A multivariate response surface methodology approach to explore the consequence of the diffusion-thermo and thermal-diffusion in off-centered stagnation flow toward a rotating disk

Numerical exploration of MHD unsteady flow of THNF passing through a moving cylinder with Soret and Dufour effects

The mathematical model of the two-dimensional steady stagnation-point flow over a stretching or shrinking sheet of nanofluid in the presence of the Soret and Dufour effects and of second-order slip at the boundary was considered in this paper. The partial differential equations were transformed into the ordinary differential equations by applying a suitable similarity transformation. The numerical results were obtained by using bvp4c codes in Matlab. The skin friction coefficient, heat transfer coefficient, mass transfer coefficient, as well as the velocity, temperature, and concentration profiles were presented graphically for different values of slip parameters, Soret effect, Dufour effect, Brownian motion parameter, and thermophoresis parameter. A dual solution was obtained in this present paper. The presence of the slip parameters (first- and second-order slip parameters) was found to expand the range of solutions. However, the presence of the slip parameters led to a decrease in the skin friction coefficient, whereas the heat transfer coefficient increased. Besides that, a larger Soret effect (smallest Dufour effect) led to the decrement of the heat transfer coefficient. The effects of the Brownian motion and thermophoresis parameters on the heat transfer coefficient were also studied in this paper. A stability analysis was performed in this paper to verify the stability of the solutions obtained.

Purpose The purpose of this study is to explore the impact of Joule heating, slip conditions, Dufour and Soret effects on three-dimensional magneto-convection of nanoliquid over a rotating surface in the existence of thermal radiation, viscous dissipation and internal heat generation/absorption. Design/methodology/approach The considered physical system is modelled by a set of partial differential equations (PDEs) with conditions at surface. Then, the nonlinear PDEs are altered into a system of ordinary differential equations and they are solved numerically by the Runge−Kutta−Fehlberg method. Plotting the collected velocity, temperature and solute concentration characteristics allows one to see how relevant parameters affect the results. Calculations are made for skin friction and the rate of heat and mass transfer. Findings The outcomes are portrayed in the form of tables and graphs with a wide range of parameter involved in the study. It is observed that the local thermal energy transfer rate enriches on increasing the value of both thermal and solute slips. The solutal slip parameter suppresses the solute transport rate and thermal slip supports the solute transport. Practical implications Combining the Dufour and Soret effects is used in oil reservoirs, binary alloy solidification and isotope separation in mixtures of gases. Heat exchangers, nuclear reactors and thermal engineering can all benefit from the usage of nanofluid with Joule heating. Social implications This study is mainly useful for thermal sciences and chemical engineering. Originality/value The investigation of the effects of slip circumstances and Joule heating on magnetohydrodynamic rotating nanoliquid stream with thermal radiation and cross-diffusion makes this work unique. The discoveries produced are valuable and distinctive, and they have applications in many areas of thermal science and technology.

Chemical reaction, Dufour and Soret effects on the stability of magnetohydrodynamic blood flow conveying magnetic nanoparticle in presence of thermal radiation: A biomedical application

Endothermic/exothermic chemical reaction applications are examined in several technical and scientific domains, most notably heat and mass transmission. The main focus of the bioconvection study is on enhancing mass species and energy, which has significance for the civil, electrical, and mechanical engineering sectors. Due to above mentioned applications, the current study investigates how bioconvection and exothermic/endothermic chemical reactions affect the flow of nanofluids via a horizontal deforming circular cone. Additionally, the current study investigates the steady incompressible Casson nanofluid flow in three dimensions around a horizontal deforming circular cone. The nonlinear partial differential equations (PDEs) are modified into ordinary differential equations (ODEs). The modified ODEs are resolved by employing the shooting technique and Runge–Kutta–Fehlberg fourth–fifth-order (RKF-45) method. Several useful and related characteristics for connected profiles are represented graphically. Additionally, the engineering factors are also studied. The main conclusions of this investigation indicate that an upsurge in the activation energy constraint causes the temperature profile to improve in the case of an endothermic chemical reaction and to drop in the case of an exothermic chemical reaction. The bioconvection profile reduces with an enhancement in the bioconvection Lewis and Peclet numbers. An improvement in solid volume fraction and the bioconvection Lewis number causes an enhancement in the density number of motile microorganisms. From nanofluid to base fluid changing the values of the porous parameter D a = (1, 2, 3), heat transmission rate is observed from 24.23%, 121.66%, and 32.53%, respectively, in the case of λ 1 * = + 1 and 297.52%, 1041.30%, and 272.86%, respectively, in the case of λ 1 * = − 1 .

