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Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials’ manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve the understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, this study aims to develop a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet.

This study developed a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant-strength magnetic field is applied transversely to the stretching flow plane. The Buongiorno nanofluid model is used to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo–Christov) model is used to simulate thermal conduction effects, of which the Fourier model is a special case when thermal relaxation effects are neglected.

The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth-order Runge–Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters, e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nanoparticle concentration distributions, is investigated.

A strong elevation in temperature accompanies an increase in Brownian motion parameter, whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nanoparticle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter, whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values, i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

To consider simultaneous heat and mass transfer by mixed convection for a non‐Newtonian power‐law fluid from a permeable vertical plate embedded in a fluid‐saturated porous medium in the presence of suction or injection and heat generation or absorption effects.

The problem is formulated in terms of non‐similar equations. These equations are solved numerically by an efficient implicit, iterative, finite‐difference method.

It was found that as the buoyancy ratio was increased, both the local Nusselt and Sherwood numbers increased in the whole range of free and mixed convection regime while they remained constant for the forced‐convection regime. However, they decreased and then increased forming dips as the mixed‐convection parameter was increased from the free‐convection limit to the forced‐convection limit for both Newtonian and dilatant fluid situations.

The problem is limited to slow flow of non‐Newtonian power‐law fluids in porous media. Future research may consider inertia effects of porous media for relatively higher velocity flows.

A very useful source of information for researchers on the subject of non‐Newtonian fluids in porous media.

This paper illustrates simultaneous heat and mass transfer in porous media for power‐law fluids with heat generation or absorption effects.

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

• It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

• It guarantees the convergence of series solutions for nonlinear problems.

• It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, u_o(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

By defining a vector u → = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , … , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

where:

Applying L⁻¹ on both sides of Equation (6), we get:

In this way, we obtain u_m for m ⩾ 1, at mth-order, we have:

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P₁) and (P₂), respectively. Moreover, temperature Θ(Ω₁) enhances for greater values of Brownian motion parameter (N_b), non-uniform heat source/sink parameter (B₁) and thermophoresis factor (N_t). Reverse behavior of concentration ϒ(Ω₁) field is remarked in view of (N_b) and (N_t). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

The purpose of this paper is to investigate the immiscible two-layer heat fluid flows in the presence of the electric double layer (EDL) and magnetic field. The effects of EDL, magnetic field and the viscous dissipative term on fluid velocity and temperature, as well as the important physical quantities, are examined and discussed.

The upper and lower regions in a horizontal microchannel with one layer being filled with a nanofluid and the other with a viscous Newtonian fluid. The nanofluid flow in the lower layer is described by the Buongiorno’s nanofluid model with passively controlled model at the boundaries. An appropriate set of non-dimensional quantities are used to simplify the nonlinear systems. The resulting coupled nonlinear equations are solved by using homotopy analysis method.

The present work demonstrates that increasing the EDL thickness and Hartmann number can restrain the fluid flow. The Brinkmann number has a significant role in the enhancement of heat transfer. It is also identified that the influence of EDL effects on microflow cannot be ignored.

The effects of viscous dissipation involved in the heat transfer process and the body force because of the EDL and the magnetic field are considered in the thermal energy and momentum equations for both regions. The detailed derivation procedure of the analytical solution for electrostatic potential is provided. The analytical solutions can lead to improved understanding of the complex microfluidic systems.

Nonlinear mixed-convective entropy optimized the flow of hyperbolic-tangent nanofluid (HTN) with magnetohydrodynamics (MHD) process is considered over a vertical slendering surface. The impression of activation energy is incorporated in the modeling with the significance of nonlinear radiation, dissipative-function, heat generation/consumption connection and Joule heating. Research in this area has practical applications in the design of efficient heat exchangers, thermal management systems or nanomaterial-based devices.

Suitable set of variables is introduced to transform the PDEs (Partial differential equations) system into required ODEs (Ordinary differential equations) system. The transformed ODEs system is then solved numerically via finite difference method. Graphical artworks are made to predict the control of applicable transport parameters on surface entropy, Bejan number, Sherwood number, skin-friction, Nusselt number, temperature, velocity and concentration fields.

