Double Diffusive Effects Research Articles

Effects of double diffusion and soret effect on mhd braking of liquid metal packed between enclosed rotating cylindrical annulus

Effects of double diffusion and soret effect on mhd braking of liquid metal packed between enclosed rotating cylindrical annulus

Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot

Abstract The convection stability of Maxwell–Cattaneo fluids in a vertical double-diffusive layer is investigated. Maxwell–Cattaneo fluids mean that the response of the heat flux with respect to the temperature gradient satisfies a relaxation time law rather than the classical Fourier one. The Chebyshev collocation method is used to resolve the linearized forms of perturbation equations, leading to the formulation of stability eigenvalue problem. By numerically solving the eigenvalue problem, the neutral stability curves in the a–Gr plane for the different values of solute Rayleigh number RaS are obtained. Results show that increasing the double diffusion effect and Louis number Le can suppress the convective instability. Furthermore, compared with Fourier fluid, the Maxwell–Cattaneo fluids in a vertical slot cause an oscillation on the neutral stability curve. The appearance of Maxwell–Cattaneo effect enhances the convection instability. Meanwhile, it is interesting to find that the Maxwell–Cattaneo effect for convective instability becomes stronger as the Prandtl number rises. That means Prandtl number (Pr) also has a significant effect on convective instability. Moreover, the occurrence of two minima on the neutral curve can be found when Pr reaches 12.

Soret-driven convection of Maxwell-Cattaneo fluids in a vertical channel

The Soret effect, also known as thermal diffusion, plays a crucial role in the phenomenon of double diffusion convection in liquids. This study investigates Soret-driven convection within a vertical double-diffusive layer of Maxwell-Cattaneo (M-C) fluids, where the boundaries maintain constant temperatures and solute concentrations that are distinct from each other. The heat transfer equation for Maxwell-Cattaneo fluids is governed by a hyperbolic rule of heat conduction, rather than the typical Fourier parabolic one. The Chebyshev collocation method is employed to solve the corresponding stability eigenvalue problem. The neutral stability curve shows significant fluctuation responses due to the M-C effect. When the Cattaneo number (C) reaches 0.02, multiple local minima appear in the critical Grashof number (Gr). The instability the thermal convection is found to be amplified by the combined effects of Maxwell-Cattaneo and Soret, along with the Grashof number, while the double diffusion effect appears to suppress the instability of convective system. The influence of Soret effect on convective instability will diminish dramatically as the Gr number rises above 8200.

Computational analysis of the bioconvective flow of Williamson–Sutterby fluid with microorganisms and activation energy subject to Cattaneo–Christov double-diffusion effects

This research aims to develop a mathematical model and outline the implications of the free convection flow within a non-Newtonian Williamson–Sutterby type nonfluid through a stretching surface placed horizontally with magnetic dipole effect. The present attempt establishes the influence of multiple factors, including double diffusion, and heat flux. Utilizing the Cattaneo–Christov heat mass flux model approximations, to shape the thermal and concentration balance equations, incorporating various generalized transport laws. Furthermore, the transportation mechanism incorporates Arrhenius activation energy and binary chemical reactions. The impact of bioconvection resulting from self-propelled microorganisms is incorporated into the fluidic model. A nonlinear set of partial differential equations (PDEs) are appropriately formulated, employing boundary layer approximations theory, to comprehensively describe the convective flow. The PDEs are converted to ordinary differential equations via similarity transformation, and then computationally computed via a well-structured RKF45 technique with a shooting algorithm. To validate the results, a comparison is made with published findings in limiting cases. It is observed that the velocity profiles exhibit an escalation in tandem with ascending values of the electric parameter and mixed convection. Conversely, the velocity diminishes with the augmentation of the magnetic factor, ferrohydrodynamic interaction parameter, porosity parameter, and Sutterby fluid parameter. Temperature profiles elevate in response to escalating values of the Eckert number, radiation parameter, and Brownian motion parameter while diminishing with the augmentation of the thermal relaxation constant, Prandtl number, and Sutterby fluid parameter. The concentration distribution exhibits an augmentation with the increasing magnitude of the thermophoresis parameter and activation energy while experiencing a reduction with the improvement in the behavior of Schmidt number and Brownian parameter. The ongoing investigation encompasses a wide spectrum of applications within the field of applied sciences, placing particular emphasis on thermal oil recovery, geothermal reservoirs, chemical engineering, and the cooling processes pertinent to nuclear reactors.

