Dufour Parameter Research Articles

Novel Investigation of Heat and Mass Transfer Under the Effects of Thermal Radiations

The investigation of the fluid flow characteristics between opening/narrowing channel attains much attention of the researchers and scientists. Such flows extensively used in the field of medical sciences and in different engineering fields. Therefore, keeping in mind the significance of the study, the heat and mass transport analysis of second grade fluid is conducted in radiative channel. The problem is formulated via similarity transform and then treated analytically by using Homotopy Analysis technique. After mathematical treatment, the role of various flow quantities on the heat and thermal transport are detected under the domain of interest. It is noted that the temperature augmented against Dufour and Deborah parameters. Further, the rate of heat transfer intensifies for higher Prandtl and Eckert numbers. The decreasing trends in the mass transfer due to Schmidt and soret parameters are observed. Finally, a comparative literature is provided which authenticate the analysis under certain assumptions.

A decoupled wavelet approach for multiple physical flow fields of binary nanofluid in double-diffusive convection

The paper aims at applications of a decoupled wavelet method for investigating multiple physical steady flow fields of binary nanofluids in double-diffusive mixed convection. The Buongiorno’s mathematical model of nanofluids is further perfected in the presence of Dufour and Soret effects, incorporating with linear and nonlinear diffusiophoresis effects based on experiments [Chemical Engineering Science 176 (2018): 632–640]. Nonhomogeneous thermal boundaries corresponding to heat flux on vertical walls and convection heat transfer at the bottom along with moving top lid are effectively approximated by interpolated Coiflet-type wavelet. Highly coupled and nonlinear governing equations for the complex fields of temperature, nanoparticles volume fraction and solute concentration have been formulated and decomposed into linear differential ones by homotopy transformation. Numerical wavelet solutions with larger range of physical parameters are finally obtained and validated by solving a set of iterative algebra equations applying Galerkin method, which are difficult to be given by traditional numerical methods. The results reveal that nanoparticles and double-diffusive buoyancy parameters, the thermo-nanofluid and thermo-solutal Lewis numbers, the heat conductivity coefficient, the periodical heat flux with different phase differences, the diffusiophoresis parameters, the nanoparticles and solute Dufour parameters, the solute Soret parameter are of great significance on characteristics of heat and mass transfer in the complex flow.

Impact of Soret and Dufour on bioconvective flow of nanofluid in porous square cavity

AbstractThis article addresses the bioconvection in a porous cavity associated with Soret and Dufour effects. The bioconvective flow in a porous medium is based on Hillesdon and Pedley's model and is governed by nonlinear partial differential equations. These equations are transformed into a dimensionless form with suitable nondimensional parameters. The finite element method is employed to solve the dimensionless equations. The outcomes of the study are presented by streamlines, temperature distributions, isoconcentrations of solute, nanoparticles, and microorganisms. Furthermore, the tendency of average Nusselt number and average Sherwood number and the influence of Soret parameter, Dufour parameter, Peclet number, and bioconvective Rayleigh number is interpreted. Thermophoresis and Soret number show a strong effect on the concentration of nanoparticles. Brownian motion and thermophoresis exhibit a significant effect on the density distributions of microorganisms. The novelty of the paper is to combine the effects of Soret–Dufour and oxytactic bioconvection. The present study can be useful in the following applications: microbial‐enhanced oil recovery, toxin removal, antibiotics, and modeling of microfluidic devices.

Convective stability of a permeable nanofluid inside a horizontal conduit: Fast chemical reactions

This problem considers the instabilities, which can occur when a horizontal sparsely filled nanofluid porous layer is saturated with a binary mixture with fast chemical reaction. The upper and lower plates are heated isothermally. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The energy equation includes cross and regular diffusion conditions. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified; hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The oscillatory and stationary convection are evaluated analytically. The reaction rate is supposed to be greater than the diffusion rate. We find that both a stationary instability and an oscillatory instability can occur as the first bifurcation, depending on the sign and the value of the heat of reaction. The execution of the porous parameter, Prandtl number, Soret parameter, Dufour parameter, Lewis number, solutal Rayleigh number, chemical reaction and the modified diffusivity ratio parameters is implemented pictorially. It is found that the presence of nanoparticles the critical Rayleigh number is increased and helps to stabilize the system. The presence of chemical reaction parameter destabilizes the system. The results of previously-published work are also obtained as special cases of the general solution.

