The Influence of Coupled Molecular Diffusion on Double-Diffusive Convection in a Porous Medium

1986 ◽  
Vol 108 (4) ◽  
pp. 872-876 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty
Keyword(s):  
Porous Medium ◽  
Molecular Diffusion ◽  
Normal Mode Analysis ◽  
Finite Amplitude ◽  
Mode Analysis ◽  
Double Diffusive Convection ◽  
Amplitude Analysis ◽  
Cross Diffusion ◽  
Diffusive Convection ◽  
Double Diffusive

The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.

scholarly journals THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN A LAYER OF NANOFLUID UNDER ROTATION

2016 ◽  
Vol 15 (1) ◽  
pp. 88
Author(s):  
G. C. Rana ◽  
R. C. Thakur
Keyword(s):  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Brownian Diffusion ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Solute Gradient ◽  
Double Diffusive

Double-diffusive convection in a horizontal layer of nanofluid under rotation heated from below is studied. The nanofluid describes the effects of thermophoresis and Brownian diffusion. Based upon perturbations and linear stability theory, the normal mode analysis method is applied to obtain the dispersion relation characterizing the effect of different parameters when both the boundaries are free. Due to thermal expansion, the nanofluid at the bottom will be lighter than the fluid at the top. Thus, this is a top heavy arrangement which is potentially unstable. In this paper we discuss the influences of various non-dimensional parameters such as rotation, solute gradient, thermo- nanofluid Lewis number, thermo-solutal Lewis number, Soret and Dufour parameter on the stability of stationary convection for the case of free-free boundaries. It is observed that rotation and solute gradient have stabilizing influence on the system. Rotation and solute gradient play important role in the thermal convection of fluid layer and has applications in rotating machineries such as nuclear reactors, petroleum industry, biomechanics etc. and solute gradient finds applications in geophysics, food processing, soil sciences, oil reservoir modeling, oceanography etc. A very good agreement is found between the present paper and earlier published results.

Double-diffusive convection caused by coupled molecular diffusion

1983 ◽  
Vol 126 ◽  
pp. 379-397 ◽  
Author(s):  
Trevor J. Mcdougall
Keyword(s):  
Molecular Diffusion ◽  
Soret Effect ◽  
Diffusion Flux ◽  
Spatial Gradient ◽  
Double Diffusive Convection ◽  
Diffusion Effect ◽  
Cross Diffusion ◽  
Coupled Diffusion ◽  
Diffusive Convection ◽  
Double Diffusive

Double-diffusive convection is studied for the case where a large coupled diffusion (or cross-diffusion) effect is present. The Soret effect is a familiar example of this cross-diffusion where the flux of the solute depends not only on its own spatial gradient but also on the in situ temperature gradient. The linear stability analysis of double-diffusive convection has been extended to include the two cross-diffusion flux terms and it has been shown that, with a sufficiently large coupled diffusion effect, fingers can form even when the concentrations of both components make the fluid's density gradient statically stable. The conditions under which the diffusive instability can occur are compared with those for the formation of fingers and it is shown that these two types of double-diffusive convection cannot occur together in any particular set of linear property gradients. We then consider finite-amplitude, steady, infinitely long fingers and show that a sufficiently large cross-diffusion effect can again allow fingers to exist when the concentrations of both solutes increase with depth. It is also shown that the diffusion of properties from an initially sharp interface may set up vertical gradients that are favourable for the formation of fingers.

Sign in / Sign up

Export Citation Format

Share Document