Dufour Parameter Research Articles

Double Diffusive Convective Flow Study of a Hybrid Nanofluid in an Inverted T-Shaped Porous Enclosure Under the Influence of Soret and Dufour Prameters

Abstract This study presents a numerical investigation to examine the influence of Soret and Dufour parameters on the double-diffusive convective flow of a hybrid nanofluid within an inverted T-shaped porous enclosure. The thermophysical properties and numerical values of the hybrid nanofluid are adopted from experimentally published data. The mathematical model is formulated based on the generalized Darcy–Brinkmann–Forchheimer equation and subsequently simulated using the penalty finite element method. A parametric study is conducted, encompassing a wide range of parameters for Rayleigh number, Darcy number, porosity value, buoyancy ratio, Lewis number, Soret parameter, and Dufour parameter. The resulting flow patterns, temperature distribution (isotherms), and concentration distribution (isoconcentration plots) provide insights into the fluid flow, heat transfer, and mass transfer phenomena within the physical domain. Furthermore, the heat and mass transfer rates at the heated (concentrated) wall are quantitatively evaluated by the mean Nusselt number and mean Sherwood number, respectively, considering various combinations of flow parameters. As a key finding, it is observed that the smaller value of the Rayleigh number remains insignificant at convective flow of thermal and solute phenomena. Moreover, the higher value of Ra reinforces the convective strength of hybrid nanofluid, and it helps to identify the real impact of each parameter. Thus, at a higher Rayleigh number, it is observed that the increasing value of Darcy number, porosity value, Lewis number, and buoyancy ratio significantly influence the convective flow of heat and solute transport activity, whereas the impact of Soret and Dufour parameters shows a relatively less influence on the heat and mass transfer phenomena.

Intelligent computing for the double-diffusive peristaltic rheology of magneto couple stress nanomaterials

Abstract In nanofluids, the effect of convection in the presence of double diffusivity on a magneto couple stress fluid with the peristaltic flow of a model in a non-uniform channel (MCSFM) is reviewed in this article. This research discusses MCSF in a non-uniform channel by applying the Levenberg–Marquardt procedure via an artificial backpropagated neural network (LMP-ABNN). For two-dimensional and two-directional flows, mathematical formulations of double-diffusivity convection of a magneto couple stress fluid in nanofluids are developed. The partial differential equations are reduced to ordinary differential equations by using appropriate transformations. The assessment of the Hartmann number, thermophoresis parameter, Dufour parameter, Soret parameter, and magnetic Reynolds number over concentration profiles and temperature profiles is made by generating a dataset for LMP-ABNN based on the ND solve method for different variations of MSCFM. To examine the approximate solution validation, training and testing procedures are interpreted, and the performance is verified through error histogram and mean square error results. The extremely nonlinear equations are reduced by employing a long-wavelength approximation and a low but finite Reynolds number. To describe the behavior of flow quantities, graphical representations of a variety of physical characteristics of importance are shown. The impact of the Hartmann number and magnetic Reynolds number over axial magnetic field and current density is also studied. The concentration increases as the thermophoresis parameter and Dufour parameter values increase. This occurs because the concentration and both these parameters have a direct relationship. We observed opposite behavior for both the magnetic Reynolds number and the Hartman number. The behavior of current density J z increases with increasing values of R m. Both the temperature distribution and solute concentration increase. The final outcome of this study is to provide the potential for these techniques to provide new insights and solutions to challenging problems in nanofluids and other areas of fluid mechanics and to facilitate the design of more efficient and effective microfluidic devices.

Mathematical Modeling on Magnetohydrodynamics Upper Convected Maxwell Fluid Flow Past a Flat Plate Using Spectral Relaxation Approach

