Triple Diffusive Convection Research Articles

Triple-diffusive instabilities in Ellis fluid-saturated porous layers: Dynamics of oscillatory convection

Triple-diffusive convection in Ellis fluid-saturated porous layers has a wide array of real-world applications, including enhanced oil recovery, optimized geothermal energy extraction, and improved food processing and drug delivery systems. It also plays a crucial role in environmental management, particularly in controlling groundwater contamination and maintaining soil health by modeling pollutant transport and nutrient dynamics. This study explores the onset of convection in an Ellis fluid-saturated porous layer, influenced by three stratifying agents with differing diffusivities. A modified Darcy porous medium, salted from below, is subjected to horizontal throughflow driven by a prescribed pressure gradient. Through normal mode analysis, a linear stability analysis is conducted, resulting in explicit threshold conditions for the onset of convection. The findings reveal that convection begins with oscillatory motion, driven by the combined effects of the pressure gradient and solute concentration gradients. Notably, the study uncovers the emergence of disconnected, closed, heart-shaped oscillatory neutral curves, indicating the presence of three critical values of the solutal Darcy-Rayleigh number required to establish linear instability criteria and novel discovery for an Ellis fluid-saturated porous medium. Moreover, the results show that increasing the solutal Darcy-Rayleigh number and the Ellis power-law index stabilizes the system, while a higher Darcy-Ellis number leads to destabilization. The results obtained in the limiting cases are found to be consistent with those reported in previous studies.

Weakly Non-linear Stability Analysis of Triple-Diffusive Convection in a Bi-viscous Bingham Fluid Layer with Cross-Diffusion Effects

Weakly Non-linear Stability Analysis of Triple-Diffusive Convection in a Bi-viscous Bingham Fluid Layer with Cross-Diffusion Effects

Stability of triple-diffusive convection in a vertical porous layer

Stability of triple-diffusive convection in a vertical porous layer

Analytical study of triple diffusive convection in a bi-viscous Bingham fluid layer using Ginzburg-Landau model

In this paper, considering bi-viscous Bingham as the base fluid, we study the thermophysical-properties (such as density, specific heat, thermal conductivity, thermal diffusivity, and thermal expansion) with different combinations of salts among NaCl, KCl, CaCl2, and NaCl2 of triple diffusive convection in a bi-viscous Bingham fluid layer with heat as one of the diffusing components. A weakly non-linear case is formulated to facilitate a solution to the problem using a series solution Ginzburg-Landau model. With regard to single, double, and triple diffusive convection, the tables are made to record the actual values of thermophysical-properties together with the critical Rayleigh-number for each combination of aqueous-salt solutions. This computation calculates the mean Nusselt and Sherwood numbers to quantify the system’s heat- and mass-transfers for various aqueous-solutions. The effect of the bi-viscous Bingham fluid parameter, for small and large values, for different aqueous-solutions, in single, double, and triple diffusive convection has been captured via 2-dimensional (2D) and 3-dimensional (3D) figures and the results are recorded and compared. The investigation reveals that the heat- and mass-transfers increase with an increase or decrease in the bi-viscous Bingham fluid parameter, which in turn depends on the values of R S 1 and R S 2 . The results confirm that the heat- and mass-transfers are least for the combination of KCl with CaCl2 and maximum for the combination of NaCl with other salts.

Effects of throughflow and gravity modulation on triple-diffusive convection in a sparsely packed porous medium

This article investigates the impact of four different gravity modulations on triple-diffusive convection in a porous layer with throughflow. The study conducts a weakly nonlinear stability analysis. Additionally, cubic Ginzburg–Landau equation is derived to observe the effects of throughflow, gravity modulation, and concentration. The solution of Ginzburg–Landau equation is used to calculate heat transfer and mass transport in terms of the Nusselt and Sherwood numbers, respectively. Furthermore, the mean Nusselt and Sherwood numbers are calculated. The study investigates the influence of Lewis numbers, solutal Rayleigh numbers, and Peclet numbers on the stability and instability of the system graphically for the four types of gravity modulations. The results show that the Sawtooth modulation destabilizes the system, while the square waveform modulation stabilizes it. The mean Nusselt number decreases with both the first Lewis number Le 1 and the second Lewis number Le 2, as well as the mean Sherwood number, which decreases with the first solutal Rayleigh number Rs 1 and the second solutal Rayleigh number Rs 2. This indicates system stability. Furthermore, it is noted that the heat and mass transport for triangular modulation fall between those of sawtooth modulation and square modulation.

