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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.

This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach.

The flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations.

Findings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force.

The novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

The purpose of this paper is to address the combined effects of thermal radiation and chemical reaction on steady MHD mixed convective heat and mass transfer flow past a vertical surface under the influence of Joule and viscous dissipation.

The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique.

With the help of graphs, the effects of the various important parameters entering into the problem on the dimensionless velocity, dimensionless temperature and dimensionless concentration fields within the boundary layer are discussed. The authors noticed that the velocity increases with an increase in the porosity parameter. An increase in the Prandtl number Pr, decreases the velocity and the temperature field. An increase in the radiation parameter, decreases the velocity and the temperature field. Also the effects of the pertinent parameters on the skin-friction coefficient and rates of heat and mass transfer in terms of the Nusselt and Sherwood numbers are presented numerically in tabular form.

To the best of the authors’ knowledge, recent this work has not been finished by any other researchers.

The purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.

To achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.

The major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.

Further research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.

The geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.

This study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

The purpose of this paper is to analyze the thermal-diffusion and diffusion-thermo effects on magnetohydrodynamics (MHD) natural convective flow through porous medium in a rotating system with ramped temperature.

Using the non-dimensional variables, the flow governing equations along with corresponding initial and boundary conditions have been transformed into non-dimensional form. These non-dimensional partial differential equations are solved by using finite element method. This method is powerful and stable. It provides excellent convergence and flexibility in providing solutions.

The effects of Soret number, Dufour number, rotation parameter, magnetic parameter, Hall current parameter, permeability parameter, thermal Grashof number, solutal Grashof number, Prandtl number, thermal radiation parameter, heat absorption parameter, Schmidt number, chemical reaction parameter and time on the fluid velocities, temperature and concentration are represented graphically in a significant way and the influence of pertinent flow governing parameters on the skin frictions and Nusselt number are presented in tabular form. On the other hand, a comparison for validation of the numerical code with previously published work is performed, and an excellent agreement is observed for the limited case existing literature.

A very useful source of information for researchers on the subject of MHD flow through porous medium in a rotating system with ramped temperature.

The problem is moderately original, as it contains many effects like thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects and chemical reaction.

The purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a linearly stretching cylinder under the influence of velocity slip, chemical reaction and thermal radiation. The Brownian motion, thermophoresis and activation energy are assimilated in this nanofluid model. Convective boundary conditions on heat and mass transfer are considered. The physical model may have diverse applications in several areas of technology underlying thermohydrodynamics including supercritical fluid extraction, refrigeration, ink-jet printing and so on.

The dimensional governing equations are nondimensionalized by using appropriate similarity variables. The resulting boundary value problem is converted into initial value problem using the method of superposition and numerically computed by employing well-known fourth-order Runge–Kutta–Fehlberg approach along with shooting technique (RKF4SM). The quantitative impacts of emerging physical parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation rate and Bejan number are presented graphically and in tabular form, and the salient features are comprehensively discussed.

From graphical outcomes, it is concluded that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with rising radiation parameter and thermal Biot number. Nanoparticle concentration is reported in decreasing form with activation energy parameter. Entropy is found to be an increasing function of magnetic field, Brownian motion and material parameters. The entropy is less generated for shear-thinning fluid compared to shear-thickening as well as Newtonian fluids in the system.

Till now no study has been documented to explore the impact of binary chemical reaction with Arrhenius activation energy on entropy generation in an MHD boundary layer flow of non-Newtonian Sisko nanofluid over a linear stretching cylinder with velocity slip and convective boundary conditions.

The purpose of this paper is a numerical analysis of natural convection in a square porous cavity filled with a water-based magnetic fluid of geothermal viscosity under the effect of inclined uniform magnetic field.

