using semi-implicit finite difference methods.

The authors present the results graphically and draw qualitative and quantitative observations and conclusions with respect to various parameters embedded in the problem. In particular the authors make observations regarding the effects of bouyancy, convective boundary conditions, suction/injection, non-Newtonian character and reaction strength on the flow velocity, temperature, wall shear stress and wall heat transfer.

The combined fluid dynamical, porous media and heat transfer effects investigated in this paper have to the authors’ knowledge not been studied. Such fluid dynamical problems find important application in petroleum recovery.

This paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.

The governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.

The analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.

In practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.

Although many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a micropolar fluid over an inclined plate. Convective thermal boundary condition and suction/injection effects are considered at the surface of an inclined plate.

The convection along with nonlinear Boussinesq approximation (i.e. quadratic convection or nonlinear convection) and usual boundary layer assumptions is employed in the mathematical formulation. Highly coupled nonlinear governing equations are tackled by a combined local non-similarity and successive linearization techniques.

The behavior of various pertinent parameters on the fluid flow characteristics is conferred through graphs and it reveals that the qualitative behaviors of velocity, temperature, skin friction and heat transfer rates of a micropolar fluid are similar for Biot number and radiation parameters. The suction/injection and activation energy parameters increase the concentration of the micropolar fluid within the boundary layer, while the chemical reaction parameter reduces the concentration in the same region. Further, this quadratic convection shows a strong influence on the fluid flow characteristics and then the impact of pertinent parameters is more prominent on the physical quantities, compared therewith results of the linear convection.

This kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures and solar collectors which are operated at moderate to very high temperatures.

This attempt is a unique contribution to the establishment of both micropolar fluid and activation energy. This kind of study even in the absence of quadratic convection is not yet noted.

The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects. Effects of various fluid parameters such as suction/injection, viscous dissipation, magnetic parameter and heat source/sink on velocity and temperature profiles are numerically analyzed. Moreover, numerically investigated on skin-friction and heat transfer coefficients when suction/injection occur.

The governing coupled partial differential equations are transformed to dimensionless form using non-similarity transformations. The non-dimensional partial differential equations are linearized by quasi-linearization technique and solved by varga's algorithm with numerical finite difference scheme on a non-uniform mesh.

The computation results are presented in terms of temperature, heat transfer and skin friction coefficients; these are useful for determining surface heat requirements. It was found that, in finite difference scheme for non-uniform mesh with quasi-linearization technique method gives smoothness of solution compared to finite difference scheme for uniform mesh, and this evidence is graphically represented in Figure 2.

The impacts of viscous dissipation (Ec) and magnetic parameter (Ha) on temperature profiles, skin friction and heat transfer are analyzed, which determine the heat generation/absorption to ensure the MHD flow of the laminar boundary layer on irregular boundary over a diverging channel.

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.

This study aims to expose the flow phenomena and entropy generation during a; magnetohydrodynamic (MHD) Poiseuille flow of water-based nanofluids (NFs) in a porous channel subject to hydrodynamic slip and convective heating boundary conditions. The flow caused by the uniform pressure; gradient between infinite parallel plates is considered steady and fully developed. The nanoparticles; namely, copper, alumina and titanium oxide are taken with pure water as the base fluid. Viscous dissipation and Joule heating impacts are also incorporated in this investigation.

The reduced governing equations are solved analytically in closed form. The physical insights of noteworthy parameters on the important flow quantities are demonstrated through graphs and analyzed elaborately. The thermodynamic analysis is performed by calculating entropy generation; rate and Bejan number. A graphical comparison between solutions corresponding to NFs and regular fluid in the channel is also provided.

The analysis of the results divulges that entropy generation minimization can be achieved by an appropriate combination of the geometrical and physical parameters of thermomechanical systems. It is reported that ascent in magnetic parameter number declines the velocity profiles, while the inverse pattern is witnessed with augmentation in hydrodynamic slip parameters. The temperature dissemination declines with the growth of Biot numbers. It is perceived that the entropy generation rate lessens with an upgrade in magnetic parameter, whereas the reverse trend of Bejan number is perceived with expansion in magnetic parameter and Biot number. The important contribution of the result is that the entropy generation rate is controlled with an appropriate composition of thermo-physical parameter values. Moreover, in the presence of a magnetic field and suction/injection at the channel walls, the shear stresses at the channel walls are reduced about two times.

In various industrial applications, minimizing entropy generation plays a significant role. Miniaturization of entropy is the utilization of the energy of thermal devices such as micro heat exchangers, micromixers, micropumps and cooling microelectromechanical devices.