The focus of this treatise is on the scrutiny of MHD heat and mass transfer motion of upper convection Maxwell (UCM) fluid in a thermally radiated flat plate. The models of the flow equations were considered when there is a temperature difference: the Cattaneo-Christov model and the Soret-Dufour mechanisms. A magnetic field of firmness was inflicted in opposition to the flow. The flow inspection is controlled by partial differential equations (PDEs). Suitable similarity variables were utilised on the PDEs to obtain a set of nonlinear ordinary differential equations (ODEs). The simplified set of ODEs shall be answered by exploiting the spectral relaxation method (SRM). The SRM is a numerical technique that solves differential equations by utilising the repetition of a sequence of operations that is iterated iteratively by first decoupling the coupled systems of equations. The magnetism was found to decline the velocity and hydrodynamic boundary layer due to the Lorentz force. The Deborah number was found to enhance the velocity contour. The Eckert number was discovered to improve the temperature profile due to the production of heat energy within the boundary layer. An increase in Prandtl number was found to enhance the hydrodynamic and thermal boundary layer thickness. The local skin friction and Nusselt number were found to be elevated by the increase in the Dufour parameter.

Effect of diffusion‐thermo on a mixed convective heat and mass transfer magnetohydrodynamic flow through a vertical porous plate including radiation absorption

AbstractThe effect of Dufour on a magnetohydrodynamics (MHD) mixed convection in the presence of radiation absorption and heat sink is performed in this work. The dimensional governing equations involved here are transferred to non‐dimensional form and then solved using perturbation technique. The changes due to the effect of several relevant parameters on the velocity field temperature field and concentration field are graphically displayed. The rates of momentum transfer, heat transfer and mass transfer are also analyzed and their influence due to the related parameters are visualized graphically. Rise in Dufour parameter enhances the fluid velocity and fluid temperature. Also, the heat sink parameter lowers the fluid velocity and temperature. The chemical reactions cause a fall in the fluid's velocity, temperature and concentration.

Impact of double diffusivity on the hyperbolic tangent model conveying nano fluid flow over the wedge

The significant thing in our analysis is to inspect the double-diffusivity convection for the hyperbolic tangent nanofluid model, under the spotlight effects of activation energy and viscosity over the wedge-shaped geometry. Activation energy enunciates chemical reaction and also Buongiorno model is applied to highlight the important features of the thermophoresis and Brownian diffusion coefficient. The convection of double diffusivity is illustrated through Soret and Dufour parameter. The mathematical modeling of demarcated flow produces a collection of non-linear partial differential equations, which are consequently transmuted into ordinary differential equations using suitable transformation. The graphical results for these ordinary differential equations are created using the Bvp4c approach. The effect of pertinent parameters on fluid flow, thermal variation, concentration and double diffusivity profiles are examined. The velocity field generally behaves as the decreasing function of thermal and nanofluid Grashof number but surges along the Solutal Grashof number. The Brownian diffusion coefficient surges the temperature profile and minors the concentration and double-diffusivity. Soret diffusivity surges the concentration distribution when fluid crosses the edge of the wedge. The nanofluid Lewis number particularly slows down the double-diffusivity profile. The graphical sketches of local skin friction, Nusselt number, Sherwood number, isothermal contour and streamlines flow elaborated our analyses more precisely.

Double-diffusive natural convection with Soret/Dufour effects and energy optimization of Nano-Encapsulated Phase Change Material in a novel form of a wavy-walled I-shaped domain

BackgroundAs building segment grows in parallel with amplifying population, the necessity for consumption of energy needed to passive and active heating or cooling buildings for thermal comfort increases. Schemes such as developing green buildings for sustainable architecture were utilized to address this issue. The utilization of Phase Change Materials (PCMs) with the aim of active and passive cooling or heating of buildings illustrates a promising and modern technique. MethodsThis study's objective is to perform a numerical analysis using the finite element method, FEM for modeling free convection produced by double-diffusion (DDNC) with Soret/Dufour effects of Nano-Encapsulated PCMs within an I-shaped enclosure equipped with a novel type of corrugated vertical walls subjected to Neumann thermal and solutal conditions. FindingsResults are interpreted and assessed in relation to the governing factors, such as buoyancy ratio (N), Rayleigh and Lewis numbers (Ra, Le), the height of corrugated walls (a), Stefan number (Ste), non-dimensional fusion temperature (θf), Dufour (Df), and Soret (Sr) parameters. High values of N and Ra, and low values of Le and a, caused in the highest rate of heat and mass exchange. The irreversibilities due to the heat and mass transfer effects increase as the flow intensity within the system decrease. Decreasing the latent heat of the NEPCM cores and increasing their fusion temperature lowering the heat transfer rates, while improving mass transfer rates. This configuration can help in the design of the storage tank in hydronic apparatus for cooling, heating, and domestic hot water in buildings.

