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I have never heard of this energy transfer mode, could you please give a reference or explanation, is it an error in translation?

Double-diffusive convection flow with Soret and Dufour effects in an irregular geometry in the presence of thermal radiation

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https://doi.org/10.1016/j.icheatmasstransfer.2022.106026Get rights and content

Abstract

In this study, the effect of radiation on double-diffusive natural convection is investigated by considering the phenomena of Soret and Dufour in complex geometry, for the first time. The multi-time relaxation lattice Boltzmann method has been adopted to calculate the momentum, energy, and species equations. The radiative transfer equation has been solved using the finite volume method. Complex boundaries have been simulated by the sharp interface-immersed boundary method. The influences of effective parameters including the optical thickness (τ = 1 to 100), Rayleigh number (Ra = 104 and 105), Planck number (Pl = 0.01 to 1), Buoyancy ratio (Br = − 5 to 5), Soret number (Sr = − 1 to 1), and Dufour number (Df = − 1 to 1) have been analyzed on the flow field, heat, and mass transfer in a square cavity with an internal circular cylinder. Moreover, temporal variations of velocity and phase space trajectory have been used to study the effects of radiation on unsteady flow behavior. Results indicate that, the increment in optical thickness significantly reduces radiation, while a sweep behavior occurs in mass and heat transfer. Increasing the Dufour (Soret) parameter depending on the value of the Soret (Dufour) parameter can increase or decrease the mass (heat) transfer.