The Velocity, Temperature and Concentration Profiles for Triple Diffusive Casson Fluid Flow Subjected to the Soret-Dufour Parameters

The triple-diffusive convection with the involvement of non-Newtonian fluid has many applications in the science and technology field, industrial processes, and also in research works. Therefore, the mathematical model of the triple-diffusive convection of Casson fluid by the mathematical approach is investigated. In addition, a mathematical model for the triple-diffusive convection of Casson fluid flow beyond a nonlinear compressing sheet has been formulated and solved by numerical approach, where this is the main objective of this study. This model is subjected to mass transfer and heat transfer, known as Soret and Dufour effect (Soret-Dufour). The Soret effect is occurred when the temperature gradient is produced, whereas the differences in mass cause the Dufour effect. The model is formed by the continuity equation, momentum equation, energy equation, and concentration equations of component 1 and 2, together with the boundary conditions. They have been reduced to ordinary differential equations, and subsequently, they have been implemented in bvp4c programme provided by MATLAB software to get the numerical solutions. The solutions obtained were profiles of velocity, temperature and concentration of both components. Next, the effect of Casson parameter, Soret parameter, and Dufour parameter have been investigated by changing their values of inside the coding in MATLAB and observing the behaviour of the related profiles due to these parameters. The main results from this study were: The velocity of the Casson fluid reduced as the Casson parameter enhanced, increment in both Soret and Dufour parameters caused the temperature to decrease, and the fluid concentration was higher for the increasing Soret number.

Analysis of convective heat transfer in triple diffusive free convection flow of Williamson nanofluid along a horizontal plate

ABSTRACTThis research investigates the concurrent effects of three different diffusion mechanisms, species diffusion, thermal diffusion, and nanoparticle diffusion, on the convective heat transfer and mass transfer properties of a nanofluid. As a part of the study, a further level of complexity is added using the convective boundary condition by considering the interaction between surface heat flow and surrounding fluid dynamics. Further the transformed governing equations are obtained with the help of similarity solutions. The Runge-Kutta-Fehlberg method is used with the shooting approach to get numerical solutions for the simplified equations. The influences of various involved parameters on velocity profiles, temperature profiles, concentration, local skin friction, local Nusselt and Sherwood numbers are discussed. The significant outcomes of the study are observed as the decrease in the velocity and fluid temperature during the increase of the suction parameters, and the indication of the evacuation of fluid from the surface that lessens the heat transmission and lowers the temperature profiles. The fluid temperature is raised by the augmentation in the conductive parameter. It has also been found that the mass transfer rate increased as the salts are included. The heat transfer decreases with higher thermophoresis strength but increases with higher Prandtl number.

Weakly nonlinear instability analysis of triple diffusive convection under internal heat generator and modulated boundaries

A nonlinear instability analysis of triple diffusive convection under the time-dependent heat and mass transfer boundary conditions in the presence of internal heat source is evaluated in this study. On various physical parameters, the momentary behavior of both Sherwood and Nusselt number profiles is examined. In the geometry, we have considered two parallel infinite horizontal plates acting gravity vertically downward z-direction. By using the weakly nonlinear analysis, the Ginzburg–Landau equation is generated for the rate of heat and mass transport. Here, we have considered the temperature and concentration of two solutes. The temperature and first concentration of the solute at the lower plate are higher than the upper plate, while the second concentration of the solute at the upper plate is higher compared to that of the lower plate. According to the different modulation, we have considered four cases based on the phase angle of the modulations. The convective heat and mass transports are measured as a function of the Nusselt number (Nu) and Sherwood number (Sh1 and Sh2) for both the concentration. From the results, it is found that the first Lewis number increases all the considered profiles, while Ri increases the Nusselt number profile only. The principal discovery elucidated by this article resides in the observation that the internal heat source, subject to modulated boundaries, maintains the convective instability if different solutes are used from both ends.

