Dufour Effects Research Articles

Impacts of Buoyancy and Joule Heating on Unsteady MHD Fluid Flow Along a Semi‐Infinite Vertical Porous Plate With Dufour, Chemical Reaction, and Radiation Effect

ABSTRACTAn analytical solution for unsteady, incompressible, laminar MHD fluid flow involving mass and heat transfer along a semi‐infinite vertical moving flat plate in a porous medium have been studied in this paper. Effects of heat radiation and absorption, Joule heating, Dufour, thermal and solutal buoyancy, and first order chemical reaction of are discussed under suitable physical conditions. It is postulated that the plate will migrate in the fluid's motion's direction due to the presence of a uniform magnetic field normal to the porous surface. The regular perturbation technique is used to solve the dimensionless governing equations. The mathematical derivations for fluid velocity, temperature, and concentration are evaluated; apart from that, skin friction, rate of mass and heat transfer at the plate are also expressed. The present outcomes are compared with previously obtained results and are found to be in excellent agreement. It is observed that the fluid velocity and temperature enhanced with thermal and solutal buoyancy forces as well as the Dufour effect. Also, with an increase in chemical reaction parameter, there is a decrease in fluid velocity, temperature, and concentration. Skin friction and Nusselt number increase with higher heat absorption parameter values. Schmidt number and chemical reaction parameter both lead to a rise in Sherwood number. Applications for these models have been observed in a number of industrial and technical methods.

DUFOUR, SORET AND DISSIPATION EFFECTS ON MAGNETOHYDRODYNAMIC FLOW PAST A STRETCHING PERMEABLE SHEET WITH RADIATIVE CHEMICAL REACTION ANDHEAT SOURCE

Present investigation explores the numerical solution of Magnetohydrodynamic laminar steady gray fluid flow with heat and mass transfer past a stretching permeable sheet, incorporating several factors such as heat source, viscous and joules dissipation effects, thermal radiation, chemical reactions, Soret and Dufour effects. The governing nonlinear PDEs are simplified into ODEs with the help of similarity transformations. Momentum equation is solved analytically. Non-Dimensional temperature and concentration calculated with the help of RK- shooting method with Nachtsheim-Swigert iteration method. Key results include the calculation of heat and mass transfer rates and Co-efficient of skin friction. The effects of various parameters such as magnetic field strength, suction, radiation, chemical reactions, internal heat generation and dissipative effects on the flow characteristics and other physical parameters are thoroughly investigated, highlighting their impact on the thermal and concentration profiles in the system. This comprehensive analysis provides insights into the behaviour of the fluid flow under the specified conditions, which can be useful for applications in engineering and industrial processes.

Non-Classical Transport Laws in Third Grade Nano liquid Flow on a Stretchable surface: A Novel Approach Incorporating Soret and Dufour Effects

Non-Classical Transport Laws in Third Grade Nano liquid Flow on a Stretchable surface: A Novel Approach Incorporating Soret and Dufour Effects

The Upshots of Dufour and Soret in Stretching Porous Flow of Convective Maxwell Nanofluid with Nonlinear Thermal Emission

In this paper, the combined upshot of Soret and Dufoue of a convective Maxwell nanofluid on a porous perpendicular surface with nonlinear thermal emission was investigated. In the present work, the impact of permeable stretching sheet, nonlinear thermal emission, heat sour sink, Dufour and Soret effect, chemical reaction, Brownian motion and thermophoresis in a convective Maxwell nanofluid flow is widely discussed. The governing equations derived for the problem are highly nonlinear coupled partial differential equations. The governing equations were transformed into ordinary differential equations using Lie symmetry group alterations. The BVP4C MATLAB solver was employed to solve the ordinary differential equations numerically after validating the convergence of the method with existing results in the literature. The numerical results were established and discussed using tables and graphs. It was found that variations in porosity parameter (K), Dufour (Du) and Soret (Sr) improves velocity, temperature and concentration profiles respectively and the present of nonlinear thermal radiation and heat source emit more heat for the flow. Also, it is exciting to report that both porosity (K) and Dufour (Du) parameters has a strong impact on the flow of skin frictions, Nusselt number and Sherwood number. However, the current results may present applications in the areas of petroleum reservoir, heat exchangers, steel industries, cooling applications, nuclear waste disposal and so on.