Thermal and concentration convection in nanofluids for peristaltic flow of magneto couple stress fluid in a nonuniform channel

This article addresses the influence of double-diffusivity convection in nanofluids in relation to peristaltic flow of magneto couple stress fluid in a nonuniform channel. Firstly, mathematical formulations of magneto couple stress fluid in the presence of double-diffusivity convection in nanofluids for 2-dimensional and 2-directional flows are described in detail. The highly nonlinear equations are simplified using approximation of long wavelength and low but finite Reynolds number. Exact solutions of stream function, axial induced magnetic field, axial pressure gradient, nanoparticle volume fraction temperature and concentration are computed. Graphical representations of numerous physical parameters of interest are presented to explain the conduct of flow quantities. It is observed from graphical plots that temperature profile and solutal concentration increases by increasing values of thermophoresis, Brownian motion, Soret and Dufour parameters.

MHD double-diffusive mixed convection of binary nanofluids through a vertical porous annulus considering Buongiorno’s two-phase model

Binary nanofluids are prepared using a binary liquid (e.g., salt water) instead of a pure liquid as their host fluid. Double-diffusive convection in this type of nanofluids is a kind of triple-diffusive process, which simultaneously includes diffusions of heat, nanoparticles, and solute. This paper is devoted to double-diffusive mixed convection of binary nanofluids flowing through a vertical porous annulus in the presence of an externally applied radial magnetic field. To simulate the problem, a new mathematical model following the Buongiorno’s two-phase model is proposed. The equations are solved numerically by means of the finite-volume method. Thereafter, effects of the involved dimensionless variables on the distributions of stream function, temperature, solute concentration, and nanoparticles fraction as well as the mean values of the Nusselt number and the solute Sherwood number are presented and discussed. Inspection of the results demonstrates the significant contributions of the Peclet number (Pe), the usual Lewis number (Le), and the Soret-solute Lewis number (Ld) on the simulation results. In spite of that, the effects of the Hartmann number (Ha) and the thermophoresis parameter (Nt) on the simulation results are weak, while the consequences of the nanofluid Lewis number (Ln), the double-diffusive ratio (Nc), the buoyancy ratio (Nr), and the Dufour parameter (Nd) on the Nusselt and Sherwood numbers are insignificant.

Entropy Generation for MHD Maxwell Nanofluid Flow Past a Porous and Stretching Surface with Dufour and Soret Effects

In this study, the entropy generation for magnetohydrodynamic (MHD) mixed convection and Maxwell nanofluid flow is discussed. The flow is considered over a stretching and penetrable surface. The thermal conductivity, velocity slip condition, and thermal radiation are also considered for the flow system. The entropy generation and irreversibility analysis have been considered and the impact of the physical parameters has been observed. The modeled equations are converted into a set of non-linear ODEs with the help of similar transformable variables. The sophisticated homotopy analysis method (HAM) is used to obtain analytic approximations for the resulting system of non-linear differential equations. Among the many outputs of the study, it is found that the velocity distribution is a decreasing function of Maxwell, magnetic parameters, and an increasing function of mixed convection factor within the boundary layer. Temperature profile upsurges with a consistent expansion in radiation thermophoretic and Dufour parameters. The Bejan number increases with an increase in the Brinkman number and radiation parameter. The concentration profile increases with an augmentation of the Soret number and decreases with increasing values of the Schmidt number.

Hybrid Effects of Thermal and Concentration Convection on Peristaltic Flow of Fourth Grade Nanofluids in an Inclined Tapered Channel: Applications of Double-Diffusivity

This article brings into focus the hybrid effects of thermal and concentration convection on peristaltic pumping of fourth grade nanofluids in an inclined tapered channel. First, the brief mathematical modelling of the fourth grade nanofluids is provided along with thermal and concentration convection. The Lubrication method is used to simplify the partial differential equations which are tremendously nonlinear. Further, analytical technique is applied to solve the differential equations that are strongly nonlinear in nature, and exact solutions of temperature, volume fraction of nanoparticles, and concentration are studied. Numerical and graphical findings manifest the influence of various physical flow-quantity parameters. It is observed that the nanoparticle fraction decreases because of the increasing values of Brownian motion parameter and Dufour parameter, whereas the behaviour of nanoparticle fraction is quite opposite for thermophoresis parameter. It is also noted that the temperature profile decreases with increasing Brownian motion parameter values and rises with Dufour parameter values. Moreover, the concentration profile ascends with increasing thermophoresis parameter and Soret parameter values.