Introduction

Double-diffusive convection is a common phenomenon in natural and industrial applications such as crystal growth, oceanography [1], pollutant movement [2], drying technologies [3], metal manufacturing processes [4], chemical reactors [5], plastic and metal extrusion industries [6]. This phenomenon is created by buoyancy forces due to the simultaneous gradients of temperature and concentration [7]. The heat transfer produced by the concentration gradient is called the Dufour effect, and the mass transfer created by the temperature gradient is called the Soret effect. These effects play an important role in the natural convection flow when the temperature and concentration gradients are large. Nithyadevi and Yang [8] performed a numerical analysis on the natural convection flow of water with mass transfer by taking the effects of Soret and Dufour. Their studied geometry was a partially heated square cavity. They considered two modes, in their study. In the first case, they assumed that the concentration of the right wall was higher than the left wall, and in the second case, the left wall had been considered at a higher concentration than the right wall. One of the obtained results was that, as the number of thermal Rayleigh numbers increases, the heat and mass transfer rates increase too. In addition, it was observed that high values of the Dufour parameters cause the fluid particle to move with higher velocity and heat transfer rate. In the first case, they found that increasing the Soret parameter causes a reduction in the velocity and increases the mass transfer rate. In contrast, in the second case, the opposite behavior occurs. Bég et al. [9] investigated the heat and mass transfer processes of natural convection from a spherical body enclosed in a micropolar fluid by considering the effects of Soret and Dufour. It was found that increasing the Soret number causes an enhancement in the rates of heat transfer. Wang et al. [10,11] investigated the oscillation of a convection flow caused by the simultaneous effect of temperature and concentration gradients by taking the effects of Soret and Dufour in a horizontal cavity. It was found that with increasing buoyancy ratio, the flow structure has variation in a way that the flow changes from a steady state to a chaotic flow and finally to a periodic oscillation. Also, as the Soret and Dufour ascend, the oscillating convection changes from chaotic flow to periodic oscillation. Kefayati [12] analyzed the convection flow of a non-Newtonian fluid by considering the effects of Soret and Dufour in a square enclosure. They found that the Dufour parameter affects heat and mass transfer. In contrast, the Soret number only has a significant effect on mass transfer. Ren and Chan [13] proposed a new numerical method based on the lattice Boltzmann method (LBM), assuming the simultaneous heat and mass transfer with the effects of the Soret and Dufour in a square cavity. Kefayati [14,15] presented a finite-difference LB model to study natural convection flow caused by mass and temperature gradients in the presence of the Soret and Dufour effects. The geometry was an inclined porous cavity filled with a non-Newtonian fluid. It was clear that, for different Rayleigh numbers, by increasing the Dufour number, the heat transfer will increase, and on the other hand, the mass transfer rate has been increased by enhancing the Soret number. Liu et al. [16] proposed a non-equilibrium multiple-relaxation-time lattice Boltzmann (MRT-LB) model to investigate the heat and mass transfer problems resulting from concentration and temperature gradients with the effects of Soret and Dufour. In this study, they used a rectangular cavity to show the capability of their method and showed that their method is more stable than other LB models. Xu et al. [17] investigated the double-diffusive natural convection (DDNC) phenomenon in the presence of the Soret and Dufour effects around a cylinder with a circular geometry within a square cavity. It has been observed that the simultaneous increase in the Soret and Dufour numbers stabilized the flow in the unsteady state and reduced heat and mass transfer. In a numerical study, Qiu et al. [18] investigated the effects of the Rayleigh number, buoyancy ratio, and aspect ratio on natural convection flow with the effects of Soret and Dufour in a horizontal enclosure filled with low Prandtl number fluids. One of their results point was found that the role of convection heat transfer becomes more significant as buoyancy ratio enhances under different Prandtl numbers. Kefayati [19] investigates the effects of Lewis number, Bingham number, Rayleigh number, Eckert number, inclined angle, Dufour number, Soret number, and buoyancy ratio on the flow characteristics, the heat and mass transfer, as well as the entropy generations in a square enclosure. It was found that with the increase in the Soret and Dufour numbers, the entropy generations increase due to fluid friction and heat transfer. Kaladhar et al. [20] investigated the effects of chemical reaction, slip, and Soret and Dufour parameters on the flow characteristics and the heat and mass transfer of mixed convection flow within an annulus. By considering the results, it was understood that raising the Soret parameter amplifies the concentration profile while the fluid flow velocity and temperature profile decreases. In numerical research work, Sardar et al. [21] studied the effects of Soret and Dufour numbers, magnetic parameter, Prandtl number, wedge angle, Schmidt number, Brownian motion parameter, variable wall temperature and concentration, and thermophoresis parameter on heat and mass transfer rates during the mixed convection flow of a Nano-fluid on a wedge. One of the presented results was that if the Dufour number takes higher values, the thickness of the thermal boundary layer increases. With increasing the Soret number and the thermophoresis parameter, the boundary layer thickness of the nanoparticle volume fraction increases. By using Buongirno's nanofluid model, Salleh et al. [22], investigated the effect of Soret and Dufour on flow behavior along with mass and heat transfer characteristics of forced convection flow around a long, narrow needle. It has been found that in a particular region, the heat and mass transfer rates were inversely related to the Dufour and directly related to the Soret, and increasing the needle thickness will cause a reduction in heat and mass transfer. Wang et al. [23] investigated the effects of Soret, Dufour, buoyancy ratio, Lewis, and Rayleigh number on the flow characteristics and the heat and mass transfer for the convection flow within an open square cavity. The results indicated that when the buoyancy ratio is −1, the lowest rate of heat and mass transfer occurs. They also found that heat and mass transfer rates enhance as the