Dufour Effects Research Articles

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.

Dufour and Soret effects on MHD squeezed nanoliquid flow between parallel plates by differential transform method

Purpose This paper aims to examine the Dufour and Soret combined effects on the study of two-dimensional squeezed flow of copper water nanofluid between parallel plates along with applied (external) magnetic field. Impact of higher order chemical reaction is also considered. Design/methodology/approach The nonlinear partial differential equations (PDEs) are changed into system of ordinary differential equations (ODEs) by employing suitable similarity transformations. These transformed ODEs are then solved by means of a semianalytical method called differential transform method (DTM). Effects of several changing physical parameters on fluid flow, temperature and concentration have been deliberated through graphs. Findings It is observed that Dufour and Soret numbers are directly related to temperature profile and a reverse trend was observed in the concentration profile. Temperature enhancement is perceived for the enhanced Dufour number. Enhancement in Dufour number shows a direct association with Sh and Nu for all values of squeezing parameter. Practical implications The combined Dufour and Soret effects are used in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The squeeze nanoliquid flow can be used in the field of composite material joining, rheological testing and welding engineering. Social implications This study is mainly useful for geosciences and chemical engineering. Originality/value The uniqueness in this research is the study of the impact of cross diffusion on chemically reacting squeezed nanoliquid flow with the chemical reaction order more than one in the presence of applied magnetic force using a semianalytical procedure, named DTM.

Entropy optimization of a FENE-P viscoelastic model: a numerically guided comprehensive analysis

AbstractThe influence of polymers on entropy generation processes is substantial, particularly in the fields of fluid dynamics and rheology. The FENE-P (Finitely Extensible Nonlinear Elastic-Peterlin) model describes the polymer’s dynamics as a result of the interaction between the stretching caused by the velocity gradient and the elastic force that restores the polymer to its equilibrium position. Models such as FENE-P aid in understanding and predicting polymer flow behaviour allowing for the reduction of entropy generation by optimizing system designs. A continuum approach is employed to express the heat flux vector and polymer confirmation tensor of the model. The study investigates the complex relationship between polymer conformation, flow dynamics, and heat transfer taking into account the thermophoresis (Soret effect) and mass diffusion-thermal diffusion coupling (Dufour effect) phenomena to optimize processes by reducing entropy. This study illuminates polymer’s significance in entropy minimization, improving engineering design methodologies and applications in materials science, chemical engineering, and fluid dynamics. As result, the presence of polymers leads to a substantial decrease in the total entropy of the system. This understanding provides opportunities for enhancing heat transfer systems, thereby facilitating the development of more efficient and sustainable technology.

Heat and mass transfer of ternary nanofluid in permeable vertical channel sandwiched between nanofluid zones with Soret and Dufour effects using sensitivity analysis

Heat and mass transfer of ternary nanofluid in permeable vertical channel sandwiched between nanofluid zones with Soret and Dufour effects using sensitivity analysis

Applications of partial differential equations to transient heat and mass transfer in MHD flow over a porous medium

The flow problem discussed in this research is an investigation of compressible viscous fluid in an unstable 2D MHD laminar driven vortex and stable boundary layer flow, passing a heated stretched sheet at varying speeds via a porous medium exposed to a magnetic field with viscous dissipation, thermal diffusion, thermal radiation, chemical reaction and Dufour effects. With the aid of similarity transformations, PDEs that come out in governing equations of this formulations are converted into non-linear sets of ODEs. Well-defined bvp4c technique used to numerically solve these converted equations. With use of various graphs, the consequences of different factors on the distributions of velocity, temperature and concentration were examined numerically and graphically. Physical parameters for this issue are also discussed.