Soret and Dufour effects on MHD mixed convective unsteady flow over stretching sheet with variable fluid properties and convective boundary condition

In several industrial and engineering applications, variable fluid properties play a major role in flow and heat transport processes. The goal of this communication is to analyse the Soret and Dufour effects for an unsteady MHD flow past a stretching sheet under the influence of temperature-dependent viscosity and thermal conductivity along with the convective boundary condition. The governing partial differential equations are transformed into nonlinear coupled ordinary differential equations with the help of similarity transformations, and a numerical analysis is done by using bvp4c, MATLAB’s built-in solver. The flow properties and heat transfer characteristics have been depicted graphically and numerically. Results show that the wall temperature gradient improves by about 8.5%, while the temperature of the fluid near the stretching sheet significantly improves upon increasing the Biot number. Employing fluids with higher viscosity and thermal conductivity consequently leads to a reduction of the wall temperature gradient by about 0.3% and 10.7%, respectively. Also, as the unsteadiness parameter increases, the wall-skin friction, heat and mass transfer rates significantly rise by about 10.4%, 4.4%, and 9.8%, respectively. Further, to verify the accuracy of the generated results, the computed results have been compared with published literature.

Cilia-assisted flow of electrically conducting micropolar fluid in a heated curved channel under Soret and Dufour effects

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the influence of heat and mass transfer on the ciliary flow of electrical conducting micropolar fluid in a curved channel. The energy and concentration equations are modulated with viscous dissipation, Soret, and Dufour effects. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). Results for velocity, pumping phenomenon, concentration, thermal field, rate of heat transfer, streamlines, skin friction coefficient, Nusselt number, and Sherwood number are analyzed subject to pertinent parameters. The study reveals that velocity is enhanced via both the micropolar parameter and curvature parameter. Temperature enhances for larger values of Dufour and Brickman numbers. Furthermore, the radial magnetic field plays a resistive role in the trapped bolus. The findings presented in this study should prove beneficial for researchers in the domains of medicine, engineering, science, and fluid mechanics. Further, it is found that the micropolar fluid model is more suitable for biofluids like blood.

Optimal Homotopy Analysis of Unsteady Second-Grade Tri-Hybrid Nanofluid Flow with Radiative impact Between Parallel Disks

The research explored the critical examination of unsteady second-grade Tri-hybrid nanofluid flow between parallel disks within a Darcy-Forchheimer medium with porosity. The study focusses on a fluid comprised of Au, TiO2, and Ag solid nanoparticles within blood, encompassing various shapes such as brick, blade, and platelet. It thoroughly investigated the impacts of Soret and Dufour effects in conjunction with MHD, joule heating, and the presence of a heat source. Furthermore, it elucidated thermally radiative effects and considers slip and convective boundary conditions, as well as mass transfer with a chemical reaction. The research also encompassed the influence of suction/injection on the squeezing flow. As the second-grade fluid parameter increases, the velocity of the fluid rises, especially when the η < 0.4. However, when η > 0.4, the velocity decreases. Additionally, the Biot numbers exhibit different effects depending on their application to the lower and upper disks. Specifically, Bi1 enhances the system's temperature, while Bi2 reduces it. The comprehensive mathematical formulation incorporates all these effects, later transformed into ODEs using similarity transformation conditions. Employing the optimal homotopy analysis technique in Mathematica software, the study graphically characterized velocity, temperature, and concentration profiles. The research's credibility is ascertained through validation against previous work by other researchers.