Scaling group analysis of a Magnetohydrodynamic Nanofluid flow with Double dispersion and Dufour effects on a vertical wedge

Mixed convection in nanofluids for varying geometries such as vertical sheets, exponentially stretching sheets etc. contributes to various fields of science and technology. Based on a wide range of applications of Dufour effects, double dispersion effects and magnetohydrodynamic (MHD) flows in engineering fields, our study focuses on the combined effects of mixed convection flow on a vertical wedge with Buongiorno model which has not been studied earlier. Similarity transformations have been utilized for transforming nonlinear partial differential equations. Lie scaling group has been adopted in our study for obtaining the required similarity transformations and the final set of equations has been solved numerically using MATLAB bvp4c routine. Skin friction coefficient, heat transfer and mass transfer coefficients have been put forward numerically for quantities like magnetic parameter, Solutal dispersion parameter, Lewis number, thermophoresis parameter, Brownian motion parameter, mixed convection parameter, thermal dispersion parameter and Dufour parameter. Increase in Sherwood number and decreasing Nusselt number values have been noted for increasing Dufour () and magnetic parameter () values. Comparative studies have been made with previously published results and the results are found to be in good agreement. This validates our study.

Numerical investigation on regulation and suppression of heat and mass transfer by varying thermal and solutal buoyancy force

In this study, a three-dimensional numerical analysis is presented for regulation and suppression of heat and mass transfer by varying thermal and solutal buoyancy force with a rotating cylinder placed at the center of the cavity. The energy and concentration equations are coupled by Dufour and Soret parameters to have a mutual effect of concentration and temperature on heat and mass transfer. The thermal buoyancy in the flow is adjusted by varying Rayleigh number of Ra = 104, 105, 106 and the mixed convection in the flow is regulated by varying Richardson number of Ri = 0.5, 1, 1.5 at unity buoyancy ratio (N = 1), Soret number, Lewis number and Dufour number. The present heat and mass transfer solver is developed and validated using the open-source computational fluid dynamics (CFD) package OpenFOAM 5.0. The two vertical opposite sides of the cavity are maintained as isothermal and isosolutal (iso-concentration), and the remaining four surfaces with rotating cylinder are kept as adiabatic. The present analysis reveals the impact of the mutual coupling of heat and mass transfer with the presence of thermal buoyancy, solutal buoyancy including mixed convection flow. The increase in the forced circulation at fixed thermal and solutal buoyancy force increases the heat and mass transfer. The variation of Nu avg and Sh avg is observed to be steady even with increasing Ra, then changes to periodic and chaotic with the implementation of a rotating cylinder. The detailed analysis on the variation of thermal buoyancy at unity buoyancy ratio, forced convection is reported by plotting streamlines, temperature and concentration contours, average Nusselt and Sherwood number.

Radiation absorption on MHD free conduction flow through porous medium over an unbounded vertical plate with heat source

The aim of the present paper is to investigate the radiation absorption and diffusion thermo on unsteady magneto hydrodynamic flow past an infinite vertical permeable moving plate in the presence of thermal radiation, heat absorption and homogenous chemical reaction, subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using perturbation technique. Graphical results for the velocity distribution, temperature distribution and concentration distribution based on the numerical solutions are presented and discussed. Also we discuss the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity and temperature distribution is observed to increase with an increase in radiation absorption and Dufour parameter, whereas it diminishes with the enhancement in magnetic field, heat absorption coefficient, radiation parameter and chemical reaction parameter with respect to velocity, temperature and concentration distributions.

Mathematical simulation of double diffusion convection on peristaltic pumping of Ellis nanofluid due to induced magnetic field in a non-uniform channel: Applications of magnetic nanoparticles in biomedical engineering

The present research explores the wave of peristalsis on magneto Ellis nanofluids within non-uniform channel by using Dufour and Soret parameters. The mathematical representation of the magneto Ellis nanofluids having double diffusion convection under magnetic flux is presented in detail. The nonlinear partial differential equations are simplified by applying long wavelength and lesser Reynolds number. The resultant differential equations are further simplified numerically, and exact solutions of concentration, temperature, and nanoparticle fraction are computed. Further, the significance of numerous material constraints of flow quantities is depicted through graphs. It is revealed that the huge value of Brownian motion and Soret number decreases the concentration of nanosolid particle. Solid nanoparticles in a nanofluid during micro-mixing procedure collide randomly hence transferring the molecular energy into thermal energy that triggers the rise in temperature.