Multi-physics analysis of squeezing fluid flow with rotational, magnetic field, and heat transfer interactions

This research paper presents a comprehensive study on the intricate interplay of rotational, magnetic field and heat transfer effects in squeezing fluid flow, utilizing the foundational framework of Navier–Stokes equations. Fluid flow in confined geometries has significant applications in various industrial processes, including lubrication systems, microfluidics, and heat exchangers. The integration of rotational motion, magnetic fields, and heat transfer phenomena into this context holds immense potential for optimizing performance and efficiency. The study commences with the derivation and analysis of the coupled Navier–Stokes equations, incorporating the Coriolis force due to rotational motion, the Lorentz force arising from magnetic fields, and the energy equation for heat transfer. This comprehensive model accounts for the complex interactions between these physical phenomena, offering a holistic perspective on squeezing fluid flow dynamics. Numerical analysis are conducted to investigate the behavior of fluids under the influence of rotational, magnetic field, and heat transfer effects. The results reveal intricate flow patterns, including vortex formation and heat transfer enhancement. Furthermore, the impact of key parameters such as rotational speed, magnetic field strength, and temperature gradients on flow characteristics is systematically analyzed. The Dufour effect pertains to the transfer of energy resulting from a gradient in mass concentration, occurring as a correlated consequence of irreversible processes. It functions as the inverse of the Soret effect. The temperature changes due to the concentration gradient, amplifying as the Dufour number increases. The most significant temperature rise is observed at the midpoint of the fluid domain. Conversely, the Soret number behaves in a similar but opposite manner. Tables 4–10 has been created to offer a comprehensive analysis of the optimal alignment between Homotopy Analysis Method (HAM) and BVP4c. Specifically, it demonstrates a continuous decrease in skin friction for ξSo, ξRd, and ξR2, while showing an increase for ξSc, ξDo, and ξRem. Meanwhile, the skin friction remains constant for ξPr. The research centers on analyzing heat and mass transfer properties within an incompressible fluid confined between two rotating and stretching disks amidst an unpredictable flow pattern. The study employs a blend of analytical and numerical approaches to solve the governing equations, delving into the intricate fluid dynamics and the intricate processes of heat and mass transfer within this intricate system.

Convection heat and mass transfer of non-Newtonian fluids in porous media with Soret and Dufour effects using a two-sided space fractional derivative model

Non-Newtonian fluids within heterogeneous porous media may give rise to complex spatial energy and mass distributions owing to non-local mechanisms, the modeling of which remains unclear. This study investigates the natural convection heat and mass transfer of non-Newtonian fluids in porous media, considering the Soret and Dufour effects. A strongly coupled model is developed to quantify the coupled transport of energy and reactive pollutants with the non-Newtonian fluid. The constitutive equation for the non-Newtonian fluid is described by a two-sided Caputo type space fractional velocity gradient. The governing equation, with a symmetric diffusion term, is effectively solved using a stable and convergent shifted Grünwald–Letnikov formula. The influences of three important parameters, which are the average skin friction coefficient, the average Nusselt number, and the Sherwood number, on fluid heat and mass transfer are calculated and analyzed. Numerical results reveal a significant interaction between the fractional derivative and the buoyancy ratio number, both of which affect the average skin friction coefficient. Furthermore, the average Nusselt number increases with the Dufour number while decreasing with the average Sherwood number. These findings enhance our understandings of the dynamics of energy and mass co-transport in non-Newtonian fluids, particularly in relation to their constitutive equation featuring spatial non-local properties.

Impacts of Stefan Blowing on Thermophoretic Particle Deposition in Sisko Nanofluid Flow Over a Riga Plate with Soret and Dufour Effects