Two-Dimensional Flow Through the Uniformly Porous Horizontal Pipe with Thermal Radiation and Cross-Diffusion Effects

This paper is dedicated to the mathematical analysis of an axisymmetric, steady Newtonian fluid flow through a horizontal pipe within the occurrence of radiation, Dufour, and Soret effects. The flow is exposed to associate outwardly functional constant suction above the pipe along Z-direction. The homotopy analysis methodology (HAM) is utilized to get semi-analytical solutions for the coupled differential equations. The results of diverse rising constraints on velocities, thermal and solutal are discussed and pictured. The flow is studied through streamlines, isotherms and pressure contours area unit likewise shown as pictured. It is identified that the temperature can increase with an increase in Dufour parameter but decelerates with an improvement in the radiation parameter. For the given increase within the Soret number, the concentration decelerates.

Convective heat and mass transfer of chemically reacting fluids with activation energy along with Soret and Dufour effects

We examine within this content of the paper the characteristics of heat transfer and transfer of mass along with activation energy about a chemically reacting viscous fluid in rotating frame. The effect of Soret and Dufour parameter is done additionally. The porous space gets filled by flow in stretched sheet. The influence of different standards of parameters like rotational, porosity, temperature difference etc., on velocity, concentration and temperature is displayed by graphs. Arithmetical results are tabulated. The concentration is increased by Soret parameter and decreased by Dufour parameter. When compared to distributions of temperature and concentration on rotary motion, the velocity has opposite effects. The Nusselt number, Sherwood number and Skin friction coefficients are discussed numerically.

Impact of power law fluid and magnetic field on double diffusive mixed convection in staggered porous cavity considering Dufour and Soret effects

This study deals the influence of power law fluid and inclined magnetic field on a porous medium in staggered cavity. The effect of Soret and Dufour parameters are also given attention. A two dimensional system of partial differential equations has been discretized by employing Galerkin finite element method. A finite element method involving the cubic polynomials (ℙ3) has been implemented to compute for velocity, temperature and concentration fields while the pressure is approximated by quadratic (ℙ2) finite element space of functions. The system of discretized equations is simplified using the adaptive Newton's method. Simulations are performed for various ranges of pertinent parameters such as power law index (between 0.6 and 1.8), Hartmann number (between 0 and 100), Lewis number (between 1 and 10), Dufour/Soret numbers (between −3 and 3), Darcy number (between 10−5 and 10−2), magnetic field inclination (between 0∘ and 90∘) and buoyancy ratio (between 0 and 10). It is inferred that the retarding effect of the rising Lorentz force is pronounced on fluid flow. The convective heat transfer is enhanced with the change of Dufour number from negative to positive. The suppression on convection at the inclination angle γ = 90∘ is much more than γ = 0∘. The increment in Dufour and Soret numbers has an improving influence on both the average Nusselt and Sherwood numbers, and thus the convective heat and mass transfer at buoyancy ratio N = 10.

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

In the current article, the analysis of magnetohydrodynamic laminar flow past a vertical permeable surface is presented. The flow is considered in the existence of Dufour as well as Soret effects. There is a diffusion-thermo process when heat transmission is encouraged by the concentration gradient and thermo diffusion process when the transfer of mass is encouraged by the thermal gradient. The set of partial differential equations (PDEs) for a modeled problem is changed into a set of ordinary differential equations by applying selected non-dimensional similarity transformations. The semi-analytical method HAM is used to determine a solution for the modeled problem. The features of flow characteristics such as velocity, temperature, and concentration profiles in response to the variations of the emerging parameters are simulated and examined in detail. This research article aims to analyze the impacts of surface tension thermo-solutal quotient, Soret parameter, Dufour parameter, Schmidt number, and Prandtl number on the fluid momentum, transfer of heat, and mass. It is noticed in this article that, the gradient of temperature and concentration at the surface is escalated with enhancement in thermo-solutal surface tension. It is further noted that augmentation in the Prandtl number augmented the transfer in heat.