It is noticed from present numerical examination that Bejan number aggravates for improved estimations of concentration-difference parameter a_2, Eckert number E_c, thermal ratio parameter ?_w and radiation parameter R_d, whereas surface entropy condenses for flow performance index n, temperature-difference parameter a_1, thermodiffusion parameter N_t and mixed convection parameter ?. Sherwood number is enriched with the amplification of pedesis-motion parameter N_b, while opposite development is perceived for thermodiffusion parameter. Lastly, outcomes are matched with formerly published data to authenticate the present numerical investigation.

To the best of the authors' knowledge, no investigation has been reported yet that explains the entropic behavior with activation energy in the flowing of hyperbolic-tangent mixed-convective nanomaterial due to a vertical slendering surface.

This paper aims to deal with the study of heat and mass transfer on double-diffusive three-dimensional hydromagnetic boundary layer flow of an electrically conducting Casson nanofluid over a stretching surface. The combined effects of nonlinear thermal radiation, magnetic field, buoyancy forces, thermophoresis and Brownian motion are taken into consideration with convective boundary conditions.

Similarity transformations are used to reduce the governing partial differential equations into a set of nonlinear ordinary differential equations. The reduced equations were numerically solved using Runge–Kutta–Fehlberg fourth-fifth-order method along with shooting technique.

The impact of several existing physical parameters such as Casson parameter, mixed convection parameter, regular buoyancy ratio parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, temperature ratio parameter on velocity, temperature, solutal and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that the solutal component increases for Dufour Lewis number, whereas it decreases for nanofluid Lewis number. Moreover, velocity profiles decrease for Casson parameter, while the Nusselt number increases for Biot number, radiation and temperature ratio parameter.

This paper is a new work related to three-dimensional double-diffusive flow of Casson nanofluid with buoyancy and nonlinear thermal radiation effect.

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

The authors believe that the presented results are original and have not been published elsewhere.

This paper aims to address the problem of double-diffusive magnetohydrodynamics (MHD) non-Darcy convective flow of heat and mass transfer over a stretching sheet embedded in a thermally-stratified porous medium. The controlling parameters such as chemical reaction parameter, permeability parameter, etc., are extensively discussed and illustrated in this paper.

With the help of appropriate similarity variables, the governing partial differential equations are converted into ordinary differential equations. The transformed equations are solved using the spectral homotopy analysis method (SHAM). SHAM is a numerical method, which uses Chebyshev pseudospectral and homotopy analysis method in solving science and engineering problems.

The effects of all controlling parameters are presented using graphical representations. The results revealed that the applied magnetic field in the transverse direction to the flow gives rise to a resistive force called Lorentz. This force tends to reduce the flow of an electrically conducting fluid in the problem of heat and mass transfer. As a result, the fluid velocity reduces in the boundary layer. Also, the suction increases the velocity, temperature, and concentration of the fluid, respectively. The present results can be used in complex problems dealing with double-diffusive MHD non-Darcy convective flow of heat and mass transfer.

The uniqueness of this paper is the examination of double-diffusive MHD non-Darcy convective flow of heat and mass transfer. It is considered over a stretching sheet embedded in a thermally-stratified porous medium. To the best of the knowledge, a problem of this type has not been considered in the past. A novel method called SHAM is used to solve this modelled problem. The novelty of this method is its accuracy and fastness in computation.

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 work is to study the flow of mixed convection and mass transfer of a steady laminar boundary layer about an isothermal vertical flat plate embedded in a non‐Darcian porous medium in the presence of chemical reaction and viscous dissipation effects.

The governing partial differential equations are converted into ordinary differential equations by similarity transformation, which are solved numerically by employing the fourth‐order Runge‐Kutta integration scheme with Newton‐Raphson shooting technique.

It was found that the local Nusselt number was predicted to decrease as either of the chemical reaction parameter or the Eckert number increased. On the other hand, the local Sherwood number was predicted to increase as a result of increasing either of the chemical reaction parameter or the Eckert number. Also, in the absence of viscous dissipation, both the local Nusselt and Sherwood numbers increased as the mixed convection increased.

The paper illustrates chemical reaction and viscous dissipation effects on Darcy‐Forchheimer mixed convection in a fluid saturated porous media.