The infinite Schmidt number limit of the salt fingering convection model and the inertial free salt convection model

Cao, Yining; Wang, Xiaoming; Xie, Jin-Han

doi:10.1016/j.mechrescom.2022.104024

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…The form of this system of partial differential equations is exactly the same as what one finds from Navier-Stokes theory except that there is now present the higher derivative term −ν 2 v i . Devi and Mahajan [22] and Mahajan and Nandal [23] develop linear instability and nonlinear stability analyses for (9) and for an analogous system with a heat source, respectively. Both sets of writers prescribe boundary conditions on v i and T , but no discussion is included initially on further boundary conditions, a topic we return to in Sect.…”

Section: 3mentioning

confidence: 99%

“…It is worth drawing attention to the fact that thermal convection studies involving a Navier-Stokes fluid are topics of much recent interest and importance in real life, see, e.g. [8][9][10][11][12][13][14]. It is interesting to wonder if these effects could be much richer with hyperstress effects introduced by the presence of higher spatial gradients in the momentum equation.…”

Section: Introductionmentioning

confidence: 99%

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Thermal convection in a higher-gradient Navier–Stokes fluid

Straughan

2023

Eur. Phys. J. Plus

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We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing models for thermal convection, analysing these in detail, and deriving critical Rayleigh and wave numbers for the onset of convective fluid motion. In addition to linear instability theory we present a careful analysis of fully nonlinear stability theory. The theories analysed all possess a bi-Laplacian term in addition to the normal spatial derivative term. The theories discussed are Stokes couple stress theory, dipolar fluid theory, Green–Naghdi theory, Fried–Gurtin–Musesti theory, and a second theory of Fried and Gurtin. We show that the Stokes couple stress theory and the Fried–Gurtin–Musesti theory involve the same partial differential equations while those of Green–Naghdi and dipolar theory are similar. However, we concentrate on boundary conditions which are crucial to understand all five theories and their differences.

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Section: 3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal convection in a higher-gradient Navier–Stokes fluid

Straughan

2023

Eur. Phys. J. Plus

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“…Schmidt number (Sc) represents the ratio of kinematic viscosity coefficient and diffusion coefficient and describes fluids with both momentum and mass diffusion. Sc was calculated using the Stokes–Einstein empirical equation, as described in eq Sc = μ / ρ D AB …”

Section: Establishing a Mathematical Model For Solid–liquid Extractionmentioning

confidence: 99%

Simulation and Experimental Study of Solid–Liquid Extraction of Coal Tar Residue Based on Different Extractants

Yang,

Fan,

et al. 2023

ACS Omega

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Coal tar residue (CTR) is recognized as a hazardous industrial waste with a high carbon content and coal tar consisting mainly of toxic polycyclic aromatic hydrocarbons (PAHs). The coal tar in CTR can be deeply processed into high-value-added fuels and chemicals. Effective separation of coal tar and residue in CTR is a high-value-added utilization method for it. In this paper, ethyl acetate, ethanol, and n -hexane were chosen as extractants to study the extraction process of coal tar from CTR, considering the mass transfer in the liquid phase outside the CTR particles and the diffusion inside the CTR particles, and a mathematical model of the solid–liquid extraction process of CTR was established based on Fick’s second law. First, the mass-transfer coefficients ( k f ) and effective diffusion coefficients ( D e ) of ethyl acetate, ethanol, and n -hexane in solid–liquid extraction at 35 °C were determined to be 1.54 × 10 –5 and 4.99 × 10 –10 m 2 ·s –1 , 1.14 × 10 –5 and 3.57 × 10 –10 m 2 ·s –1 , and 1.01 × 10 –5 and 3.48 × 10 –10 m 2 ·s –1 , respectively. Furthermore, the simulated values obtained by the model also maintained a high degree of agreement with the experimental results, which indicates the high accuracy prediction of the model. Finally, the model was used to investigate the effects of the solvent–solid ratio, temperature, and stirring speed on the extraction rates with the three extractants. According to the analysis with gas chromatography–mass spectrometry (GC-MS), among the three solvents, n -hexane extracted the highest content of aliphatic hydrocarbons (ALHs), ethyl acetate extracted the highest content of oxygenated compounds (OCs), and ethanol extracted the highest content of aromatic hydrocarbons (ARHs). The model and experimental data can be used to provide accurate predictions for industrial utilization of CTR.

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Ginzburg–Landau equations for the salt fingering region with the onset of microorganisms

Hingis

Muthtamilselvan

2024

Mathematics and Computers in Simulation

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The infinite Schmidt number limit of the salt fingering convection model and the inertial free salt convection model

Cited by 3 publications

References 16 publications

Thermal convection in a higher-gradient Navier–Stokes fluid

Thermal convection in a higher-gradient Navier–Stokes fluid

Simulation and Experimental Study of Solid–Liquid Extraction of Coal Tar Residue Based on Different Extractants

Ginzburg–Landau equations for the salt fingering region with the onset of microorganisms

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