The results of this article can be useful in science and technology advancement, such as nanofluidics, micro mixing and energy conversion. The purpose of this article is to examine the impacts of nanoparticle shape on Al2O3-water nanofluid and heat transfer over a non-linear radically stretching sheet in the existence of magnetic field and thermal radiation. The different shapes of Al2O3 nanoparticles that have under contemplation are column, sphere, hexahedron, tetrahedron, and lamina. The governing partial differential equations (PDEs) of the problem are regenerated into set of non-linear ordinary differential equations (ODEs) by using appropriate similarity transformation. The bvp4c program has used to solve the obtained non-linear ordinary differential equation (ODEs). The Nusselt number for all shapes of Al2O3 nanoparticle shapes in pure water with is presented in graphical form. It has reported that the heat transfer augmentation in lamina shapes nanoparticles is more than other shapes of nanoparticle. The relation of thermal boundary layer with shapes of nanoparticles, solid volume fraction, magnetic field and thermal radiation has also presented with the help of graphical representation. It is also demonstrated that lamina shape nanoparticles have showed large temperature distribution than other shapes of nanoparticles.

ABSTRACTThe Lie group transformation method is applied for solving the problem of mixed convection flow with mass transfer over a permeable stretching surface with Soret and Dufour effects. The application of Lie group method reduces the number of independent variables by one and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. Further, the reduced non-linear ordinary differential equations are solved numerically by using the shooting method. The effects of various parameters governing the flow and heat transfer are shown through graphs and discussed. Our aim is to detect new similarity variables which transform our system of partial differential equations to a system of ordinary differential equations. In this work a special attention is given to investigate the effect of the Soret and Dufour numbers on the velocity, temperature and concentration fields above the sheet.

An analysis of two-dimensional steady magneto-hydrodynamic free convection flow of an electrically conducting, viscous, incompressible fluid past an inclined stretching porous plate in the presence of a uniform magnetic field and thermal radiation with heat generation is made. Both the Dufour and Soret effects are considered for a hydrogen-air mixture as the non-chemically reacting fluid pair. The equations governing the flow, temperature and concentration fields are reduced to a system of joined non-linear ordinary differential equations by similarity transformation. Non-linear differential equations are integrated numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Finally the significance of physical parameters which are of engineering interest are examined both in graphical and tabular form.

This paper deals with the examination effect of Dufour and Soret Effect on MHD heat and mass transfer with radiative heat flux in a liquid over a rotating dick. The problem is solved by HAM (Homotopy Analysis Method). The arrangement of Non-Linear Partial Differential Equations (PDEs) which administer the stream, heat and mass exchange qualities is changed into Ordinary Differential Equations (ODEs). It is discovered from the current exploration that Dufour and radiation impacts cause diminishments in the liquid temperature. The effect of suction diminishes the speed, temperature, what’s more, focus profiles essentially in the limit layer.

PurposeThe purpose of this study is to investigate the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction.Design/methodology/approachThe similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Then, they are solved numerically by the fourth-order Runge–Kutta–Gill method along with the shooting technique and the Newton–Raphson method. In addition, the ordinary differential equations are also analytically solved by the homotopy analysis method.FindingsThe results for dimensionless velocity, temperature, solutal concentration and nanoparticle volume fraction profiles, as well as local skin friction coefficient and local Nusselt and local Sherwood numbers are presented through the plots for various combinations of pertinent parameters involved in the study. The heat transfer rate increases on increasing the Soret parameter and it decreases on increasing the Dufour parameter. The mass transfer behaves oppositely to heat transfer.Practical implicationIn engineering applications, a wedge is used to hold objects in place, such as engine parts in the gate valves. A gate valve is the valve that opens by lifting a wedge-shaped disc to control the timing and quantity of fluid flow into an engine.Originality/valueNo such investigation is available in literature, and therefore, the results obtained are novel.