Successive over relaxation (SOR) methodology for convective triply diffusive magnetic flowing via a porous horizontal plate with diverse irreversibilities

Entropy generation and triple diffusive convection is not explored yet taking the combined effects of suction and magnetohydrodynamic in a flow through porous medium. Irreversibility in mass diffusivity due to magnetic field has substantial effects on mass and heat transport rate. A novel model obeying Darcy law and Boussinesq approximation is developed for the entropy generation analysis under the influence of coupling effects of concentrations of two heterogeneous salts in the flow of a Newtonian fluid. Magnetic Bejan number and mass Bejan number have been defined for the estimation of novel irreversibilities due to salts’ concentrations and magnetic retardation. Governing equations are transformed by employing similarity variables; the dimensionless system thus obtained is discretized by the finite differences and, then simulated numerically via Successive over Relaxation (SOR) methodology. It’s worth noting that suction at the surface along with magnetic force and porosity tends to decrease local as well as surface entropy generation rates and also the novel magnetic Bejan number considerably. Furthermore, entropy generation rate in triple diffusion is higher than double diffusion.

Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer

One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the x-direction and between two concurrent plates at z=0 and z=d was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates (Nu), Sherwood number proportional to mass transfer of solute 1 (Sh1) and Sherwood number proportional to mass transfer of solute 2 (Sh2) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection.

Insightful into dynamics of magneto Reiner-Philippoff nanofluid flow induced by triple-diffusive convection with zero nanoparticle mass flux

The motive behind this article is to investigate the impact of triple diffusive convective flowing on Reiner-Philippoff (R-Ph) past a stretchable surface with Avramenko-Blinov-Shevchuk boundary restrictions. The governing determined partial differential equation (PDEs) are converted into ordinary differential equations (ODEs) with the utilization of similarity conversions and handled these equations computationally with the application of a well-recognized computational structure called Cash and Carp method. The dimensionless parameters used in figures and tables range between 0.1 ≤ γ ≤ 1.1 , 0.1 ≤ λ ≤ 2.1 , 0 ≤ Nc 1 ≤ 2 , 0.1 ≤ Nc 2 ≤ 1.3 , 0.1 ≤ Le 1 , L e 2 , Ld 1 , a n d Ld 2 ≤ 2 , 0.1 ≤ Nd 1 ≤ 0.5 , 0.1 ≤ Nd 2 ≤ 0.5 , 0 ≤ R d ≤ 3 , 0.1 ≤ ∊ ≤ 0.5 , 0 ≤ N b ≤ 1 , 0 ≤ N t ≤ 1.2 . From numerical outcomes, it is revealed that the velocity field devalues outstanding to an incremental change in the Grashof number factor and the solutal profile escalates by the benefit of an intensification in the Dufour Lewis number. The heat of the fluid amplifies as a consequence of amplification in both linear heat radiation and Brownian diffusion parameters.

Effects of heat source/sink on Darcy–Bènard triple-diffusive convection in a porous-fluid system

In the presence of a constant heat source/sink in both layers of the porous–fluid system, the Darcy–Bènard Triple-Diffusive Convection (DBTDC) problem is investigated for two types of Thermal Boundary Combinations (TBCs). For type (i) adiabatic–adiabatic and type (ii) adiabatic–isothermal TBCs, the system of ordinary differential equations derived from normal mode analysis is solved in closed form for the eigenvalue, Thermal Marangoni Number (TMN). The depth ratio thoroughly explains the influence of several parameters on the eigenvalue, hence on DBTDMC. It is noticed that the parameters in the study have a larger influence on the porous layer dominant composite layer systems than that on the fluid layer dominant composite systems.