Effects of double diffusion and induced magnetic field on convective flow of a Casson nanofluid over a stretching surface

Magnetohydrodynamic (MHD) flows have several applications in a wide area of engineering such as industrialized processes, including generating MHD electrical power, processing of magnetic materials, etc. The present examination focuses on incorporating the induced magnetic field (IMF) and multiple slips on the convective MHD Casson nanofluid flow over an elongating sheet with Brownian motion and thermophoresis effects. Heat source/sink, non-linear radiation, and suction/injection impacts are added to strengthen the study. The governing equations are framed with the above assumptions and converted from PDE to ODE using a suitable transformation. The MATLAB solver “bvp5c” is engaged to solve the governing equations and the results are depicted through graphs and tables. Moreover, a good agreement is found while comparing these results with pre-existing results. It is established that an increase in the Casson fluid parameter diminishes the fluid's velocity. Also, the induced magnetic field plays a vital role in decreasing the speed of the fluid. Further, with an increase in the double-diffusive parameters, the temperature rises. As the chemical process and Schmidt number parameter elevate, the concentration drops. The convective parameter and the velocity slip parameter both enhance skin friction. The Nusselt number rises when the Prandtl number gets larger. This investigation makes major contributions to reactor safety devices, crystal growth in liquids, chemical-catalyzed reactors, geophysics, solar technology, etc.

Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study

AbstractThe present study explores the nanofluid boundary layer flow over a stretching sheet with the combined influence of the double diffusive effects of thermophoresis and Brownian motion effects. For the purpose of transforming nonlinear partial differential equations into the linear united ordinary differential equation method, the similarity transformation technique is used. The Runge–Kutta–Fehlberg method was used to solve the equations of flow, along with sufficient boundary conditions. The effect on hydrodynamic, thermal and solutes boundary layers of a number of related parameters is investigated and the effects are graphically displayed. In conclusion, a strong agreement between the current numerical findings and the previous literature results is sought.

Finite element solutions of Double diffusion effects on three-dimensional MHD Nano-Powell-Erying fluid flow in presence of thermal and mass Biot numbers

This work uses a numerical method to investigate the effects of diffusion on the flow of three-dimensional magnetohydrodynamic (MHD) nanofluids. The applicable equations for this problem are derived from the Nano-Powell-Erying fluid model. The result of the differential equation is calculated by solving the problem using the finite element method. The numerical solutions are used to study the three-dimensional structures with the flow of nanofluid to investigate the influence of well-known fluid parameters. The study found that the Hartmann number and buoyancy ratio parameter have a significant impact on the velocity profile, while the Brownian motion and thermophoresis parameters, as well as the thermal and mass Biot numbers, are the main factors influencing the temperature and concentration fields. This study aims to analyse the effect of two different parameters on the flow of MHD nanofluids to improve our basic understanding of this phenomenon. The findings that were produced are compared to the previous work and incipiently, the present numerical results are veritably in good agreement with the previous results. The results of this study can be useful for the optimization and design of various engineering applications.

Radiative heat transport of Cattaneo‐Christov double diffusive Casson nanofluid flow between two rotating disks with Hall current and activation energy

AbstractThe present research uncovers the mathematical exploration of the magnetohydrodynamic radiative Casson nanofluid flow produced due to stretching and coaxially rotating surfaces of two disks inside a non‐Darcy porous medium under the dominance of the diacritic Hall current and heat generation. The energy field is displayed under the dominance of radiative and dissipative heat transport by involving the consequences of distinctive nonlinear thermal radiation, viscous dissipation, and Joule heating. The present study overcomes the barrier of heat and mass transport by annexing Cattaneo‐Christov double diffusion effects. The current exploration shows the characteristics of the concentration field due to arising chemical reaction incited by activation energy. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with convective boundary conditions. A compatible similarity transformation comprised in the current study is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via dispensing the SLM. The present article deals with an in‐depth exploration of diagnostic flow parameters' attributes against the flow field and efficient physical quantities with the help of distinctive graphs and tables. As per the current investigation, the energy field becomes potent due to enhancing the stretching of each of the disks. Besides, augmenting the thermophoretic diffusion and chemical reaction boosts diluting the concentration of nanoparticles. The flow along the radial direction gets controlled near the upper disk under the increasing influence of the Hall current, intensity of the magnetic field, and stretching rate of the lower disk. On the other hand, the enlarging Casson parameter, rotation parameter, and stretching parameter for the lower disk lead to controlling the flow along the radial direction adjacent to the lower disk. Apart from that, the intense effects of the stretching rate of the upper disk and rotation rein axial flow throughout the flow region.