Dynamics of lorentz force and cross-diffusion effects on ethylene glycol based hybrid nanofluid flow amidst two parallel plates with variable electrical conductivity: A multiple linear regression analysis

This research investigates how the presence of Dufour and Soret parameters affect the properties of hybrid nanofluid flow amidst two parallel plates with temperature dependent electrical conductivity. Heat transport procedure is studied using thermal radiation parameter and Eckert number. Equations that characterize the current problem are turned into a set of ordinary differential equations, which are then solved with the assistance of a built-in function in MATLAB called the bvp4c solver. Multiple linear regression is used to explain physical parameters of interest including Sherwood number. The main conclusions of this study are that the velocity decreases with increasing nanoparticle volume fraction parameter and the concentration profile minifies with the rise in Soret parameter. It is observed that the increase in Dufour number causes a corresponding increase in the fluid temperature. It is discovered that, when the magnetic field parameter (M) is set to 0≤M≤2.5, the decreasing rate in the skin friction parameter is 0.02215. It is observed that, when φ1 is set to 0≤φ1≤0.25, Nusselt number drops by 3.82891. It is detected that, when Sr is set to 0≤Sr≤2.5, Sherwood number increases at a rate of 0.037225.

MHD flow in a rotating vertical cone through a porous medium

AbstractIn the context of advancements in both heat and mass transfer, the current study intends to analyze the impacts of thermal radiation, Soret, and Dufour on the magnetohydrodynamic boundary layer flow through a vertical spinning cone in porous media. The Dufour effect is the energy flux due to the mass concentration gradient with a reciprocal phenomenon, the Soret effect. Energy expression considers the physical aspects of heat generation and absorption. It is expected that the tangential, circumferential, and normal directions will all have velocity components in flow through a porous media. The governing equations are nonlinear partial differential equations that are rearranged into ordinary differential equations via similarity transformation, and then they are numerically solved using the Runge–Kutta method along with a proper shooting strategy. Graphs are used to examine the impacts of many parameters on flow characteristic velocity, temperature, and concentration, including magnetic parameters, porous parameters, Dufour and Soret parameters, chemical reaction parameters, and more. The numerical findings of the gradient of velocity, the Nusselt and Sherwood numbers, and the surface drag force are tabulated and compared with the current result and the one from the literature. The findings are found to be in good agreement. Circumferential and normal velocities are improved visually for greater values of the porosity parameter, but the tangential velocity behavior of the magnetic parameter exhibits the reverse behavior. In addition, the Dufour parameter and chemical reaction both exhibit diminishing behavior when the Soret parameter increases.

Chemical reaction, Soret and Dufour impacts on magnetohydrodynamic heat transfer Casson fluid over an exponentially permeable stretching surface with slip effects

This paper discusses the impacts of velocity, temperature, and solutal slip on the mass and heat transfer characterization of MHD mixed convection Casson fluid flow along an exponential permeable stretching surface with chemical reaction, Dufour and Soret effects. The Casson fluid is supposed to flow across an exponentially stretched sheet, together with the exponential temperature and concentration fluctuations of the fluid. As governing equations, the momentum, energy and species concentration equations are constructed and represented as PDEs. Following that, these equations were converted via the similarity transformation into ODEs. Finally, the ODEs are numerically solved using the Keller-box method with MATLAB software’s algorithm. Expressions are produced for the fluid flow, temperature and concentration gradients. We also determined the physical variables from which the friction factor, rate of mass and heat transfer are attained for engineering purposes. Using graphs and tables, the impacts of altered physical characteristics on flow amounts are explored. The consistency and validity of our outcomes revealed a significant degree of agreement when comparing them to previously published studies. The findings reveal that raising the Soret and Dufour parameter enhances the velocity profile at the wall, but the converse is true for increasing the velocity slip factor.

