On the stability of convective motion of a binary mixture in a plane thermal diffusion column

Tubin, A. A.

doi:10.1016/0021-8928(71)90027-x

Cited by 9 publications

(4 citation statements)

References 3 publications

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“…In this case, considerable temperature and concentration inhomegeneities in the layer are observed. Solutions (23)-(25) extend the well-known solutions of the convection equations for a homogeneous liquid [1] and for a binary mixture [2][3][4][5] to the case of thermal diffusion of a mixture under various boundary conditions (the presence or absence of longitudinal temperature or concentration gradients and their various directions).…”

Section: The Interpretation Of Solution (19) Found In Example No mentioning

confidence: 87%

“…In particular, the stability of convective flows of a binary mixture in a vertical channel in the presence of longitudinal concentration and (or) temperature gradients ignoring thermal diffusion was studied in [2,3]. The effect of thermal diffusion on the stability of a vertical layer with a constant temperature difference between the walls was investigated in [4,5] (in the layer there was also a longitudinal concentration gradient). The instability of a plane horizontal layer of an incompressible binary gas mixture subjected to a time-dependent transverse temperature gradient was studied in [6].…”

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Invariant Solutions of the Thermal-Diffusion Equations for a Binary Mixture in the Case of Plane Motion

Ryzhkov

2006

J Appl Mech Tech Phys

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UDC 519.46:533.375 I. I. RyzhkovThe group properties of the thermal-diffusion equations for a binary mixture in plane flow are studied. Optimal systems of first-and second-order subalgebras are constructed for the admissible Lie operator algebra, which is infinite-dimensional. Examples of the exact invariant solutions are given, which are found by solving ordinary differential equations. Exact solutions are found that describe thermal diffusion in an inclined layer with a free boundary and in a vertical layer in the presence of longitudinal temperature and concentration gradients. The effect of the thermal-diffusion parameter on the flow regime is studied.Introduction. Thermal diffusion is molecular transfer of material due to the presence of a temperature gradient in the medium (liquid solution or gas mixture). In the case of thermal diffusion, the components have different concentrations in the regions of elevated and decreased temperature. The presence of concentration gradients results in ordinary diffusion. A steady state is established when the diffusion and thermal-diffusion processes compensate for each other (i.e., the process of separation of the mixture components is compensated by the process of their mixing). In practice, a frequently occurring case is normal thermal diffusion, in which the heavier components move to the colder regions and the lighter components pass to the more heated regions. In some cases, there may be anomalous thermal diffusion, in which the direction of motion of the components is opposite.The present paper considers a model for the convective motion of a binary mixture taking into account thermal diffusion. The model is based on the Navier-Stokes equations supplemented by diffusion and heat-transfer equations. The Oberbeck-Boussinesq approximation, intended to describe convective flows under natural earth conditions, is used. It is assumed that the density of the mixture depends linearly on the temperature and concentration of the light component: ρ = ρ 0 (1 − β 1 T − β 2 C). Here ρ 0 is the density of the mixture for the average values of the temperature and concentration, T and C are small deviations from the average values, β 1 is the thermal-expansion coefficient of the mixture, and β 2 is the density concentration coefficient (β 2 > 0 since C is the concentration of the light component). The motion of the mixture is described by the system [1]where u is the velocity, p is the pressure deviation from the hydrostatic value, ν are χ are the kinematic viscosity and thermal diffusivity of the mixture, respectively, d is the diffusion coefficient, α is the thermal-diffusion parameter, and g is the free-fall acceleration. It is assumed that all characteristics of the medium are constant and correspond

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Section: The Interpretation Of Solution (19) Found In Example No mentioning

confidence: 87%

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confidence: 99%

Invariant Solutions of the Thermal-Diffusion Equations for a Binary Mixture in the Case of Plane Motion

Ryzhkov

2006

J Appl Mech Tech Phys

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“…It was assumed that the vertical temperature and (or) concentration gradients were present in the layer. The influence of Soret effect on the flow in a vertical layer was studied in [12,13]. The solutions presented in the above papers are generalized to the case of a binary mixture with Soret effect in [14] by using the symmetry analysis method.…”

Section: Introductionmentioning

confidence: 98%

On double diffusive convection with Soret effect in a vertical layer between co-axial cylinders

Ryzhkov

2006

Physica D: Nonlinear Phenomena

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“…One of the first was conducted by Rudakov [18,19] regarding pure liquids. Convective stability analyses of a binary incompressible fluid on normal perturbations to a thermal gradient were performed later by Nikolaev and Tubin [20] and accounted for the dependency on a concentration gradient. Gershuni et al [21] examined a binary mixture in which the buoyancy force was a function of temperature difference only.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis under thermogravitational effect

Šeta

Gavaldà

Bou-Ali

et al. 2020

International Journal of Thermal Sciences

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On the stability of convective motion of a binary mixture in a plane thermal diffusion column

Cited by 9 publications

References 3 publications

Invariant Solutions of the Thermal-Diffusion Equations for a Binary Mixture in the Case of Plane Motion

Invariant Solutions of the Thermal-Diffusion Equations for a Binary Mixture in the Case of Plane Motion

On double diffusive convection with Soret effect in a vertical layer between co-axial cylinders

Stability analysis under thermogravitational effect

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