Heat and mass transfer of elastico‐viscous MHD fluid flow through a porous medium bounded by an oscillating porous plate in slip‐flow regime under Soret and Dufour effects

Heat and mass transfer of elastico‐viscous MHD fluid flow through a porous medium bounded by an oscillating porous plate in slip‐flow regime under Soret and Dufour effects

Mixed convection flow and heat-mass transfer of cross liquid near a stagnation region with Dufour, Soret effects and chemical reaction

Heat-mass transfer in a liquid flow over a stretching surface at a stagnation regime is significant in optimal manufacturing and quality assurance depending on the rheological behavior of viscoelastic fluids in process machinery. Stretching sheet flow at a stagnation point is a standard procedure used in the metallurgical industries for manufacturing of different equipment and cooling systems. Due to its various applications in industrial operations, the current study aims to explore the heat-mass transfer of buoyancy-driven flow of cross liquid over a stretching sheet at a stagnation point. The heat and mass transfer under the framework of Dufour and Soret effects, radiant heat, and chemical reactions are assessed. Furthermore, the analysis also takes into account the linear and nonlinear convection-diffusion phenomena. The model findings are obtained by merging the Bvp4c in MATLAB using a local similarity technique up to the fourth truncation threshold. The findings illustrate that the action of magnetic field can be used to control the flow across the sheet. Temperature increases with thermal radiation, Biot number and Dufour number. The action of buoyancy ratio parameter result in improvement in fluid flow. With increasing trend of magnetic and Weissenberg number, the flow field and skin friction coefficient drops.

Exploring integrated heat and mass transfer in von-Kármán dynamics involving Reiner-Rivlin fluid with regression models

The rotating disk system is widely used in several important applications, including turbomachinery design, mixing and stirring processes, centrifugal blood pumps development, optimizing electronic component, cooling efficiency, and various others. Moreover, regression models offer comprehensive and reliable prediction for important parameters in flows developed by revolving disks. This article presents similarity solutions for coupled heat and mass transfer with viscous dissipation in an inelastic non-Newtonian fluid flow across a permeable revolving disk. The inclusion of diffusion terms due to Dufour and Soret effects establishes coupling between energy and concentration equations. Temperature and concentrations at disk surface are supposed to vary quadratically along the radial direction. The impacts of MHD, heat source/sink dynamics and Joule heating effects on thermal boundary layer are also scrutinized. MATLAB's bvp5c tool, based on collocation scheme, generates numerical results. Homotopy analysis method, a widely accepted analytical solution procedure, is then applied to produce the series solution. Selection of the optimal auxiliary parameter values featured in the series solution is also included. The impact of Reiner-Rivlin fluid assumption on the torque required by the disk is assessed. Furthermore, linear and quadratic regression models are developed for the skin friction factors, Nusselt number and Sherwood number.

Generation of entropy for MHD flow of Casson fluid past a vertical cone with Dufour effect

Generation of entropy for MHD flow of Casson fluid past a vertical cone with Dufour effect

Effect of slip on MHD flow of fluid with heat and mass transfer through a plate

Fractional order derivatives are recognized as advanced mathematical tools with broad applications in physics and engineering for deriving real-world solutions. This study examines a fractional order model of a non-linear Casson fluid, highlighting the widespread utility of fractional derivatives. Additionally, the problem incorporates the Dufour and slip effects. Specifically, the constant proportional Caputo fractional model is formulated using generalized Fick's and Fourier's laws. Initially, the governing equations are transformed into a non-dimensional form and subsequently solved using the Laplace transform. Analysis of the figures indicates that the Casson parameter reduces fluid motion, while the diffusion thermo effect enhances it. Furthermore, the study includes a comparison between fractionalized and ordinary velocity fields. Highlight: Introduction of novel CPC fractional derivative model of Casson fluid flow. Semi-analytically solutions using Laplace transform method for accurate fluid behavior representation. comprehensive parametric analysis linking theoretical findings. Temperature contour affected by significant values of Du?

