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The purpose of this paper is to study analytically and numerically the Soret effect on double diffusive natural convection induced in a horizontal Darcy porous layer subject to lateral heat and mass fluxes. The work focuses on the particular situation where the solutal to thermal buoyancy forces ratio, N, is related to the Soret parameter, S_P, by the relation. For this particular situation, the rest state is a solution of the problem. The analytical identification of the parallel flow bifurcations counts among the objectives of the study. The effect of the governing parameters on the fluid flow properties and heat and mass transfer characteristics is also examined.

Both the Darcy model and the Boussinesq approximation are used for the mathematical formulation of the problem. The geometry under study is a horizontal porous cavity filled with a binary fluid. The problem is solved analytically on the basis of the parallel flow approximation, valid in the case of a shallow cavity. The analytical results are validated numerically using a second‐order finite difference method.

The main finding is the absence of a supercritical bifurcation for this problem. More precisely, in the studied case, only the subcritical convection was found possible for the parallel flow structure and its threshold was determined analytically versus the governing parameters. It is also shown that the S_P‐Le plane can be divided into two parallel flow regions; in one region the flow is counterclockwise while it is clockwise in the other. At sufficiently large values of R_T, two solutions of ψ0, termed as “stable” and “unstable” and varying, respectively, as R_T^1/3 and R_T⁻¹ were obtained. The flows corresponding to these solutions are rotating in the same direction with different intensities. An analytical expression is established for the critical Rayleigh number which allows a control of the onset of motion in the system.

The thermodiffusion phenomenon in saturated porous geometries is of practical interest in several natural and technological processes such as the migration of moisture through air contained in fibrous insulations, food processing, contaminant transport in ground water, electrochemical processes, etc.

The study concerns the Soret effect within a system subject to outside mass flux. Only one type of bifurcation (subcritical bifurcation) was found possible for the parallel flow structure in the present configuration instead of two kinds of bifurcations (supercritical and subcritical).

The purpose of this paper is to study analytically and numerically the effect of a transverse magnetic field on the separation of species induced in an inclined rectangular porous cavity saturated with an electrically conducting mixture.

The porous layer is assumed homogeneous and submitted from its long sides to uniform heat fluxes and to a magnetic field of strength B. The Darcy model combined with the Boussinesq approximation are used to study the heat and solute transfer in the medium. An analytical solution is developed on the basis of the parallel flow approximation. Numerical simulations are also performed in order to validate the analytical solution. The controlling parameters of this problem are the thermal Rayleigh number, the inclination of the enclosure, the separation parameter, the Hartmann number and the Lewis number.

For given values of the thermal Rayleigh number, the inclination of the enclosure, the separation parameter and the Lewis number, there is an optimal magnetic field which leads to a maximum of separation. At relatively high Rayleigh numbers, where convection destroys the separation process, it is possible, with an optimal choice of the Hartman number, to recover a good level of separation.

Since the problem is governed by several parameters (five parameters), only the Darcy model was used in this study instead of the Darcy-Brinkman extended model even if the latter model allows to cover the pure fluid and Darcy porous media as limiting cases.

In separation experiments, it is very difficult technically to work with small Rayleigh numbers due to technical difficulties. However, the process of separations is canceled at high Rayleigh number by the strength of convection which causes a mixing in the binary mixture. This study shows that, by using adequate combinations of the controlling parameters, it becomes possible to reach a good level of separation even at relatively high Rayleigh numbers.

Optimum choice of the magnetic field and the inclination of the cavity may lead to a good level of the separation process. For large Lewis numbers, the separation vanishes far above and far below the optimal Ha. However, for small Lewis numbers, an important level of separation is maintained for any Ha located below the optimal value of the latter parameter.

Thermodiffusion or Soret effect is a phenomenon that can be encountered in many applications. However only little is known about this phenomenon, particularly in the case of sparsely packed media (i.e. Brinkman media). The aim of this paper is to study numerically and analytically the effect of thermodiffusion on the onset of natural convection in a horizontal Brinkman porous layer with a free‐stress upper boundary.

The study is performed by solving numerically the governing equations for different combinations of the governing parameters. An analytical solution is also developed in the case of a shallow layer using the approximation of a parallel flow in the core region to predict the critical conditions corresponding to the onset stationary, subcritical and Hopf convection.

The results obtained show that, in the presence of Soret effect, the numerical and analytical solutions agree well for long enough layers. The thermodiffusion parameter can affect considerably the supercritical and sub‐critical Rayleigh numbers and heat and mass transfer characteristics in the layer. It is also shown that the plane Le‐φ can be divided into three main regions with specific and different behaviours.

The Soret effect can play a stabilizing or a destabilizing role and this, depending on the sign of the separation parameter, φ.

The purpose of this paper is to study numerically thermosolutal natural convection within an inclined rectangular cavity in the presence of Soret effect and heat generation. The enclosure is heated and salted from its long sides with constant but different temperatures and concentrations. The study focuses on the effects of three main parameters which are, the Soret parameter (Sr = 0 and –0.5), the internal to external Rayleigh numbers ratio 0 ≤ R ≤ 80 and the cavity inclination γ, varied from 0° (vertical position) to 60°. The combined effects of these parameters on fluid flow and heat and mass transfer characteristics are examined for the external Rayleigh number Ra_E = 10⁵, the Prandtl number Pr = 0.71, the buoyancy ratio N = 1, the Lewis number Le = 2 and the aspect ratio of the cavity A = 2.

A hybrid lattice Boltzmann-finite difference method (LBM-FD) was used to tackle the problem under consideration. The LBM with the simple relaxation time was used for the fluid flow in the presence of the gravity force, while the temperature and concentration equations were solved separately using an explicit finite-difference technique at the Boltzmann scale.

The monocellular nature of the flow, obtained for R = 0 is not destroyed by varying the cavity inclination and the Soret parameter but rather by the increase of the parameter R. The Soret parameter and the cavity inclination become perceptible at high values of R. The inclination γ = 60° leads to high mean temperatures compared to the other inclinations. The effect of R on mean concentration is amplified in the presence of Soret effect but limited in the absence of the latter. The negative Soret parameter combined with high internal heat generation and a relatively high inclination is important when the objective is to maintain the fluid at a high concentration of species. The presence of bicellular flow combined with the important elevation undergone by the fluid temperature, makes both the cold and hot walls playing a cooling role with the most important exchanges taking place at the upper part of these walls. The analysis of the mean mass transfer shows that the increase of the inclination may lead to an increase or a decrease of the mass transfer depending on the range of R, in the case of Sr = 0. However, for Sr = −0.5, it is observed that the increase of γ is generally accompanied by a reduction of the mass transfer.

To the best of the authors’ knowledge, the hybrid LBM-FD was not used before to study such a problem. Combined effect of R and inclination may be useful in charging the fluid with species when the objective is to maintain high concentrations in the medium.

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.

Based on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R² = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.

The research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.

The paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

In order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.

Based on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R²) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.

The model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.