The proposed framework considers the thermosolutal Marangoni convective flow of Sisko [Formula: see text] nanofluid over a Riga surface with the effects of Stefan blowing and thermophoretic particle deposition. The phenomena of mass and heat are discussed in relation to Soret and Dufour impacts. Electrodes and magnets are arranged on a plate to make up the Riga plate. Since the fluid conducts electricity, the Lorentz force upsurges exponentially in the vertical direction. There are numerous possible uses for this study in different disciplines. The design and production of thin films, coatings, and nanostructured materials can be enhanced by knowledge of how nanoparticles settle onto surfaces under various fluid flow conditions. By optimizing fluid flow and particle deposition processes, engineering insights from this work can guide the development of more efficient heat transfer systems, such as heat exchangers and cooling technologies. The nonlinear governing PDEs are converted into nonlinear ODEs using appropriate transformations. The resultant system of highly nonlinear equations can be solved analytically by using the homotopy analysis method (HAM). The significance of factors on the flow, thermal, and concentration fields are thoroughly explained with the use of tables and figures. Higher Marangoni convection parameter in more effective heat and mass transport within the liquid as well as higher induced flows when the Marangoni convection parameter is increased. A more uniform distribution of these properties throughout the liquid is the result of decreasing temperature and concentration profiles.

The impact of double‐diffusive convection on electroosmotic peristaltic transport of magnetized Casson nanofluid in a porous asymmetric channel

AbstractThe primary objective of the present article is to investigate the heat and mass transfer in mixed convection peristaltic flow of Casson nanofluid through an asymmetric permeable channel filled with a porous medium in the presence of electroosmosis. Magnetohydrodynamics and radiative heat transfer are also considered. The study is motivated by industrial micro‐pumping systems utilizing multi‐functional nanomaterials. Researchers have investigated the distinct temperature and rheological properties of Casson nanofluids. Solutal molecular diffusion and nanoparticle diffusion are both examined. Mixing nanoparticles with Casson fluid alters its flow characteristics and heat transmission, amalgamating different properties that are useful in a wide range of industrial and scientific applications. Buongiorno's two‐component nanoscale model is deployed for simulating nanofluid transport, and the Rosseland diffusion flux is utilized for optically thick electromagnetic liquids. Heat generation or absorption and cross‐diffusion (Soret and Dufour) effects are also incorporated in the model. An efficient analytical approach known as the long wavelength‐low Reynolds number lubrication approximation (LWL‐LRN) is utilized to solve the non‐dimensional boundary value problem. Validation of the solutions with previous studies is included. Graphs are presented using MATLAB 2022b to visualize the influence of key parameters including permeability, magnetic field, thermal radiation, Grashof number, Brownian motion, thermophoresis, electrical field and Prandtl number on transport characteristics (velocity, temperature, concentration), and trapping phenomena associated with peristaltic propulsion. As thermophoresis and Brownian parameters are intensified, there is a strong response in nanoparticles which induces axial acceleration, as observed at locations y = 0.15, where u = 0.191, and y = 0.33, where u is elevated to 0.14. An increase in radiation parameter () results in a depletion in axial velocity magnitudes along the left half of the wall and also modifies velocity distribution in the right section of the microchannel. An increase in the thermal radiation parameter (Rn) and heat absorption (sink) is found to suppress temperatures. Increasing heat generation, thermal Grashof number (Gr), and solutal Grashof number (Gc) decelerate axial flow in the left half space but accelerate flow in the right half space of the micro‐channel. Increasing radiation parameters and thermal Biot number boost temperatures when heat sink is present but reduce them when heat source (generation) is present. Increasing radiation parameter boosts nanoparticle volume fraction (concentration) whereas an elevation in heat generation and thermal Biot number both induce the opposite effect. Increasing the magnetic field damps the flow and reduces the number of boluses present. However, bolus volume increases with greater thermal Grashof Number , Darcy (permeability) number , and Helmholtz‐Smoluchowski velocity , that is, stronger axial electrical field.

Analyzing the exothermic reactions of [formula omitted] nanoparticles with the Dufour effect and the influence of the heat generation and permeability past a porous moving surface

The heat and mass concept is analyzed through the properties of the Dufour number, chemical reactions, and the heat generation parameters on MHD incompressible nanofluids flow. The MATLAB software with the finite difference method (FDM) was employed to find and graphically present the system’s numerical solutions. This study finds an increased Dufour number enhancing the flow speed and hotness of the nanofluid. The chemical reactions released heat energy to the surrounding environment, escalating the nanofluid’s temperature and decreasing the concentration of the nanoparticles. The rate of permeability strengthens the flow velocity by improving the flow network. The increased heat generation parameter influenced the increase in nanofluids’ velocity and temperature. This study can be considered in some applications, such as designing heat exchangers, solar cells, climate changes, and separation process industries.