Numerical study on the behavior of a polymeric MHD nanofluid: entropy optimization and thermal analysis

PurposeAnalyzing and reducing entropy generation is useful for enhancing the thermodynamic performance of engineering systems. This study aims to explore how polymers and nanoparticles in the presence of Lorentz forces influence the fluid behavior and heat transfer characteristics to lessen energy loss and entropy generation.Design/methodology/approachThe dispersion model is initially used to examine the behavior of polymer additives over a magnetized surface. The governing system of partial differential equations (PDEs) is subsequently reduced through the utilization of similarity transformation techniques. Entropy analysis is primarily performed through the implementation of numerical computations on a non-Newtonian polymeric FENE-P model.FindingsThe numerical simulations conducted in the presence of Lorentz forces provide significant insights into the consequences of adding polymers to the base fluid. The findings suggest that such an approach minimizes entropy in the flow region. Through the utilization of polymer-MHD (magnetohydrodynamic) interactions, it is feasible to reduce energy loss and improve the efficiency of the system.Originality/valueThis study’s primary motivation and novelty lie in examining the significance of polymer additives as agents that reduce entropy generation on a magnetic surface. The author looks at how nanofluids affect the development of entropy and the loss of irreversibility. To do this, the author uses the Lorentz force, the Soret effect and the Dufour effect to minimize entropy. The findings contribute to fluid mechanics and thermodynamics by providing valuable insights for engineering systems to increase energy efficiency and conserve resources.

Powell-Eyring Nanofluid Flow over a Stretching Sheet

This research investigates the flow of a Powell-Eyring Nanofluid flowing over an exponentially stretching sheet. Thermal radiation, Soret, dissipation, and Dufour effects have been put into consideration. The obtained partial differential equations(PDE) have been transformed into ordinary differential equations (ODE) using similarity transformation. Numerical solutions are obtained in MATLAB using bvp4c frame work of fourth order accuracy integration scheme. It has been observed that the boundary layer for momentum increases with the velocity ratio while the boundary layers for thermal and concentration decrease. The velocity diminishes with increasing magnetic parameter while the temperature and concentration increased. The temperature increases with an increase in thermophoresis and Brownian motion. Increasing the fluid parameter resulted in decreased Nusselt number, skin friction, and Sherwood number. Increasing Powell-Eyring fluid parameter decreases the Nusselt number and Sherwood number but increases skin friction. This research may find use in the development of microelectronics, chemical processes, human targeted drug delivery, and heating and cooling system.

Thermal radiation, Soret and Dufour effects on MHD mixed convective Maxwell hybrid nanofluid flow under porous medium: a numerical study

PurposeScientists have been conducting trials to find ways to reduce fuel consumption and enhance heat transfer rates to make heating systems more efficient and cheaper. Adding solid nanoparticles to conventional liquids may greatly improve their thermal conductivity, according to the available evidence. This study aims to examine the influence of external magnetic flux on the flow of a mixed convective Maxwell hybrid non-Newtonian nanofluid over a linearly extending porous flat plate. The investigation considers the effects of thermal radiation, Dufour and Soret.Design/methodology/approachThe mathematical model is formulated based on the fundamental assumptions of mass, energy and momentum conservation. The implicit models are epitomized by a set of interconnected nonlinear partial differential equations, which include a suitable and comparable adjustment. The numerical solution to these equations is assessed for approximate convergence by the Runge−Kutta−Fehlberg method based on the shooting technique embedded with the MATLAB software.FindingsThe findings are presented through graphical representations, offering a visual exploration of the effects of various dynamic parameters on the flow field. These parameters encompass a wide range of factors, including radiation, thermal and Brownian diffusion parameters, Eckert, Lewis and Soret numbers, magnetic parameters, Maxwell fluid parameters, Darcy numbers, thermal and solutal buoyancy factors, Dufour and Prandtl numbers. Notably, the authors observed that nanoparticles with a spherical shape exerted a significant influence on the stream function, highlighting the importance of nanoparticle geometry in fluid dynamics. Furthermore, the analysis revealed that temperature profiles of nanomaterials were notably affected by their shape factor, while concentration profiles exhibited an opposite trend, providing valuable insights into the behavior of nanofluids in porous media.Originality/valueA distinctive aspect of the research lies in its novel exploration of the impact of external magnetic flux on the flow of a mixed convective Maxwell hybrid non-Newtonian nanofluid over a linearly extending porous flat plate. By considering variables such as solar radiation, external magnetic flux, thermal and Brownian diffusion parameters and nanoparticle shape factor, the authors ventured into uncharted territory within the realm of fluid dynamics. These variables, despite their significant relevance, have not been extensively studied in previous research, thus underscoring the originality and value of the authors’ contribution to the field.