The domain of interest includes the square porous cavity filled with a water-based magnetic fluid (W40). Horizontal walls are supposed to be adiabatic, while right vertical wall is kept at constant low temperature and left vertical wall is kept at constant high temperature. An inclined uniform magnetic field affects the fluid flow and heat transfer inside the cavity. The viscosity of the working fluid is proportional to the linearly decreasing function of depth (vertical coordinate) and inversely proportional to the linear function of temperature. It is assumed in the analysis that the flow is laminar. The fluid is Newtonian and the Boussinesq approximation is valid. The governing equations have been discretized using the finite difference method with the uniform grid. Simulations have been carried out for different values of the Rayleigh number, Hartmann number, Darcy number, magnetic field inclination angle and viscosity variation parameters.

It has been revealed that an increase in the viscosity parameters leads to the heat transfer enhancement and convective flow intensification. At the same time, this intensification is more essential for high values of the Rayleigh number.

The originality of this work is to analyze MHD natural convection in a square porous cavity filled with a water-based magnetic fluid of geothermal viscosity. The results would benefit scientists and engineers to become familiar with the analysis of convective heat and mass transfer in nanofluids, and the way to predict the properties of nanofluid convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

This paper aims to report the investigation of over heat and mass transfer of convective Casson fluid flow over a moving vertical plate with nonlinear thermal radiation and convective boundary conditions.

The main partial differential equations of the flow, heat and concentration profiles were rehabilitated to nonlinear ordinary differential equations by using an appropriate similarity transformation. The resultant nonlinear ordinary differential equations (ODEs) are solved numerically applying fourth-order Runge–Kutta shooting technique and functions of ODE45 from MATLAB.

The effect of convective heat transfer, buoyancy ratio parameter, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number over velocity, temperature and concentration profiles, equivalent to abundant somatic parameters were graphically scrutinized.

All the results are very promising and further there is got good agreement of results when compared with earlier published results at limiting conditions.

The purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite vertical cylinder with heat transfer

The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. The fluid is a water-based nanofluid containing nanoparticles of copper. The Brinkman model for dynamic viscosity and Maxwell–Garnett model for thermal conductivity are used. The governing boundary layer equations are written according to The Tiwari–Das nanofluid model. A robust, well-tested, implicit finite difference method of Crank–Nicolson type, which is unconditionally stable and convergent, is used to find the numerical solutions of the problem. The velocity and temperature profiles are studied for significant physical parameters such as the magnetic parameter, nanoparticles volume fraction and the thermal Grashof number Gr. The local skin-friction coefficient and the Nusselt number are also analysed and presented graphically.

The present computations have shown that an increase in the values of either magnetic parameter M or nanoparticle volume fraction decreases the local skin-friction coefficient, whereas the opposite effect is observed for thermal Grashof number Gr. The local Nusselt number increases with a rise in Gr and ϕ values. But an increase in M reduces the local Nusselt number.

This paper is relatively original and presents numerical investigation of transient two-dimensional laminar boundary layer free convective flow of a nanofluid over a moving semi-infinite vertical cylinder in the presence of an applied magnetic field. The present study is of immediate application to all those processes which are highly affected by heat enhancement concept and a magnetic field. Further the present study is relevant to nanofluid materials processing, chemical engineering coating operations exploiting nanomaterials and others.

The purpose of this paper is to review previous research studies on mathematical models for entropy generation in the magnetohydrodynamics (MHD) flow of nanofluids. In addition, the influence of various parameters on the velocity profiles, temperature profiles and entropy generation was studied. Furthermore, the numerical methods used to solve the model equations were summarized. The underlying purpose was to understand the research gap and develop a research agenda.

This paper reviews 141 journal articles published between 2010 and 2022 on topics related to mathematical models used to assess the impacts of various parameters on the entropy generation, heat transfer and velocity of the MHD flow of nanofluids.

This review clarifies the application of entropy generation mathematical models, identifies areas for future research and provides necessary information for future research in the development of efficient thermodynamic systems. It is hoped that this review paper can provide a basis for further research on the irreversibility of nanofluids flowing through different channels in the development of efficient thermodynamic systems.

Entropy generation analysis and minimization constitute effective approaches for improving the performance of thermodynamic systems. A comprehensive review of the effects of various parameters on entropy generation was performed in this study.