Cross-diffusion Effects Research Articles

Cattaneo-Christov heat flux effect on hydromagnetic radiative Oldroyd-B liquid flow across a cone/wedge in the presence of cross-diffusion

The present article scrutinizes the prominent characteristics of the Cattaneo-Christov heat flux on magnetohydrodynamic Oldroyd-B radiative liquid flow over two different geometries. The effects of cross-diffusion are considered in the modeling of species and energy equations. Similarity transformations are employed to transmute the governing flow, species and energy equations into a set of nonlinear ordinary differential equations (ODEs) with the appropriate boundary conditions. The final system of dimensionless equations is resolved numerically by utilizing the R-K-Fehlberg numerical approach. The behaviors of all physical pertinent flow controlling variables on the three flow distributions are analyzed through plots. The obtained numerical results have been compared with earlier published work and reveal good agreement. The Deborah numbers $ \gamma_{1}$ and $ \gamma_{2}$ have quite opposite effects on velocity and energy fields. The increase in thermal relaxation parameter $ \beta$ corresponds to a decrease in the fluid temperature. This study has salient applications in heat and mass transfer manufacturing system processing for energy conversion.

INFLUENCE OF CROSS DIFFUSIONS ON MIXED CONVECTION CHEMICAL REACTION FLOW IN A VERTICAL CHANNEL WITH NAVIER SLIP: HOMOTOPY APPROACH

This paper is to examine the incompressible, laminar mixed convective Navier slip flow between vertical plates with cross diffusion effects. This research includes the first order chemical reaction also. The resulting equations with boundary conditions are reduced into dimensionless form using appropriate transformations. The series solutions are developed through a modern technique known as the homotopy analysis method. The convergent expressions of velocity components and temperature are derived. The influence of emerging parameters on fluid flow quantities have been presented graphically. Also, the nature of physical quantities are shown in tabular form.

Non-Linear Boussinesq Approximation and Cross-Diffusion Effects on an Ostwald-de-Waele Power-Law Fluid Flow with Convective Boundary Condition

Non-Linear Boussinesq Approximation and Cross-Diffusion Effects on an Ostwald-de-Waele Power-Law Fluid Flow with Convective Boundary Condition

Flow Over an Exponentially Stretching Porous Sheet with Cross-diffusion Effects and Convective Thermal Conditions

This article investigates the influence of cross-diffusion on the viscous fluid flow over a porous sheet stretching exponentially by applying the convective thermal conditions. Velocity slip at the boundary is considered. The numerical solutions to the governing equations are evaluated using successive linearisation procedure and Chebyshev collocation method. It is observed from this study that the rate of heat transfer escalated with enhance in the Biot number and reduced with increase in dufour number. While, the rate of mass transfer from the sheet to the fluid reduced with increase in both soret and Biot numbers. Finally, the obtained results for rate of heat transfer are compared with the published results in the literature for special cases. The influence of the pertinent parameters on the physical quantities are displayed through graphs.

Cross-diffusion effects on an exponentially stretching sheet in a doubly stratified viscous fluid

This article analyses the influence of double stratification and cross-diffusion effects on the viscous fluid flow over a porous sheet stretching exponentially by applying the velocity slip at the boundary. The numerical solutions to the governing equations are evaluated using successive linearisation procedure and the Chebyshev collocation method. The results obtained are compared with the existing results in the literature for special cases. The influence of the pertinent parameters on the physical quantities are displayed through graphs.

Free Convection from a Rotating Vertical Porous Plate in a Dissipative Micropolar Fluid with Cross Diffusion Effects

Free Convection from a Rotating Vertical Porous Plate in a Dissipative Micropolar Fluid with Cross Diffusion Effects

Nonlinear Thermal Convection in Jeffrey Liquid Flow with Cross Diffusion Effects Past a Stretched Surface

Nonlinear thermal convection in heat and mass transfer mechanism of dissipating Jeffrey liquid is investigated. The impact of cross diffusion and convective conditions are also accounted. Before integrating pertinent partial differential equations; a set similarity variables are employed to reduce them into multidegree ordinary differential equations. The validation process comprised a comparison with existing data, reaching an excellent agreement. Later, the influence of distinct physical parameters on diverse flow characteristics are comprehensively discussed and analyzed. It is established that the nonlinear convection is favourable for the escalation of the thickness of momentum boundary layer. Further, the convective conditions are used as controlling constraints.

Numerical Solutions by EFGM of MHD Convective Fluid Flow Past a Vertical Plate Immersed in a Porous Medium in the Presence of Cross Diffusion Effects via Biot Number and Convective Boundary Condition

In this investigation, the numerical results of a mixed convective MHD chemically reacting flow past a vertical plate embedded in a porous medium are presented in the presence of cross diffusion effects and convective boundary condition. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved numerically using a highly accurate and thoroughly tested element free Galerkin method (EFGM). The effects of the Soret number, Dufour number, Grashof number for heat and mass transfer, the viscous dissipation parameter, Schmidt number, chemical reaction parameter, permeability parameter and Biot number on the dimensionless velocity, temperature and concentration profiles are presented graphically. In addition, numerical results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are discussed through tabular forms. The discussion focuses on the physical interpretation of the results as well as their comparison with the results of previous studies.