Non-Darcian Triple diffusive convection in a combined layer with heat source/sink

In the presence of a constant heat source and sink in each layer, the Non-Darcian Triple Diffusive Convection (NDTDC) problem in a combined layer that is horizontally infinite is examined. This composite layer is rigid and adiabatic in the lower enclosure of the porous layer and free as well as isothermal in the higher enclosure of the fluid layer. The thermal Marangoni number (tMn) for two cases of thermal boundary combinations (TBCs), case (i) adiabatic–adiabatic and case (ii) adiabatic–isothermal, is determined by solving the system of ordinary differential equations obtained following normal mode analysis in closed form. The effect of important parameters on NDTDC is studied in detail and illustrated visually versus the thermal ratio. It is noticed that case (i) is observed to be stable because the Eigenvalue obtained is higher than that for case (ii) and NDTDC can be postponed by making the upper boundary of the combined layer adiabatic and the same is augmented by converting the upper boundary of the combined layer to isothermal, as isothermal boundaries support early convections.

Onset of triple diffusive thermosolutal convection in a composite system

AbstractIn a composite system possessing rigid‐rigid boundaries, the significance of thermal diffusion on the onset of triple diffusive convection is analyzed. The Darcy–Brinkman–Rayleigh–Benard model is employed to model the porous media. The regular perturbation methodology has been used to solve the governing equations of the composite system with the Boussinesq approximation. The critical thermal Rayleigh number, which determines the stability of the system, is estimated analytically. A graphical assessment of the impact of multiple physical attributes on the stability of the system is made. It is observed that the Soret parameters and solute Rayleigh numbers have a stabilizing effect, whereas the Darcy number exhibits a destabilizing effect upon the onset of triple diffusive convection in the composite system.

Triple diffusive magneto convection in a fluid-porous composite system

A study on triple diffusive magneto convection is made for a fluid – porous composite system with rigid-rigid boundaries insulated to temperature and concentration. The porous layer of the composite system is modeled using Darcy–Brinkman model. The method of regular perturbation approach is employed to find the eigen-value for the problem considered. The critical Rayleigh number as criterion for the onset of convection is derived for step function, salting below and desalting above salinity profiles. The effect of various physical parameter on the onset of convection is graphically depicted and the stability of the system is analyzed.

Onset of triple-diffusive convective stability in the presence of a heat source and temperature gradients: An exact method

<abstract> <p>In the current work, in the presence of a heat source and temperature gradients, the onset of triple-diffusive convective stability is studied for a fluid, and a fluid-saturated porous layer confined vertically by adiabatic limits for the Darcy model is thoroughly analyzed. With consistent heat sources in both layers, this composite layer is subjected to three temperature profiles with Marangoni effects. The fluid-saturated porous region's lower boundary is a rigid surface, while the fluid region's upper boundary is a free surface. For the system of ordinary differential equations, the thermal surface-tension-driven (Marangoni) number, which also happens to be the Eigenvalue, is solved in closed form. The three different temperature profiles are investigated, the thermal surface-tension-driven (Marangoni) numbers are calculated analytically, and the effects of the heat source/sink are studied in terms of corrected internal Rayleigh numbers. Graphs are used to show how different parameters have an impact on the onset of triple-diffusive convection. The study's parameters have a greater influence on porous layer dominant composite layer systems than on fluid layer dominant composite layer systems. Finally, porous parameters and corrected internal Rayleigh numbers are stabilize the system, and solute1 Marangoni number and ratio of solute2 diffusivity to thermal diffusivity of fluid are destabilize the system.</p> </abstract>