Non-Darcy-Benard Double Diffusive Marangoni Convection with Dufour Effect in a Two-Layer System

Two - component / Double Diffusive Marangoni (DDM) convection with Dufour effects, in a two-layered system, has been studied analytically by using Darcy – Brinkmann Model. For fluid layer, the upper boundary is free with surface tension depending on both temperature and concentration, for porous layer the lower boundary is rigid and both the boundaries are insulating to both heat and mass. At the interface, the normal velocity, normal stress, shear stress, mass, mass flux, heat, heat flux is assumed to be continuous. The effect of different physical parameters on DDM convection is investigated in detail and results are presented graphically. The effect of Dufour parameter, which plays vital role in diffusion-thermal process, when the energy flux due to mass gradient appears, on DDM convection in a two- layer system, has been explored.

Hybrid double-diffusivity convection and induced magnetic field effects on peristaltic waves of Oldroyd 4-constant nanofluids in non-uniform channel

The aim of this work is to relate the Soret and Dufour parameters of peristaltic flow in magneto Oldroyd 4-constant nanofluids in non-uniform channel. The discussion explores the numerical modelling of Oldroyd 4-constant nanofluids with convective double diffusion under induced magnetic flux. The use of a low finite Reynolds number and a long wavelength simplify non-linear partial differential equations. Numerical method is applied to solve reduced differential equation. Furthermore, the exact solutions of nanoparticle, temperature and concentration are computed. The graphical and numerical presentation show the significance of different physical parameters. The results reveal the fact that the greater value of Soret number and Brownian motion parameter decreases the concentration nanosolid particle. In addition, molecular kinetic energy transforms into thermal energy by random collision in the process of micro-mixing of nanoliquid resultantly raise the temperature of the liquid. Moreover, the magnetic force function increases due to enhancing electric field and magnetic Reynolds number.

Combined influence of cross‐diffusion and variable fluid properties on free convection flow past a vertical cone

AbstractThe free convective flow of an incompressible viscous fluid over an isothermal vertical cone with variable viscosity and variable thermal conductivity is examined in the presence of the Soret and Dufour effects. As thermal and solutal boundary conditions at the cone's surface, the constant temperature and concentration (WTC) and constant heat and mass flux (HMF) cases are taken into account. The successive linearization method is applied to linearize a system of nonlinear differential equations that describes the flow under investigation. The numerical solution for the resulting linear equations is attained by means of the Chebyshev spectral method. The obtained numerical results are compared and found to be in good agreement with previously published results. The impact of significant parameters on the heat and mass transfer rates is evaluated and presented graphically for the WTC and HMF situations. In both cases, the Soret number increases the skin friction coefficient and rate of heat transfer while decreasing the Sherwood number. With an increase in the Dufour parameter, the coefficient of skin friction and Sherwood numbers increase while the heat transmission rate decreases.

Thermosolutal convection under cross-diffusion effect in SGSP with porous layer

Salt gradient solar pond (SGSP) is a promising alternative for low-temperature industrial applications. Thermal and solutal transfer processes occur simultaneously at SGSP, which induce the cross-diffusive effects and make the internal flow more complicated. In the present work, thermosolutal convection under cross-diffusive effects inside a simplified SGSP enclosure attached with a porous layer are investigated through Lattice Boltzmann Method (LBM). Influences of internal heat generation, buoyancy ratio, thickness and permeability of porous layer combined with Soret and Dufour parameters are considered on the thermal and solutal transport characteristics. Average Nusselt and Sherwood numbers as well as mean temperature and concentration are presented to analyze the thermal and solutal transport processes in the SGSP enclosure. Results indicate that Soret effect mainly boosts the solutal transport process, while Dufour effect can greatly enhance both the thermal and solutal transport processes. Internal heat generation can inhibit the thermal and solutal transport processes and reduce the positive influence of Soret and Dufour effect. Buoyancy ratio can boost thermal and solutal transport processes. In the opposing situations (N < 0), Soret effect weakens the thermal transport process, while Dufour effect is reverse. Furthermore, attaching a porous layer at the bottom wall can suppress the thermal and solutal transfer processes, and then increases the thermal storage capacity. Permeability and thickness of porous layer have a significant influence on thermal and solutal transport processes. Present study is beneficial to the thermal storage enhancement and the future development of SGSP.