An attentive review of the literature discloses that quite a few studies have been conducted on entropy generation analysis of a fully developed MHD Poiseuille flow of NFs through a permeable channel subject to the velocity slip and convective heating conditions at the walls.

The purpose of this paper is to study the Blasius flat plate with viscous dissipation in the presence of suction or injection effects in the boundary layer of a viscoelastic fluid.

The governing partial differential equations are derived as a first order ordinary differential equation using similarity (Blasius) variables. Velocity profiles, temperature profiles, skin friction parameters, and heat transfer parameters are computed numerically for various values of the viscoelastic parameter K, the suction or injection parameter f _w , the Prandtl number Pr, the Eckert number Ec, and the moving parameter λ.

The effects of the viscoelastic, moving, and suction/injection parameters on the skin friction and heat transfer of the flat plate are studied. The effects of these parameters on the velocity and temperature profiles are also presented for 0≤Pr≤3.

To the best of the authors' knowledge, this important classical problem has not been studied before for the case of a viscoelastic fluid. Thus, the results are original and new for this type of fluid.

The purpose of this paper is to study the effect of non‐uniform double slot suction (injection) into a steady laminar boundary layer flow over a yawed cylinder when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Non‐similar solutions have been obtained from the starting point of the streamwise co‐ordinate to the exact point of separation.

The governing equations are tackled by the implicit finite difference scheme in combination with the quasi‐linearization technique. Quasi‐linear technique can be viewed as a generalization of the Newton‐Raphson approximation technique in functional space. An iterative sequence of linear equations is carefully constructed to approximate the nonlinear equations for achieving quadratic convergence and monotonicity. The quadratic convergence and monotonicity are unique characteristics of the quasilinear implicit finite difference scheme, which makes this scheme superior to built‐in iteration of upwind or finite amplitude techniques.

The results indicate that the separation can be delayed by non‐uniform double slot suction and also by moving the slot downstream. However, the effect of non‐uniform double slot injection is just the opposite. Yaw angle has very little affect on the location of the point of separation.

This analysis is useful in understanding many boundary layer problems of practical importance for undersea applications, for example, in suppressing recirculating bubbles and controlling transition and/or separation of the boundary layer over submerged bodies.

The purpose of this paper is to consider a two-dimensional unsteady Casson magneto-nanfluid flow over an inclined plate embedded in a porous medium. The novelty of the present study is to investigate the effects of Soret–Dufour on unsteady magneto-nanofluid flow.

Appropriate similarity transformations are used to convert the governing non-linear partial differential equations into coupled non-linear dimensionless partial differential equations. The transformed equations are then solved using spectral relaxation method.

The effects of controlling parameters on flow profiles is discussed and depicted with the aid of graphs. Results show that as the non-Newtonian Casson nanofluid parameter increases, the fluid velocity decreases. It is found that the Soret parameter enhance the temperature profile, while Dufour parameter decreases the concentration profile close to the wall.

The novelty of this paper is to consider the combined effects of both Soret and Dufour on unsteady Casson magneto-nanofluid flow. The present model is in an inclined plate embedded in a porous medium which to the best of our knowledge has not been considered in the past. The applied magnetic field gives rise to an opposing force which slows the motion of the fluid. A newly developed spectral method known as spectral relaxation method (SRM) is used in solving the modeled equations. SRM is an iterative method that employ the Gauss–Seidel approach in solving both linear and non-linear differential equations. SRM is found to be effective and accurate.

The purpose of this paper is to consider the influence of slip flow and thermal jump and to investigate its effects on unsteady mixed convection along an exponentially stretching surface. It is also intended to explore the influence of suction/injection and volumetric heat source/sink on the fluid flow.

The assumed problem is modelled into governing equations which are dimensional non-linear partial differential equations in nature. To obtain solutions, initially the governing equations were made non-dimensional by the suitable non-similar transformations. Then, the dimensionless non-linear partial differential equations are linearized with the aid of Quasilinearization technique. The so obtained equations are discretized by the implicit finite difference method.

The detailed analysis of the considered problem displays that the non-similarity variable reduces the velocity and temperature profiles. For higher values of mixed convection parameter, the magnitude of velocity profile as well as the Nusselt number increase. The unsteady variable diminishes the fluid flow. The higher values of velocity ratio parameter reduce the skin-friction coefficient. Further, the magnitude of skin-friction coefficient and heat transfer rate are to minimize for increasing values of partial slip and thermal jump parameters, respectively. Volumetric heat source and injection parameters are to rise the flow behavior within the momentum and thermal boundary layers significantly.

To the best of authors’ knowledge, no such investigation has been found in the literature.