Peristaltic flow of bioconvective Ree–Eyring nanofluid through an inclined elastic channel with partial slip effects

Pharmaceutical fluid processing is a procedure of medication manufacturing, utilizing a particular kind of heat transfer in a biofluid designed to maintain the desired temperature for extended periods. Choosing a suitable fluid can have a positive effect on the operating efficacy of the system and lengthen the fluid’s and system’s life spans. As an outcome of this development, we investigate the influence of the partial slip and gyrotactic microorganisms on the peristaltic transport of a magnetohydrodynamic Ree–Eyring nanofluid via an aligned porous conduit with thermal radiation, energy generation, along with cross and double diffusion effects. By invoking suitable nondimensional parameters, the proposed dimensional governing equations are transformed into a system of dimensionless partial differential equations. The analytical solutions for the system of partial differential equations are obtained by incorporating the homotopy perturbation method. Further, tabular and graphical presentations are used to examine the characteristics of the various sundry parameters on the temperature, concentration, motile microorganism density, axial velocity, trapping, and other relevant flow quantities. The observations of this study indicate that the Darcy number and thermal Grashof number have the capability to enhance the velocity distribution of the Ree–Eyring nanofluid in the presence of bioconvection. The trapped bolus size and the skin friction coefficient increase noticeably because of an enhancement in the Ree–Eyring fluid parameter. Also, the Darcy number and the Hall current parameter increase the skin friction coefficient. Furthermore, validation of the results is carried out to examine the consistency between the current and the previous findings for some special cases and excellent agreements are found.

Spatial–temporal analysis of magnetohydrodynamics flow and energy flux of power-law nanofluid in a confined domain

Energy flux analysis of power-law fluid is a novel contribution to recent developments in computational fluid dynamics. The study of the unsteady two-dimensional flow with double diffusive effect inside a complex enclosure exhibits great potential in optimizing the heat transfer rate due to the wavy nature of the side walls. The enclosure is confined with the flow circulation due to the thermal and solutal gradients acting along the left and right wavy walls. The computational time and accuracy in results are estimated and compared by implementing the finite volume method and element-free Galerkin technique. The results are obtained in terms of streamlines, isotherms, isoconcentrations, average Nusselt number, Sherwood number, and total entropy generation due to the effect of conventional parameters, namely, power-law index, Rayleigh number, buoyancy ratio parameter, thermophoresis parameter, Brownian motion parameter, and Lewis number with a fixed Prandtl number throughout the computation. The optimized double-diffusive natural convection analysis is based on entropy generation and a calculated Bejan number. The novelty of this paper lies in the implementation of a mesh-free approach, which may be useful for the further analysis of elliptical/semi-elliptical structures.

Analyses of entropy generation and Hall influence in the Cattaneo–Christov double diffusive radiative Non-Darcy flow of a Casson nanofluid within rotating disks

The present research work interprets the entropy generation in the magnetohydrodynamic multiple slip flow of Casson nanofluid initiated due to stretching and coaxially rotating surfaces of two disks inside a non-Darcy porous medium under the dominance of the diacritic Hall current and heat generation. The energy field is explored by incorporating the consequences of distinctive thermal radiation, viscous dissipation, and Joule heating. The present study overcomes the barrier of heat and mass transport by annexing Cattaneo–Christov double diffusion effects. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with multiple slip boundary conditions. A compatible similarity transformation comprised in the current study is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via dispensing the successive linearization method. The present article deals with an in-depth exploration of diagnostic flow parameters’ attributes against the flow field and efficient physical quantities with the help of distinctive graphs and tables. As per regression analysis, the maximum relative error for the regression model on the skin friction coefficient in the radial direction ranging from .0097236 to .017225% is less than that of the other physical quantities. Besides, augmenting the thermophoretic diffusion boosts diluting the concentration of nanoparticles.

Double-diffusive bioconvection effects on multi-slip peristaltic flow of Jeffrey nanofluid in an asymmetric channel

Double-diffusive bioconvection effects on multi-slip peristaltic flow of Jeffrey nanofluid in an asymmetric channel

Chemically reactive MHD peristaltic flow of Jeffrey nanofluid via a vertical porous conduit with complaint walls under the effects of bioconvection and double diffusion

Inspired by significant physiological applications of peristaltic transport, a mathematical model for the peristaltic pumping of a Jeffrey nanofluid containing gyrotactic microorganisms through a flexible and vertical symmetric channel is investigated, along with the effects of thermal radiation, heat source/sink, chemical reaction, porous medium and Hall current. Swimming microorganisms in a model of non-Newtonian fluid has several biological and ecological benefits, including in the pharmaceutical industry, biofertilizers, biofuel technology, biosensors, etc. With these presumptions in mind, a conducting Jeffery fluid flow containing microorganisms via a porous vertical conduit is proposed. The expressions for the flow quantities are established by solving the governing equations of this study analytically using the homotopy perturbation method (HPM). A detailed examination is performed using the tables and graphical representations to comprehend the impact of significant components on this analysis. In addition, the results for Newtonian nanofluid are obtained as a special case and discovered that its velocity is lower than the Jeffrey nanofluid. It is observed that the best velocity distribution can be seen at larger thermal Grashof number and Darcy number. The size of the trapped bolus enhances with the increase of the Hall parameter. Furthermore, the density of the motile microorganism distribution declines for higher bioconvection Peclet number and bioconvection constant.