Soret and Dufour numbers increase. In contrast, the Soret and Dufour impact on the heat and mass transfer rate is not obvious when Lewis number equal to 1. Hussain et al. [24] investigated the mixed convection flow with heat and mass transfer in the presence of a magnetic field in a cavity with a porous medium. In that study, they analyze the effects of buoyancy ratio, Soret and Dufour numbers, Darcy number, the inclination of the magnetic field, Lewis number, Hartmann number, and power low index on flow, temperature, and concentration patterns, as well as heat and mass transfer rates along with entropy generation. By considering their result, we can find that an increase in the Dufour number, Darcy number, and power low index leads to an increase in the heat and mass transfer rates. The mass transfer has an upward relationship with the Soret and Lewis number. In all of the above studies, researchers have concluded that two important physical phenomena, the effect of Soret and Dufour, play a significant role in fluid flow behavior, heat, and mass transfer of DDNC. On the other hand, it has been shown that DDNC has numerous practical applications inside closed spaces at low temperatures that can ignore the effects of radiative heat transfer. However, in high-temperature situations, radiation, due to its proportionality to the fourth power of absolute temperature, has an important effect on DDNC in the processes such as nuclear reactors, crystal growth, combustion chambers, etc. [25]. Hence, this issue has received a lot of attention in recent decades. Laouar-Meftah et al. [25] studied the DDNC phenomenon in the presence of radiation heat transfer in a two-dimensional enclosure with a non-gray medium. It was indicated from their result that at any given value of the buoyancy ratio and in all flow regimes, radiation reduces the total heat transfer. The unsteady and two-dimensional natural convection flow in the presence of radiation around a semi-infinitely moving vertical cylinder has been studied by Ganesan and Loganathan [26] and considering the mass transfer. It was seen that the radiation parameter has a significant effect on temperature and velocity distributions. Ibrahimi and Lemonnier [27] investigated the transient convection flow combined with radiation in a square enclosure under the presence of thermal and solutal buoyancy forces. They obtained that in aiding situation, the radiation accelerates the transition to a steady state. At the same time, while in the opposing, it takes longer for the flow to reach the steady-state, from the oscillating state. Abidi et al. [28] presented a numerical study on the effect of radiation on three-dimensional DDNC in a cubic enclosure. They investigated the conduction-radiation parameter and the optical thickness on flow behavior. They observed that in thermally dominated flow, increasing the conduction-radiation parameter causes a change from a multicellular inner core to a unicellular one. In a solutally dominated flow, the opposite behavior occurs. In addition, they found that at all values of the buoyancy ratio, the radiation will cause an increase in the transverse velocity. Moufekkir et al. [29,30] presented a numerical analysis in which the effects of various physical parameters on DDNC in a square cavity filled with a gray fluid have been studied. They concluded that volumetric radiation modifies the flow structure and temperature distributions. Serrano-Arllano and Gijón-Rivera [31] analyzed the DDNC phenomenon coupled with radiation in a two-dimensional enclosure. They concluded that radiative heat transfer, especially at high Rayleigh number values, reduces convection heat transfer while it will increase the total heat transfer. In a numerical study, Laouar-Meftah et al. [32] studied the effect of radiation on natural convection flow along with heat and mass transfer within a two-dimensional enclosure filled with a non-gray gas. They considered two modes. In the first case, they assumed that the thermal and solutal buoyancy forces were cooperating, and in the second case, they were opposing. It has been found from their result that in the first case, radiation has a significant effect on temperature and concentration characteristics and also reduces the total heat transfer while having little effect on mass transfer. But in the second case, radiation has a greater effect, which depends on the nature of the flow regime. Cherifi et al. [33] analyzed the effect of thermal radiation on DDNC in a cubic cavity filled with a non-gray gas. It was found that radiation creates oblique stratification in the structure of constant temperature and concentration lines, and also, the total heat transfer on the vertical walls is reduced. At the same time, there is little change in mass transfer. In a numerical study, Nee [34] investigated the DDNC phenomenon of a participant fluid in a rectangular enclosure. One of the results was that increasing the radiation parameter reduces the transfer heat rate while having little effect on the mass transfer rate. The effect of thermal radiation on the flow, heat, and mass transfer characteristics of double diffusion convection has been investigated many times by considering the effects of Soret and Dufour in simple one-dimensional geometries [[35], [36], [37], [38], [39]]. Reza-E-Rabbi et al. [35] have performed numerical work to indicate the effect of radiation on the magnetic multiphase nanofluid flow over a stretching sheet. They also considered the presence of a nonlinear chemical reaction in this modeling. The results revealed that increasing the radiation, magnetic, and heat source parameters along with the Dufour number causes a reduction in the heat transfer coefficient profiles. Ijaz Khan et al. [36] investigated the effects of different flow controlling parameters on nonlinear mixed convection MHD flow in the presence of radiative heat transfer. Our outcomes illustrated that the rate of heat transfer decreases under the influence of the Prandtl number and the intensity of the magnetic field, and the rate of mass transfer increases against large values of the Schmidt number and the activation energy parameter. Ijaz Khan et al. [37] investigated the entropy generation and fluid transport properties of tangent hyperbolic nanofluid over a sheet in mixed convection flow by considering a binary chemical reaction and thermal radiation. In all of the mentioned research, the volumetric radiation has been simulated by the Rosseland approximation. While obtaining the radiation source term in the energy equation is simplified using the Rosseland appr

Suresh Ahuja Thank you for the detailed explanation. Combined heat and mass transfer are fairly common, but, including a radiation effect is new to me. I can see that in Plasmas and MHD that radiation could easily have a dominant role due to the low gas density.