Thermo diffusion and diffusion thermo effects on unsteady flow over a curved surface

Application, Purpose, and Methodology: The Soret and Dufour effects, which are also referred to as cross-diffusion gradients, are advantageous to the manufacturing of binary alloys, the transmission of groundwater contamination, the extraction of oil, and the separation of gas. These are an example of a gradient, which occurs when substances diffuse over one another. The Dufour effect is responsible for the transfer of heat, whereas the Soret effect is concerned with the movement of materials. Both effects are caused by differences in concentration. Temperature differences are the link between the two effects. The Soret and Dufour statistics, in conjunction with the joule heating process, are utilized by us. Through the use of the convergent series, solutions for temperature, speed, and concentration are ultimately found. Core Findings: The findings of these investigations may give researchers engineering and industrial solutions that are unique and advantageous. The computation that is being done right now demonstrates that the sense of radial velocity diminishes as the Hartman number increases. In addition, the temperature of the fluid drops when there is a greater quantity of Prandtl and Soret than before. Methodology: Using the proper transformations, the numerical solution to the micropolar fluid flow problem over a curved stretched disk entails simplifying the partial differential equation system into an ordinary differential equation. This is done to solve the problem. In the process of converting partial differential equations into ordinary differential equations, similarity transformations are utilized. During the shooting process, we use the Runge-Kutta method to solve coupled equations and obtain numerical solutions. By utilizing the nondimensional radius of curvature, we can determine the nondimensional radius of curvature and report the fluid. Future Work: When compared to flat sheets, curved stretched sheets exhibit differences that result in significant boundary layer strain. This is something that will be worked on in the future. Research in the future might concentrate on further investigating these distinctions and the practical ramifications they have, with the possibility of expanding the scope of the investigation to include a variety of engineering and industrial applications in which these effects play an important role.

Impact of activation energy and cross-diffusion effects on 3D convective rotating nanoliquid flow in a non-Darcy porous medium

PurposeThis study aims to investigate numerically the impact of the three-dimensional convective nanoliquid flow on a rotating frame embedded in the non-Darcy porous medium in the presence of activation energy. The cross-diffusion effects, i.e. Soret and Dufour effects, and heat generation are included in the study. The convective heating condition is applied on the bounding surface.Design/methodology/approachThe control model consisted of a system of partial differential equations (PDE) with boundary constraints. Using suitable similarity transformation, the PDE transformed into an ordinary differential equation and solved numerically by the Runge–Kutta–Fehlberg method. The obtained results of velocity, temperature and solute concentration characteristics plotted to show the impact of the pertinent parameters. The heat and mass transfer rate and skin friction are also calculated.FindingsIt is found that both Biot numbers enhance the heat and mass distribution inside the boundary layer region. The temperature increases by increasing the Dufour number, while concentration decreases by increasing the Dufour number. The heat transfer is increased up to 8.1% in the presence of activation energy parameter (E). But, mass transfer rate declines up to 16.6% in the presence of E.Practical implicationsThe applications of combined Dufour and Soret effects are in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The nanofluid with porous medium can be used in chemical engineering, heat exchangers and nuclear reactor.Social implicationsThis study is mainly useful for thermal sciences and chemical engineering.Originality/valueThe uniqueness in this research is the study of the impact of activation energy and cross-diffusion on rotating nanoliquid flow with heat generation and convective heating condition. The obtained results are unique and valuable, and it can be used in various fields of science and technology.