Comment on the paper “Convection from an inverted cone in a porous medium with cross-diffusion effects, F.G. Awad, P. Sibanda, S.S. Motsa, O.D. Makinde, Comput. Math. Appl. 61 (2011) 1431–1441”

The present comment concerns some doubtful results included in the above paper.

Homotopy analysis for the influence of Navier slip flow in a vertical channel with cross diffusion effects

This research is to examine the laminar, incompressible free convective Navier slip flow between vertical plates with cross diffusion effects. This investigation includes the first order chemical reaction also. The resulting equations with boundary conditions are reduced into dimensionless form using suitable transformations. Homotopy analysis method has been applied to solve the system. The influence of emerging parameters on fluid flow quantities have been presented graphically. In addition, the nature of physical quantities are shown in tabular form.

Effect of cross-diffusion on the stationary problem of a Leslie prey-predator model with a protection zone

In this work, we study the change of behavior of positive solutions in a Leslie predator-prey model when a simple protection zone and cross-diffusion for the prey are introduced. We analyze the effects of cross-diffusion and protection zone on the bifurcation continuum of positive solutions. The asymptotic behavior of positive solutions is also discussed as the cross-diffusion and the birth rate of the predator tend to infinity, respectively. Finally, for small birth rates of two species and large cross-diffusion for the prey, the detailed structure and stability of positive solutions are established. Our results indicate that the environmental heterogeneity, together with large cross-diffusion, can produce much more complicated stationary patterns, moreover, our research here reveals significant difference from those studied in Du et al. (J Differ Equ 246:3932-3956, 2009), Oeda (J Differ Equ 250:3988-4009, 2011) and Wang and Li (Nonlinear Anal Real World Appl 14:224-245, 2013).

Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel: Effects of Joule heating and Helmholtz-Smoluchowski velocity

The present article studies theoretically the electrokinetic pumping of nanofluids with heat and mass transfer in a micro-channel under peristaltic waves, a topic of some interest in medical nano-scale electro-osmotic devices. The microchannel walls are deformable and transmit periodic waves. The Chakraborty-Roy nanofluid electrokinetic formulation is adopted in which Joule heating effects are incorporated. Soret and Dufour cross-diffusion effects are also considered. Under low Reynolds number (negligible inertial effects), long wavelength and Debye linearization approximations, the governing partial differential equations for mass, momentum, energy and solute concentration conservation are derived with appropriate boundary conditions at the micro-channel walls. The merging model features a number of important thermo-physical, electrical and nanoscale parameter, namely thermal and solutal Grashof numbers, the Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) and Joule heating to surface heat flux ratio. Closed-form solutions are derived for the solute concentration, temperature, axial velocity, averaged volumetric flow rate, pressure difference across one wavelength, and stream function distribution in the wave frame. Additionally expressions are presented for the surface shear stress function at the wall (skin friction coefficient), wall heat transfer rate (Nusselt number) and wall solute mass transfer rate (Sherwood number). The influence of selected parameters on these flow variables is studied with the aid of graphs. Bolus formation is also visualized and analyzed in detail.

Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation

AbstractThe problem of an unsteady MHD Casson fluid flow towards a stretching surface with cross diffusion effects is considered. The governing partial differential equations are converted into a set of nonlinear coupled ordinary differential equations with the help of suitable similarity transformations. Further, these equations have been solved numerically by using Runge-Kutta fourth order method along with shooting technique. Finally, we studied the influence of various non-dimensional governing parameters on the flow field through graphs and tables. Results indicate that Dufour and Soret numbers have tendency to enhance the fluid velocity. It is also found that Soret number enhances the heat transfer rate where as an opposite result is observed with Casson parameter. A comparison of the present results with the previous literature is also tabulated to show the accuracy of the results.

The onset of double-diffusive convection in a nanofluid saturated porous layer: Cross-diffusion effects

The onset of double-diffusive convection in a horizontal porous layer saturated with a nanofluid with the Soret and Dufour effects is studied using both linear and nonlinear stability analyses in a three-dimensional way. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, and the modified Darcy model is used for the porous medium that includes the time derivative term to describe the momentum transport. The thermal energy equation includes the diffusion and cross-diffusion terms. The linear theory depends on the normal mode technique, and the nonlinear analysis depends on the minimal representation of double Fourier series. The effects of the Soret and Dufour parameters, solutal Rayleigh number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are presented graphically. It is found that for the stationary mode, the Soret and Dufour parameters, viscosity ratio, and thermal conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret and Dufour parameters, viscosity ratio, and Vadász number have a stabilizing effect, while the solutal Rayleigh number and the thermal conductivity ratio destabilize the system. We also study the effects of time on transient Nusselt number, which is found to be oscillatory when the time is small. However, when the time becomes very large, all three transient Nusselt number values approach the steady-state values.

