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This paper aims to focus on the mathematical modeling of magnetohydrodynamic natural convective boundary layer flow of nanofluids past a stationary and moving inclined porous plate considering temperature and concentration gradients with suction effects.

The transformed non-dimensional and coupled governing partial differential equations are solved numerically using the finite element method.

The obtained numerical results for physical governing parameters on the velocity, temperature and concentration distributions are exemplified graphically and presented quantitatively. The boundary layer thickness increased with the increasing values of Soret, Dufour and Grashof numbers, while the thickness of boundary layer decreased with increasing values of suction for both stationary and moving plate cases. The primary and secondary velocity profiles are decreasing with an angle of inclination for moving plate and inclination has no significant effect for the stationary plate. An increase of the Soret number and Dufour number tend to increase the heat and mass transfer, while an increase of suction reduces the heat and mass transfer.

The problem is an important contribution to the field of nanofluid science and technology and is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids. This study is relatively original in nanofluids.

In recent years, nanofluids are being widely used in many thermal systems because of their higher thermal conductivity and heat transfer rate. The higher thermal conductivity depends on many parameters such as size, shape and volume and the Brownian motion and thermophoresis of added nanoparticles. The purpose of this paper is to analyze the influence of the Brownian motion and thermophoresis on natural convection heat and mass transfer boundary layer flow of nanofluids over a vertical cone with radiation.

Using similarity variables, the non-linear partial differential equations, which represent momentum, energy and diffusion, are transformed into ordinary differential equations. The transformed conservation equations are solved numerically subject to the boundary conditions by using versatile, extensively validated, variational finite-element method.

The sway of significant parameters such as magnetic field (M), buoyancy ratio parameter (Nr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), thermal radiation (R), Lewis number (Le) and chemical reaction parameter (Cr) on velocity, temperature and concentration evaluation in the boundary layer region is examined in detail. The results are compared with previously published work and are found to be in agreement. The velocity distributions are reduced, while temperature and concentration profiles elevate with a higher (M). With the improving values of (R), the velocity and temperature sketches improve, while concentration distributions are lowered in the boundary layer region. The temperature and concentration profiles are elevated in the boundary layer region for higher values of (Nt). With the increasing values of (Nb), temperature profiles are enhanced, whereas concentration profiles get depreciated in the flow region.

In recent years, it has been found that magneto-nanofluids are significant in many areas of science and technology. It has applications in optical modulators, magnetooptical wavelength filters, tunable optical fiber filters and optical switches. Magnetic nanoparticles are especially useful in biomedicine, sink float separation, cancer therapy, etc. Specific biomedical applications involving nanofluids include hyperthermia, magnetic cell separation, drug delivery and contrast enhancement in magnetic resonance imaging.

To the best of the authors’ knowledge, no studies have assessed the impact of the two slip effects, namely, Brownian motion and thermophoresis, on the natural convection of electrically conducted heat and mass transfer to the nanofluid boundary layer flow over a vertical cone in the presence of radiation and chemical reaction; therefore, this problem has been addressed in this study. Comparison of the results of this study’s with those of previously published work was found to be in good agreement.

The purpose of this paper is to analyze the influence of curvature on the transport of low-density lipoprotein (LDL) through a curved artery and concentration boundary layer characteristics numerically.

By using a projection method based on the second-order central difference discretization, the authors solve the set of governing equations, which consists of Navier–Stokes, continuity and species transport. The effects of initial straight length, as well as the curvature and wall shear stress (WSS) on LDL transport in a curved artery are established in this paper.

The obtained numerical results imply that the LDL concentration boundary layer thickness decreases in the outer part of the curved artery and increases in the inner part for both with or without initial straight length. The effect of Reynolds number on the concentration distribution in a curved artery with initial straight length is more pronounced than that on a fully curved artery, although an opposite trend was seen for the curvature ratio. The maximum surface LDL concentration is related to the regions with minimum WSS in the inner part of the curved artery, which has more potential the formation of atherosclerosis.

The authors present a comprehensive concentration distribution of LDL in the concentration boundary layer of the curved artery. The authors also characterize and predict the influence of curvature on the formation and development of atherosclerosis within the arterial wall.

In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation.

The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables.

Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile.

The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken.

Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration.

An implicit finite difference scheme in combination with the quasilinearisation technique is employed to obtain non‐similar solutions of the governing boundary layer equations for momentum, temperature and concentration fields.

The numerical results are reported here to display the effects of mixed convection parameter, ratio of buoyancy forces, surface mass transfer (suction and injection), the ratio of free stream velocity to the composite reference velocity, Prandtl number and Schmidt number on velocity, temperature and concentration profiles as well as on skin friction, Nusselt number and Sherwood number.

Thermophysical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate density changes, and to couple in this way the temperature and concentration fields to the flow field. The concentration of diffusing species is assumed to be very small in comparison with other chemical species far away from the surface. Hence the Soret and Dufour effects are neglected. The stretching sheet is assumed to be subject to a power‐law wall temperature as well as to a power‐law wall concentration, in a parallel free stream.

Convective heat and mass transfer over a vertical stretching sheet in a parallel stream is very important for various design of technological process are hot rolling, wire drawing, glass‐fiber paper production, both metal and polymer sheets, for instance, in cooling of an infinite metallic plate in a cooling bath, the boundary layer along material handling conveyors, etc.

The paper studies the combined effects of thermal and mass diffusion over a vertical stretching sheet with surface mass transfer.

The steady two-dimensional laminar boundary layer flow, heat and mass transfer over a flat plate with convective surface heat flux was considered. The governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations and then solved numerically by Runge–Kutta method with the most efficient shooting technique. Then, the effect of variable viscosity and variable thermal conductivity on the fluid flow with thermal radiation effects and viscous dissipation was studied. Velocity, temperature and concentration profiles respectively were plotted for various values of pertinent parameters. It was found that the momentum slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the momentum slip.

Numerical Solution is applied to find the solution of the boundary value problem.

Velocity, heat transfer analysis is done with comparing earlier results for some standard cases.

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The purpose of this paper is to study the flow, heat and mass transfer of MHD Casson nanofluid due to an inclined stretching sheet using similarity transformation, the governing PDE’S equations of flow, heat and mass transfer are converted into ODE’S. The resulting non-linear ODE’S are solved numerically using an implicit finite difference method, which is known as Kellor-box method. The effects of various governing parameters on velocity, temperature and concentration are plotted for both Newtonian and non-Newtonian cases. The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters. It is noticed that the effect of angle of inclination enhances the temperature and concentration profile whereas velocity decreases. The temperature decreases due to the increase in the parametric values of Pr and Gr due to thickening in the boundary layer.

Numerical method is applied to find the results.

Flow and heat transfer analysis w.r.t various flow and temperature are analyzed for different values of the physical parameters.

The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters.

The study of the boundary layer flow, heat and mass transfer is important due to its applications in industries and many manufacturing processes such as aerodynamic extrusion of plastic sheets and cooling of metallic sheets in a cooling bath.

Here in this paper the authors have investigated the MHD boundary layer flow of a Casson nanofluid over an inclined stretching sheet along with the Newtonian nanofluid as a limited.

Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field.

The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included.

The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables.

Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration.

The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment.

This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream.

The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

The purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.

The resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.

An interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.

Very little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.

The governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.

Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.

Study of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.