This research work is aimed at examining the significance of viscous dissipation, magnetic field alongside thermal radiation on the flow of Casson fluid. The fluid flow was considered in the presence of gyrotactic microorganisms and nanoparticles. The physics of the problem is governed with partial differential equations (PDEs). The set of PDEs are changed to ordinary differential equations (ODEs) by utilizing an appropriate similarity variables. To examine the pertinent flow parameters, a numerical approach called spectral relaxation method (SRM) was employed. This SRM approach employs the basic Gauss-seidel method to decouple and descritize the set of differential equations. The choice of this approach is due to its consistency and accuracy. The viscous dissipation parameter (Ec) was found to enhance fluid temperature, velocity and boundary layers (thermal and momentum boundary layer). The strong opposition of magnetic parameter give rise to lorenz force which drags the fluid flow within the boundary layer. The nanoparticles was found to bare great effect on the gyrotactic microorganisms.

This research investigates the influence of thermodiffusion (Soret effect) and diffusion-thermo (Dufour effect) on transient Magneto-Hydro-Dynamic (MHD) free convective flow adjacent to a heated, inclined plate within a porous medium. The analysis incorporates thermal radiation as a key heat transfer mechanism, accounting for time-dependent variations in both velocity and temperature distributions. The porous structure introduces hydraulic resistance, altering fluid motion and thermal transport properties, while the plate's inclination modifies buoyancy-driven convection patterns. The applied magnetic field further complicates the dynamics through Lorentz force interactions. By addressing the coupled Soret and Dufour effects— frequently overlooked in basic models—the study enhances understanding of multispecies heat and mass transfer. The governing nonlinear partial differential equations are solved numerically via the finite difference method.Graphical results demonstrate how critical parameters affect velocity, temperature, and concentration profiles. This computational framework elucidates the complex interdependencies among electromagnetic, thermal, and hydrodynamic phenomena in porous media flows. Major Findings: Soret and Dufour effects significantly influence MHD free convection near an inclined plate in a porous medium. Radiation, magnetic field, and inclination modify flow and heat transfer. Numerical results show complex velocity, temperature, and concentration profiles.

The entropy generation analysis for the nanofluid flowing over a stretching/shrinking curved region is performed in the existence of the cross-diffusion effect. The surface is also subjected to second-order velocity slip under the effect of mixed convection. The Joule heating that contributes significantly to the heat transfer properties of nanofluid is incorporated along with the heat source/sink. Furthermore, the flow is assumed to be governed by an exterior magnetic field that aids in gaining control over the flow speed. With these frameworks, the mathematical model that describes the flow with such characteristics and assumptions is framed using partial differential equations (PDEs). The bvp4c solver is used to numerically solve the system of non-linear ordinary differential equations (ODEs) that are created from these equations. The solutions of obtained through this technique are verified with the available articles and the comparison is tabulated. Meanwhile, the interpretation of the results of this study is delivered through graphs. The findings showed that the Bejan number was decreased by increasing Brinkman number values whereas it enhanced the entropy generation. Also, as the curvature parameter goes higher, the speed of the nanofluid flow diminishes. Furthermore, the increase in the Soret and Dufour effects have enhanced the thermal conduction and the mass transfer of the nanofluid.

Analysis of boundary layer MHD Darcy-Forchheimer radiative nanofluid flow with soret and dufour effects by means of marangoni convection

The present research paper highlights the effect of multiple slips and inclined magnetic fields on chemically reacting Casson-Williamson with Buongiorno modeled nanofluid flow past a permeable stretching surface. Considered physical factors associated with heat transfer are viscous dissipation, Joule's heating, radiation, and double diffusion effects. The ordinary differential equations (ODEs) are formulated from governing system of highly nonlinear Partial differential equations (PDEs) by a suitable implementation of similarity invariants. The numerical results are obtained by programming the resulting equations in MATLAB software via Runge-Kutta (R-K) fourth-order technique along with the shooting scheme. The graphical illustration provides the behavior of velocity, temperature, and concentration on different non-dimensional parameters. It is worth to notice the slip parameters are greatly analogs with various physical properties of the flow field. The effect of a magnetic parameter ([Formula: see text]), Casson parameter ([Formula: see text]), Williamson parameter ([Formula: see text]), velocity slip effect ([Formula: see text]), and the inclination ([Formula: see text]) on axial velocity are shown graphically. The outstanding agreement is observed after a comparison of numerical outcomes with previously published work. The applied magnetic field and thermal radiation insert more energy into the system which improves the thermal boundary layer.