MHD Oldroyd-B fluid flow across a melting surface with cross diffusion and double stratification

In this study, we analyzed the Oldroyd-B flow across a horizontal melting surface with cross-diffusion and double stratification (thermal and solutal) effects. We reconstructed the controlling equations as a group of nonlinear ODEs and solved by employing the RK-based shooting technique. The influence of important specifications on the three common profiles (velocity, temperature and concentration) is discussed through the plots. Tables are utilized to discuss the heat and mass transfer rates. We verified that the thermal stratification improves the heat transfer rate. Cross diffusion regulates the concentration and thermal fields.

Dynamic analysis of the light scattered by the non-equilibrium fluctuations of a ternary mixture of polystyrene-toluene-n-hexane.

Dynamic analysis of the light scattered by non-equilibrium fluctuations in a thermodiffusion experiment has been performed on a sample of polystyrene-toluene-n -hexane, at 0.9-49.55-49.55% mass fraction. Time decays of the non-equilibrium fluctuations have been obtained revealing the accurate detectability of three modes. The slowest mode has been attributed to the mass diffusion of the polymer into the binary solvent; the intermediate one to mass diffusion of the two molecular components of the solvent; finally, the fastest one has been attributed to the thermal diffusivity of the overall mixture. The two eigenvalues of the mass diffusion matrix have been evaluated with accuracy in the order of 1%. Neglecting cross-diffusion effects we obtain a simplified expression for the relative amplitude of the two mass diffusion modes, allowing a parameterized determination of polystyrene and toluene Soret coefficients in the ternary mixture. We suggest that a two wavelength shadowgraph experiment is needed for a complete determination of all the coefficients.

UCM flow across a melting surface in the presence of double stratification and cross-diffusion effects

Abstract In this article, we analyzed the upper convected Maxwell fluid (UCM) flow across a horizontal melting surface in the presence of cross-diffusion and double stratification (thermal and solutal) effects. We reconstructed the controlling equations as a group of nonlinear ordinary differential equations and then resolved by enforcing Runge-Kutta method with shooting technique. The influence of important parameters on the three common profiles (velocity, temperature, and concentration) is discussed through plots. Tables are utilized to discuss the wall friction, heat and mass transfer rates of both Newtonian and UCM flows. We witnessed that the thermal stratification, Soret number, Schmidt number and temperature dependent viscous parameter improve heat transfer rate. Setting the two flows side by side, it is worthy to mention that the temperature and concentration profiles looking high in the Newtonian fluid flow.

Application of Finite Element Method to MHD Mixed Convection Chemically Reacting Flow past a Vertical Porous Plate with Cross Diffusion and Biot Number Effects

Application of Finite Element Method to MHD Mixed Convection Chemically Reacting Flow past a Vertical Porous Plate with Cross Diffusion and Biot Number Effects

MHD slip flow of a dissipative Casson fluid over a moving geometry with heat source/sink: A numerical study

A Mathematical model is developed for investigating the heat and mass transfer of magnetohydrodynamic Casson fluid over a moving wedge with slip, nonlinear thermal radiation, uniform heat source/sink and chemical reaction. For regulating the momentum and concentration gradients we also considered the viscous dissipation and cross diffusion effects. Numerical solutions are carried out by employing Runge-Kutta and Newton's methods. The effects of the physical governing factors on the flow, temperature and concentration profiles are illustrated graphically for accelerating and decelerating flow cases. We also computed the local Nusselt and Sherwood numbers along with friction factor for the same cases. It is found that increasing the temperature jump parameter encourages the heat transfer rate. It is also concluded that the local Nusselt number is high in accelerating flow case when equated with the decelerating flow case.

Bio-convection on the nonlinear radiative flow of a Carreau fluid over a moving wedge with suction or injection

In modern days, the mass transfer rate is challenging to the scientists due to its noticeable significance for industrial as well as engineering applications; owing to this we attempt to study the cross-diffusion effects on the magnetohydrodynamic nonlinear radiative Carreau fluid over a wedge filled with gyro tactic microorganisms. Numerical results are presented graphically as well as in tabular form with the aid of the Runge-Kutta and Newton methods. The effects of pertinent parameters on velocity, temperature, concentration and density of motile organism distributions are presented and discussed for two cases (suction and injection flows). For real-life application we also calculated the local Nusselt and Sherwood numbers. It is observed that thermal and concentration profiles are not uniform in the suction and injection flow cases. It is found that the heat and mass transport phenomenon is high in the injection case, while heat and mass transfer rates are high in the suction flow case.