MHD-driven chemically active and thermally radiative Prandtl hybrid nanofluid flow on stretching device with Ohmic heating, dissipation, and diffusion effects

This study explores the magnetohydrodynamics of reactive hybrid nanofluid flow with the Prandtl fluid model. The flow is past a linear stretching device and its physical characteristic are studied for the novel effects of viscous dissipation, Joule heating, chemical reaction, thermal radiation, and double diffusion. Furthermore, the multiple slip conditions are considered while framing the governing system of equations. The mathematical set of equations is transmuted with similarity invariants and obtained from the nonlinear set of ordinary differential equations. The numerical simulation is carried out via the Runge–Kutta fourth-order method with a shooting scheme. The graphical illustration of numerical outcomes is sketched through MATLAB. The code validation is achieved via comparative analysis with recent publications. It is observed that the applied magnetic field retard the fluid motion and increases the thermal boundary. Dissipation and radiation effects also boost the thermal boundary regime.

Double diffusion and Hall effects on MHD sinusoidal natural convection flow of silver water-based nanofluid from a porous vertical plate

This paper scrutinizes Hall current, Soret and Dufour impacts on natural convective flow of nanofluid attributable to variation in sinusoidal surface temperature over a vertical plate through a porous medium with strong transverse magnetic field applied normally to the flow. In this regard, the silver metal is considered as nanoparticles with water as base fluid. The overlapping multi-domain bivariate spectral local linearization method (OMD-BSLLM) has been utilized to solve the dimensionless governing equations which are attained by means of appropriate transformations. The obtained results are portrayed via graphical and tabular formations to inspect flow fields, shear stresses, heat and mass transmission characteristics for varying thermo-physical parameters. We found that there is an enhancement in the flow fields, shear stresses and heat transportation with the use of silver nanoparticles. Thermal and concentration boundary layer thickness enhance by using porous material, whereas diminish with improvement in Hall effect and ratio of buoyancy forces. The flow characteristics decline with the inclusion of porous medium while elevates with increment in Hall parameter. Moreover, an upgrade in thermal-diffusion correspond to a substantial growth in concentration field along with mass transfer rate. Current analysis can be useful in MHD energy generators, and industrial applications such as heating and cooling procedures owing to the involvement of nanoparticles having superior thermal conductivity features.

Double diffusion effect on the bio-convective magnetized flow of tangent hyperbolic liquid by a stretched nano-material with Arrhenius Catalysts

The idea of activation energy appearing in a chemical reaction has been widely applied to the production of biodiesel, hydrogen, oil storage, geothermal manufacturing, base liquid mechanics, oil emulsified, food manufacturing, a significant renewable energy source, as well as sewage systems. This study aims to investigate the resultant repercussions of double diffusion, activation energy, Brownian motion, thermal radiation, thermophoresis, viscous dissipation, magnetic field, and Joule heating on bioconvection of a tangent hyperbolic nanofluid flow over a vertical stretching porous surface containing microbe (gyrotactic microorganisms). The fluid transport equations are converted into ordinary differential equations using appropriate self-similarity variables after being solved using the finite difference method. The impacts of key parameters on the fluid's transport properties are depicted in graphs and tables. When the dimensionless activation energy is higher, the mass transfer rate at the stretched nanomaterial sheet drops. The nanofluid concentration near the sheet minimizes by increasing the porosity parameter value, but the opposite behavior happens far from the sheet.