Ternary hybrid nanofluid flow through an inclined shrinking sheet when soret, dufour and quadratic thermal radiation are significant: an irreversibility analysis with various shape factors

As nanofluid technology continues to evolve, the knowledge gained from studying flow over an inclined shrinking sheet can be applied to various emerging applications. These could include heat pipes for spacecraft thermal management, thermal management systems for wearable electronics, or even designing microfluidic channels for efficient desalination processes. A ternary hybrid nanofluid (Ethylene Glycol, Copper (II) oxide, Titanium dioxide, and Silicon dioxide) is the main focus of this study, which aims to theoretically analyse its behaviour through a tilted shrinking sheet in the presence of heat source, Dufour, and Soret effects. Governing equations are transformed into a set of ordinary differential equations using appropriate similarity transformations and then solved using bvp4c solver. The main findings of this study are that enhancing the value of the couple stress parameter leads to a decline in fluid velocity, and increasing the Dufour number will upsurge the temperature of the fluid. It has been noticed that the Sherwood number exhibits a decline when the Soret number increases. We find that the Nusselt number noticeably increases by 0.147404161 (spherical), 0.151277029 (brick), and 0.156726935 (cylinder) for values of the Dufour number within the range of 0 to 3.

Joule heating, Dufour and Soret effects on MHD hybrid nanoliquid flow over a moving thin needle in a porous medium with thermal radiation

Joule heating, Dufour and Soret effects on MHD hybrid nanoliquid flow over a moving thin needle in a porous medium with thermal radiation

Induced magnetic field and Soret–Dufour effects on viscous dissipative Casson fluid flow through porous medium over a stretching sheet

Induced magnetic field and Soret–Dufour effects on viscous dissipative Casson fluid flow through porous medium over a stretching sheet

Soret and Dufour effects on Sutterby nanofluid flow over a Riga stretching surface with variable thermal conductivity

Soret and Dufour effects on Sutterby nanofluid flow over a Riga stretching surface with variable thermal conductivity

Dufour Effect on Chemically Reacting Casson Fluid Flow Over a Nonlinearly Stretching Sheet with Radiation Absorption

Dufour Effect on Chemically Reacting Casson Fluid Flow Over a Nonlinearly Stretching Sheet with Radiation Absorption

Rotation and Dufour Impact on Unsteady Flow Past a Parabolic Accelerated Vertical Plate with Uniform Temperature and Mass Diffusion

Objective : Fluid dynamics and heat transfer theory examine the Dufour phenomenon and the rotational influence of unstable parabolic flow across an accelerating infinite vertical plate. This scenario involves several parameters, including the "mass Grashof number (Gr), thermal Grashof number (Gc), Prandtl number (Pr), Hartmann number (Ha), Schmidt number (Sc), Dufour number (Dc), and acceleration parameter". Method : We have applied the Laplace transform method to the resulting PDE. This method converts the equations to algebraic form, making it easier to solve for velocity, temperature, and concentration in terms of time and space. Graphs can show the relationship between the acceleration parameter and numerous parameters such as mass and thermal Grashof, Hartmann (Ha), and Dufour (Df), as well as the consequent velocity profile. If the velocity increases when these variables change, we'll look at the physical reasons that generate this behaviour. We will examine the conclusions using experimental data or existing theoretical models, considering the model's assumptions and limits. Finally, highlight the significant facts and insights gained from the analysis. We will discuss potential future research possibilities, such as exploring more complex geometries or accounting for new physical effects. Findings : The increase in Dufour parameter value causes an increase in temperature and level trends, demonstrating the significant influence of these factors on the researched phenomena. Novelty: This research advances our understanding of heat and mass transfer phenomena by isolating the Dufour effect in a novel scenario involving unsteady flow around a rotating vertical plate, filling a gap in the existing body of knowledge that is dominated by MHD-inclusive investigations. Suggestions: This approach is fairly general and may be applied to find analysis of heat and mass transfer on Dufour effect for other effects such as Soret effect, Hall current of heat and mass transfer. Keywords: Uniform Temperature, Thermo diffusion (Dufour), Inverse Laplace, Rotational, Constant Mass