Unsteady MHD on Convective Flow of a Newtonian Fluid Past an Inclined Plate in Presence of Chemical Reaction with Radiation Absorption and Dufour Effects

In this study, emission incorporation and Dufour belongings are investigated for uneven magnetohydrodynamic assorted convection stream over a disposed holey moving shield with thermal emission, heat assimilation, and homogenous substance reactions subjected to changeable suction. The governing momentum equation, as well as the energy and mass diffusion equations, have analytical solutions. The Nusselt number, the Sherwood number, in addition to velocity, temperature, attentiveness, and skin friction, are computed and examined analytically and visually in order to observe the manipulate of a variety of parameters. Grashof number (Gr), modified Grashof number (Gm), magnetic parameter (M), permeability parameter (K), Prandtl number (Pr), Heat Sink (Q), Radiation parameter (F), Dufour parameter (Du), Radiation absorption constraint (R), Schmidt number (Sc), and Chemical reaction parameter (K0) are all non-dimensional parameters with different values. In porous medium, slow-moving chemical reaction fluids are the only source of the issue. In the future, researchers may look at the inertia effects of porous medium for high-velocity flows. Researchers interested in radiation absorption effects in porous media will find this a highly helpful resource.

Influence of Triple Diffusive Convection in Peristaltic Flow of Jeffrey Nanofluid Through Non-Uniform Channel

In this investigation, we considered the effect of triple diffusive convection on peristaltic flow through a non-uniform Channel. We also considered the incompressible non-Newtonian Jeffrey nanofluid. On the assumption of a long wavelength and low Reynolds number, the governing equations were transformed into a non-dimensional form. The reduced non-dimensional highly nonlinear partial differential equations are solved using the Homotopy Perturbation Sumudu transformation method (HPSTM). The influence of different physical parameters on dimensionless velocity, pressure gradient, temperature, the concentration of salt 1 and salt 2, and volume fraction was graphically represented. The Dufour solutal Lewis number of salt 1 and salt 2 on the velocity profile increases. The Dufour solutal Lewis number and modified Dufour parameter of salt 1 rises on nanoparticle volume fraction profile. It is found that the presence of the triple diffusing components with small diffusivity can change the convection in the system. The change in density in a triple diffusive is caused by the thermal and solutal diffusivities of two separate chemical species. So this study is applicable in engineering and scientific fields like geology, astrophysics, disposal of nuclear waste, deoxyribonucleic acid (DNA), and chemical engineering. This work is compared with the exact solution, and it is in good agreement with this method.

Further analysis of double-diffusive flow of nanofluid through a porous medium situated on an inclined plane: AI-based Levenberg–Marquardt scheme with backpropagated neural network

The present article exploits a novel application of AI-based Levenberg–Marquardt scheme with backpropagated neural network (LMS–BPNN) to analyze the double-diffusive free convection nanofluid flow model (DDFC-NFM) over an inclined plate in the existence of Brownian motion and thermophoresis properties embedded in a porous medium. The governing PDEs representing DDFC-NFM are transformed into system of nonlinear ODEs by applying suitable transformation. The reference data set is generated from Lobatto III-A numerical solver by variation of magnetic field parameter (M), thermal Grashof number (Gr), angle of inclination (α), Brownian motion parameter (Nb), Dufour-solutal Lewis number (Ld), modified Dufour parameter (Nd) and thermophoresis parameter (Nt) for all scenarios of the designed LMS–BPNN. The approximate solution and its comparison with standard solution are analyzed by execution of training, testing and validation procedure of the designed LMS–BPNN. The effectiveness and reliable performance of LMS–BPNN are endorsed with MSE-based fitness curve, regression analysis, error histogram analysis and correlation index. Results reveal that velocity increases with the rise in Gr, whereas reverse trend has been noticed for angle of inclination and magnetic field parameter and the temperature profile increases with the increase in Nb, Nd and Nt. The solutal concentration profile increases with the increment in Ld, while an increase in Nd causes a decrease in it. When Nt increases, the enhancement in the nanoparticle volume frictions occurs, but an opposite behavior is depicted for Brownian motion parameter.