LTNE Effects on Triple-Diffusive Convection in Nanofluids

Abstract Triple-diffusive convection for nanofluids in which differences in density are derived because of triple diffusion process, i.e., with three diffusing components: nanoparticles, solute, and heat, using more realistic two temperature model with separate thermal energy equations for the two phases of the considered nanofluid has been investigated by making use of the method of superposition and one term Galerkin technique. A complex system with local thermal non-equilibrium (LTNE) effects along with the Brownian motions and thermophoresis to account for nanoparticles has been considered. The problem is solved for top-heavy arrangement of nanoparticles leading to stationary mode of convection and numerical computations are carried out by using Mathematica software. An additional solute concentration equation supplements the conservation equations due to the existence of solute, which introduces two additional nondimensional parameters, whereas three additional parameters came into existence due to the consideration of LTNE effects. The critical Rayleigh number remains constant for smaller values of interphase heat transfer parameter, whereas it diminishes for the intermediate range and approaches to constant value for higher ranges of the parameters. What all this means is that only the intermediate range of Nield parameter shows stabilizing/destabilizing effects. Interestingly, the additional parameters Lewis number and solute Rayleigh number enhance the effect of destabilization of considered nanofluid layer.

Influence of Triple Diffusive Convection in Peristaltic Flow of Jeffrey Nanofluid Through Non-Uniform Channel

In this investigation, we considered the effect of triple diffusive convection on peristaltic flow through a non-uniform Channel. We also considered the incompressible non-Newtonian Jeffrey nanofluid. On the assumption of a long wavelength and low Reynolds number, the governing equations were transformed into a non-dimensional form. The reduced non-dimensional highly nonlinear partial differential equations are solved using the Homotopy Perturbation Sumudu transformation method (HPSTM). The influence of different physical parameters on dimensionless velocity, pressure gradient, temperature, the concentration of salt 1 and salt 2, and volume fraction was graphically represented. The Dufour solutal Lewis number of salt 1 and salt 2 on the velocity profile increases. The Dufour solutal Lewis number and modified Dufour parameter of salt 1 rises on nanoparticle volume fraction profile. It is found that the presence of the triple diffusing components with small diffusivity can change the convection in the system. The change in density in a triple diffusive is caused by the thermal and solutal diffusivities of two separate chemical species. So this study is applicable in engineering and scientific fields like geology, astrophysics, disposal of nuclear waste, deoxyribonucleic acid (DNA), and chemical engineering. This work is compared with the exact solution, and it is in good agreement with this method.

Cattaneo–Christov model for triple diffusive natural convection flows over horizontal plate with entropy analysis embedded in porous regime

This research interprets the features of triple diffusion in naturally convected viscous material flow through a horizontal plate embedded in a porous regime. The heat and mass transmission process is evaluated by the implication of Cattaneo and Christov (CC) models of energy and mass diffusions. Entropy analysis is executed with the help of the second law of thermodynamics. The homogeneous and local thermal equilibrium is assumed for porous medium. The physically modeled expressions are reframed into an ordinary differential system. This re-structured system of expressions is computed numerically by the implication of the Runge–Kutta Fehlberg method. The computed solutions are visualized graphically and in numeric forms. The validation of present solutions is reported by the comparative benchmark with already available results in a limiting sense. It is evident that the opposing and assisting flows show higher entropy generation at the convective wall. An increment in surface entropy generation rate is achieved for higher thermal and solutal relaxation times.

Influence of mixed convection nanofluid flow over a rotating sphere in the presence of diffusion of liquid hydrogen and ammonia

This work concentrates on the triple diffusive mixed convection nanofluid flow over a rotating sphere in view of cooling of rotating spherical products in various industries, machinery fields, heat and mass transfer applications. Diffusive components such as liquid hydrogen, ammonia, and nanoparticles have various practical applications for cooling in various industrial processes. This study is considered innovative because it examines the effect of multi diffusive components and nanoparticles on mixed convection flow over a rotating sphere reported for the first time. The physical problem is modelled mathematically as a set of coupled nonlinear dimensional partial differential equations. We employ the implicit finite difference scheme equipped with the Quasilinearization technique to solve the set of non-dimensional partial differential equations obtained via a non-similar approach. The numerical results are discussed through graphs. This work illustrates the significance of sphere rotations on flow, heat and mass transfer and boundary layer separation. This work also accounts for the impacts of thermophoresis and the Brownian motion of nanoparticles. The so obtained numerical results are compared with earlier results, and they are found to be in excellent agreement.