Double-diffusive transport in multicomponent vertical convection

Motivated by the ablation of vertical ice faces in salt water, we use three-dimensional direct numerical simulations to investigate the heat and salt fluxes in two-scalar vertical convection. For parameters relevant to ice-ocean interfaces in the convection-dominated regime, we observe that the salinity field drives the convection and that heat is essentially transported as a passive scalar. By varying the diffusivity ratio of heat and salt (i.e., the Lewis number $Le$), we identify how the different molecular diffusivities affect the scalar fluxes through the system. Away from the walls, we find that the heat transport is determined by a turbulent Prandtl number of $Pr_t\approx 1$ and that double-diffusive effects are practically negligible. However, the difference in molecular diffusivities plays an important role close to the boundaries. In the (unrealistic) case where salt diffused faster than heat, the ratio of salt-to-heat fluxes would scale as $Le^{1/3}$, consistent with classical nested scalar boundary layers. However, in the realistic case of faster heat diffusion (relative to salt), we observe a transition towards a $Le^{1/2}$ scaling of the ratio of the fluxes. This coincides with the thermal boundary layer width growing beyond the thickness of the viscous boundary layer. We find that this transition is not determined by a critical Lewis number, but rather by a critical Prandtl number $Pr\approx 10$, slightly below that for cold seawater where $Pr=14$. We compare our results to similar studies of sheared and double-diffusive flow under ice shelves, and discuss the implications for fluxes in large-scale ice-ocean models. By coupling our results to ice-ocean interface thermodynamics, we describe how the flux ratio impacts the interfacial salinity, and hence the strength of solutal convection and the ablation rate.

EFFECTS OF MAGNETIC FIELD AND THERMAL RADIATION ON DOUBLE DIFFUSION OF A SOLID PHASE IN THE TWO CONNECTED CIRCULAR CYLINDERS SUSPENDED BY NEPCM AND POROUS MEDIA

The novelty of the present work is studying the influences of thermal radiation and magnetic field on the double diffusion of solid phase in the novel cavity of two linked cylinders suspended by nano-encapsulated phase change materials (NEPCMs) and porous media. The complex cavity contains two circular cylinders connected by an open gate occupied by solid particles. Two different boundary conditions including hot and cold for the solid phase are conducted in this work. The incompressible smoothed particle hydrodynamics (ISPH) method is improved to solve the time-fractional governing equations of the physical problem. The mesh-free nature of the ISPH method helps in treating the different materials of the solid and fluid phases efficiently. The physical parameters are dimensionless time parameter τ, Hartmann number Ha, thermal radiation parameter Rd, fractional time-derivative α, Darcy parameter Da, Rayleigh number Ra, and fusion temperature θ<sub>f</sub>. The main findings of the numerical simulations indicated that the fractional time-derivative parameter changes the transmission of heat-mass and nanofluid developments during the initial time steps. The Rayleigh number works well in improving the interactions between the solid and fluid phases due to the high buoyancy forces. Increasing the Rayleigh number improves the intensity of the temperature, concentration, and nanofluid speed in a cavity at Case 1 (C1) and Case 2 (C2). The phase change zone is changing according to the alterations of boundary conditions, Rayleigh number, and fusion temperature. Increasing thermal radiation parameter shrinks the nanofluid movements and mean Nusselt number Nu.

Double diffusion effects on hybridity of Cu–Al2O3/water nanofluid with viscous heating

An analysis of heat and mass transfer that occur in copper–alumina/water nanofluids flow past a stretching surface is presented. This flow is influenced by cross-diffusion effects and viscous dissipation. After the application of appropriate similarity transformations on governing equations, the resultant system is solved by Spectral Relaxation Method. The variations of velocity, temperature, concentration and results for skin friction coefficient, local Nusselt number and local Sherwood number for Cu–Al2O3/ water nanofluids with different flow parameter values are manifested through graphs and tables. Temperature enhancement is observed due to an increase in the Dufour number. Concentration distribution increased for higher Soret numbers and decreased for higher Schmidt numbers. Also, numerical values are calculated for effective local Nusselt number as well as local Sherwood number due to the influences of Dufour and Soret and are tabulated. The validation of the present investigation is ensured by comparing it with already published studies.

Double Diffusion, Chemical Reaction, and Heat Source Effects on Magnetohydrodynamic Flow of Copper and Silver Water-based Nanofluids over a Moving Vertical Porous Plate

In this manuscript, the impact of Soret and Dufour numbers on magnetohydrodynamic (MHD) flow for Silver (Ag) and Copper (Cu) water-based nanofluids past a moving plate over a porous medium are investigated numerically. The influences of heat sources and chemical reactions are also considered, as their applications are prevalent in several industries. The flow's constituents' governing equations are coupled with Partial differential equations (PDEs) that are converted into a dimensionless form using appropriate flow parameters. Subsequently, the finite-difference technique is used to resolve the resulting equations. The varied effects of flow parameters on the momentum, temperature, and concentration boundary layers are investigated using various graphs. The results presented in terms of non-dimensional parameters like shear stress factor, Sherwood number, and Nusselt number of fluids are tabulated for the nanofluids Ag-water and Cu-water. It is found that the augmented values of Dufour and Soret numbers enhance the fluid velocity. However, the species concentration decreases in the existence of Dufour and chemical reaction effects.