Dufour Effects on Unstable MHD Viscoelastic Fluid Flow in Porous Vertical Media Current Pressure Gradient

Dufour Effects on Unstable MHD Viscoelastic Fluid Flow in Porous Vertical Media Current Pressure Gradient

Influence of Heat and Mass Transmission on the MHD Fluid Circulation in Conjunction with an Upright Surface in the Emergence of Radiation Thermophoresis and the Dufour Repercussions

The current research simulates the mass and heat energy transmission model on MHD fluid flow under concentration and temperature deviations on a two-dimensional viscous fluid along an upright facet. Following boundary layer estimations, mathematical simulations for the movement of fluids, the conveyance of heat and mass exposed to radiation, thermophoresis, and Dufour consequences are generated as a set of partial differential equations. The surface's resilient suction was assessed. The built-in solver bvp4c in MATLAB is used for numerically debugging the aforementioned models. Through the inclusion of visualizations and tables, the detrimental effects of influencing variables are examined on the velocity, temperature as well as concentration gradients in conjunction with on the skin friction, Nusselt number, and Sherwood number. Excellent coherence may be shown when comparing between the most present findings and those that have previously been made available in the literature in specific limited circumstances. The Dufour effect, radiation, thermophoresis, and the Grashof number are all factors that influence fluid motion and heat transmission at the interface layer of dirt. Moreover, developments in the Shearing stress, Nusselt number, and Sherwood number coefficient are calculated. The findings are crucial for optimizing a variety of fluid-based technologies and systems, allowing developments in a number of industries including energy-effectiveness, electronics cooling, pursued medicine administration, and many more.

Turbulent pipe flow and heat transfer of a binary mixture at supercritical pressure: Influences of cross-diffusion effects

Cross-diffusion effects, including Soret and Dufour effects, are enhanced around the pseudo-critical temperature (Tpc) of a binary mixture. Their influences on heat transfer at supercritical pressure have been scarcely studied. To bridge this gap, large-eddy simulations (LES) are conducted to investigate forced convective heat transfer of a CO2–ethane mixture at supercritical pressures in a circular pipe subject to a uniform heat flux. Both heating and cooling conditions, along with varying initial concentrations and thermodynamic pressures, are included in the simulations. The LES results reveal that the Soret effect causes concentration separation, resulting in a concentration boundary layer. The magnitudes of the thermodiffusion factor (kT) and the radial temperature gradient control the intensity of separation, which is more pronounced at near-critical pressure and high heat flux. Since kT is significant only around Tpc, downstream decay of the concentration separation is observed as the loci of T=Tpc migrate away from the wall so that the local radial temperature gradient diminishes. The primary factors affecting heat transfer are the variations in thermal conductivity and isobaric specific heat resulting from concentration separation. In contrast, the Dufour effect and the accompanying inter-diffusion play negligible roles. In deterioration scenarios, the bulk Nusselt number (Nub) shows a maximum relative drop of 8%, whereas in enhancement scenarios, Nub shows a maximum relative increase in 10%, with both deterioration and enhancement decaying downstream. Cross-diffusion effects have negligible impacts on density and streamwise velocity, but noticeably alter streamwise velocity fluctuation and turbulent kinetic energy.