WITHDRAWN: 2D model of Casson fluid flow considering Soret and dufour effects in presence of radiation

In this analysis, within the sight of compound response and warmth age/ingestion over a stretched, surface in permeable medium the impacts of sore, dufour and thermal radiation on two-dimensional MHD Casson liquid flows are studied. Utilizing the Homotopy investigation strategy, the governing dimensionless arrangement of standard differential conditions is solved by reducing the unique arrangement of halfway differential conditions utilizing sufficient variable adjustment. Effects of various predominant parameters: radiation parameter, soret parameter, dufour parameter, magnetic parameter, synthetic response, heat age/ingestion, and Casson fluid parameter are discussed and represented by graph on heat and mass transfer of two-dimensional MHD flow. Skin contact, Nusselt number, and Sherwood number expressions are derived and evaluated for various parameter values.

Double diffusion in a rectangular duct using metals or oxides suspended in a viscous fluid

In this study, double diffusive free convection of nanofluid within a confined rectangular duct is investigated numerically. The momentum and energy equations are placed in the form of difference equations and solved numerically. The left wall conditions for the concentration and temperature are lesser than those of the right wall and the upper and lower walls are insulated. Different nanofluids are considered such as mixtures with copper, diamond, silicon oxide and titanium oxide, suspended in water. Brinkman and Maxwell models are used to characterize the nanofluid. Tiwari and Das model is opted to define the nanofluid behavior. The simulations are conducted using different nanoparticles, thermal Grashof number 1 ≤ GrT ≤ 20, solute Grashof number 1 ≤ GrC ≤ 15, solid volume fraction 0 ≤ Φ ≤ 0.05, Dufour number 0 ≤ Df ≤ 1, Brinkman number 0 ≤ Br ≤ 2, and Soret number 0 ≤ Sr ≤ 5. Additionally, behavior of volumetric flow strength, skin friction, heat transport intensity and Sherwood number is also examined. The thermal Grashof number, Brinkman number, Dufour, Soret and Schmidt parameters accelerate the velocity and temperature and dwindle the concentration whereas the reversal effect was obtained for the solid volume fraction. The concentration Grashof number diminishes the velocity and temperature and intensifies the concentration. The silver nanoparticles produce the highest velocity whereas diamond nanoparticles cause the lowest velocity and temperature. The maximum temperature is attained with silicon oxide.

Half-breed effects of thermal and concentration convection of peristaltic pseudoplastic nanofluid in a tapered channel with induced magnetic field

Study the significance of double-diffusive convection and induced magnetic field on peristaltic flow of pseudoplastic nanofluid in a tapered asymmetric channel with different four wave forms have been investigated. Formulation and governing equations of this problem were deduced representing by highly partial differential equations. Hence, exact and analytical solutions of the resulting equations were deduced. Therefore, effects of pressure rise, pressure gradient, temperature, concentration, nanoparticle volume fraction, magnetic force function and stream functions were graphical represented and discussed. It was found that, on rising in the tapered asymmetric channel parameter, the pumping rate increases (decreases) in copumping region (in the retrograde pumping and free pumping regions). Further, the temperature distributions increase with growing in Brownian motion, Soret, Dufour and thermophoresis parameters while the concentration profile decreases with these parameters.

Hall and ion slip impact on magneto-titanium alloy nanoliquid with diffusion thermo and radiation absorption

The radiation-absorption, diffusion-thermo and Hall and ion slip effects, on MHD-free convective rotating flow of nanofluid (Ti6Al4V-H2O) past a semi-infinite permeable moving plate with a constant heat source, are discussed. Making use of the Perturbation technique, we found that velocity, temperature and concentration are discussed through graphs. We evaluated the skin friction, Nusselt number and Sherwood number analytically and then discussed computationally. The resultant velocity reduces with increasing rotation parameter, magnetic parameter, suction parameter and enhances with increasing Hall and ion slip parameters and Dufour parameter. Nusselt number decreases with Dufour parameter and Sherwood number increases with chemical reaction parameter.

Thermo diffusion aspects in Jeffrey nanofluid over periodically moving surface with time dependent thermal conductivity

Double diffusion flow of Jeffrey fluid in presence of nanoparticles is studied theoretically under time dependent thermal conductivity. The considered nanoparticles are evaporated over convectively heated surface which moves periodically in its own plane. The appropriate dimensionless variables are employed to obtain the dimensionless forms of governing equations. We computed the analytical solution of non-linear differential equations by utilizing homotopy analysis method. The present investigation reveals the features of various emerging parameters like Deborah number, combined parameter, oscillation frequency to stretching rate ratio, Prandtl number, Lewis number, thermophoresis parameter, Brownian motion parameter, nano Lewis number, modified Dufour parameter, and Dufour solutal Lewis number. A useful enhancement in movement of nanoparticles is observed by utilizing the combined magnetic and porosity effects. Unlike traditional studies, present analysis is confined with the unsteady transportation phenomenon from periodically moving surfaces. Such computation may be attributable in flow results from tensional vibrations due to stretching and elastic surfaces. The simulation presented here can be attractable significance in the bioengineered nanoparticles manufacturing. It is observed that the heat transportation of nanoparticles may efficiently enhance through the utilization of variable thermal conductivity. The solutal concentration decreases with increasing Deborah number and Lewis number. It is further noted that the nano Lewis number causes reduction of nanoparticles concentration.

Effects of thermal and concentration convection and induced magnetic field on peristaltic flow of Williamson nanofluid in inclined uniform channel

Noteworthiness of double-diffusive convection with nanofluids by induced magnetic field and diverse wave shapes for peristaltic stream of Williamson fluid in a uniform channel has been theoretically examined. Mathematical formulation of two-directional and two-dimensional flow of a Williamson fluid model is explained in detail. The exact solutions of nanoparticles are described. Perturbation solutions of nonlinear PDEs are also calculated. Numerical and graphical results are displaced to see the conduct of temperature, concentration, nanoparticle volume fraction, pressure rise, pressure gradient, magnetic force function and stream functions. It is concluded that the profile of temperature increases and profile of concentration decreases by increasing values of Brownian motion parameter $$ N_{\text{b}} $$ , thermophoresis parameter $$ N_{\text{t}} $$ , Dufour parameter $$ N_{TC} $$ and Soret parameter $$ N_{CT} $$ .

Numerical simulation of double diffusive convection and electroosmosis during peristaltic transport of a micropolar nanofluid on an asymmetric microchannel

A numerical computation is performed to analyze the double diffusive convection in micropolar nanofluids flow governed by peristaltic pumping in an asymmetric microchannel, in the presence of thermal radiation and an external magnetic field. The highly nonlinear governing equations are diluted by using desirable physical assumptions such as lubrication approximation and low zeta potential. Convective boundary conditions are employed. This enables us to determine numerical estimates of various physical flow variables such as velocity, pressure gradient, spin velocity, temperature of the nanofluid, concentration of solute, and volume fraction of nanoparticles for sundry parameters like micropolar parameter, coupling parameter, solutal Grashof number, thermophoretic diffusion coefficient, Grashof number, thermal radiation parameter and Helmholtz–Smoluchowski velocity with the aid of bvp4c function built-in command of MATLAB 2012b. Influence of each relevant parameter on flow, thermal and species characteristics are computed in this study. Influence of Soret and Dufour parameters are also simulated. This model is applicable to the study of chemical fraternization/separation procedures and various thermal management systems like of heat sinks, thermoelectric coolers, forced air systems and fans, heat pipes, and many more.

Entropy production minimization and non-Darcy resistance within wavy motion of Sutterby liquid subject to variable physical characteristics

Non-Darcy resistance in peristaltic transport of Sutterby liquid in curved configuration is modeled. Variable characteristics of material (i.e., thermal conductivity and viscosity) are taken as temperature-dependent. Soret and Dufour features have also been retained. Problem is modeled by using conservation laws. Long wavelength and small Reynolds number have been invoked. Resulting problems have been solved numerically. Entropy optimization analysis is made. Axial velocity, temperature, concentration, entropy, Bejan number and heat transfer rate are examined for influential variables. It is found that velocity increases for variable viscosity coefficient and porous-space parameter. Temperature decreases for increased values of variable thermal conductivity. Opposite behavior of mass and energy is noted for Soret and Dufour parameters. Entropy minimized for thermal conductivity and viscosity coefficients. Entropy enhancement is noticed for Soret and Dufour parameters. Heat transfer rate at upper wall is enhanced for Soret and Dufour variables.