Buongiorno’s radiative Prandtl-Eyring nanofluid flow through porous medium over a stretching surface with cross-diffusion effects

The main focus of the current analysis is to describe the thermo-magnetic flow, heat and mass transport features of two-dimensional dissipative Prandtl-Eyring nanofluid (PE-NF) flow over a stretching sheet under the influence of porous medium and magnetic Ohmic dissipation numerically. An innovative Buongiorno’s nanofluid model in terms of Brownian motion and thermophoresis is deployed to accurately simulate the nano behavior in Prandtl-Eyring within the boundary layer regime. The thermal radiation and heat source/sink effects are also included to describe the thermal transport process. In addition to this, the thermo-diffusion and diffusion-thermo effect are included to demonstrate the temperature and concentration diffusion mechanism under the presence of chemical reaction process. The emerged coupled nonlinear two-dimensional time-independent partial differential equations are rendered to their dimensionless form through appropriate similarity transformations and solved by deploying Matlab-based BVP4C technique. The graphical visualization showed that, the increasing magnetic number diminished the flow field and enhanced the temperature and concentration profiles in the flow regime. Rising porous parameter decayed the Prandtl-Eyring nanofluid velocity. Increasing radiation and Eckert numbers enhance the temperature field in the flow regime. Magnifying Prandtl-Eyring parameter suppressed the velocity diffusion. Increasing Brownian motion and thermophoresis parameters increases the temperature profile. Amplifying Soret parameter upsurges the concentration profile. Skin-friction coefficient amplified with enhanced magnetic and porous numbers. Heat transfer rate acts as increasing function of thermophoresis and Brownian motion parameters. The main objective of this study is the addition of magnetic Ohmic dissipation, radiation, porous medium, thermal source/sink, Soret and Dufour effects and Buongiorno nanofluid model and this consideration generalizes former studies and gives a new re-defined mathematical formulation of heat and mass transport features of Prandtl-Eyring nanofluid flow over a stretching sheet. Finally, the numerical accuracy of the current similarity results is validated with available solutions and noticed a good agreement.

Magnetized dissipative Soret-Dufour effects on Walter’s-B fluid flow over a stretching sheet with nonuniform heat source/sink and thermal radiation under chemical reaction

The main motivation behind this numerical analysis is to disclose the salient magneto-thermo characteristic features of two-dimensional viscous incompressible magnetized Soret and Dufour effects on the boundary layer flow of Walter’s-B fluid over a stretching sheet under the influence of viscous dissipation. The novel physical effects such as nonuniform heat source/sink and magnetic Ohmic heating are included in the governing equations. Further, prescribed surface temperature condition is introduced in the boundary conditions to describe the thermal transport features. However, the deployed non-Newtonian Walter’s-B fluid rheology model finds its innumerable applications in numerous areas of science and engineering including electronic cooling, polymer processing, nuclear reactor cooling, extraction of polymer sheet, plastic sheet drawing, chemical engineering, metallurgy, injection molding and many more. Therefore, authors have motivated with these applications and advantageous of considered fluid model. Hence, an effort is made to describe the dynamic characteristic features of non-Newtonian Walter’s-B rheology model about a stretching sheet. However, present physical flow model produces highly nonlinear coupled two-dimensional partial differential equations and which are not acquiescent to available analytical methods. Owing to this, a robust MATLAB-based BVP4C technique is deployed to produce the appropriate numerical solutions through suitable similarity transformations. The graphical representations of velocity, temperature and concentration profiles along with skin-friction coefficient, Nusselt and Sherwood numbers are presented. Magnifying magnetic number decays the velocity profile and enhances the thermal and concentration fields. Rising viscoelastic parameter diminishes the thermal and concentration fields and magnifies the velocity field. Rising the radiation parameter diminish the thermal field. Magnifying Soret number raises the concentration field. Rising the space and temperature dependent heat source/sink coefficient amplifies the thermal diffusion field. Magnifying Dufour and Eckert numbers amplifies the thermal field. Finally, the guarantee and accuracy of the investigated problem is presented through a comparison with previous studies.