The Onset of Double-Diffusive Convection in a Vertical Cylinder With Vertical Throughflow

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Vertical Cylinder ◽  
Double Diffusion ◽  
Linear Stability Theory ◽  
Double Diffusive Convection ◽  
Vertical Temperature Gradient ◽  
Vertical Temperature ◽  
Onset Of Convection ◽  
Diffusive Convection ◽  
Vertical Throughflow ◽  
Double Diffusive

The effect of vertical throughflow on the onset of convection, induced by an applied vertical temperature gradient in a vertical cylinder is studied analytically using linear stability theory. This problem is important to hydrologists to investigate under what conditions convection is taking place in a well or borehole. The effect of double diffusion is included. Both nonoscillatory and oscillatory situations are studied.

scholarly journals Reply

2008 ◽  
Vol 65 (3) ◽  
pp. 1095-1097 ◽  
Author(s):  
David M. Schultz ◽  
Adam J. Durant ◽  
Jerry M. Straka ◽  
Timothy J. Garrett
Keyword(s):  
Volcanic Ash ◽  
Effective Means ◽  
Double Diffusive Convection ◽  
Vertical Temperature ◽  
Effective Mechanism ◽  
Gravitational Forces ◽  
Salt Fingers ◽  
Diffusive Convection ◽  
Double Diffusive

Abstract Doswell has proposed a mechanism for mammatus called double-diffusive convection, the mechanism responsible for salt fingers in the ocean. The physics of salt fingers and mammatus are different. Unlike the ocean where the diffusivity is related to molecular motions within solution, the hydrometeors in clouds are affected by inertial and gravitational forces. Doswell misinterprets the vertical temperature profiles through mammatus and fails to understand the role of settling in volcanic ash clouds. Furthermore, given that mixing is a much more effective means of transferring heat in the atmosphere and given idealized numerical model simulations of mammatus showing that the destabilizing effect of subcloud sublimation is an effective mechanism for mammatus, this reply argues that double-diffusive convection is unlikely to explain mammatus, either in cumulonimbus anvils or in volcanic ash clouds.

scholarly journals Modeling of the Surface Convective Layer of Salt-Gradient Solar Ponds

1982 ◽  
Vol 104 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Y. S. Cha ◽  
W. T. Sha ◽  
W. W. Schertz
Keyword(s):  
Double Diffusive Convection ◽  
Vertical Temperature ◽  
Solar Ponds ◽  
One Dimensional ◽  
Diffusive Convection ◽  
Combined Action ◽  
Salt Gradient ◽  
Wind Mixing ◽  
Convective Layer ◽  
Double Diffusive

A one-dimensional numerical model is developed to predict the diurnal variations of vertical temperature and concentration profiles in salt-gradient solar ponds. The model employs augmented thermal and mass diffusivities due to turbulent wind mixing and double-diffusive convection. Numerical results indicate that the thickness of the surface convective layer increases with wind speed (or the wavelength of the surface wave). Double-diffusive convection is, in the absence of wind, capable of sustaining a mixed layer at the surface when strong cooling occurs over the pond. In field ponds, the surface convective layer is probably maintained as a result of the combined action of wind-generated turbulent mixing and double-diffusive convection.

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.

scholarly journals Double-Diffusive Convection of Synovial (Couple-Stress) Fluid in the Presence of Hall Current Through a Porous Medium

2018 ◽  
Vol 23 (4) ◽  
pp. 963-976
Author(s):  
M. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Synovial Fluid ◽  
Couple Stress ◽  
Hall Current ◽  
Couple Stress Fluid ◽  
Double Diffusive Convection ◽  
Onset Of Convection ◽  
Diffusive Convection ◽  
Double Diffusive

Abstract An investigation made on the effect of Hall currents on double-diffusive convection of a compressible synovial (couple-stress) fluid in the presence of a horizontal magnetic field through a porous layer is considered. The analysis is carried out within the framework of linear stability theory and normal mode technique. A dispersion relation governing the effects of viscoelasticity, compressibility, magnetic field and porous layer is derived. For the stationary convection, a synovial fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. The stable-solute gradient, compressibility, and magnetic field have postponed the onset of convection, whereas Hall currents and medium permeability have not postponed the onset of convection, moreover, a synovial fluid has a dual character in the presence of Hall currents, whereas in the absence of Hall current in synovial fluid have postponed the onset of convection, which is in contrast in case of thermal convection couple-stress fluid with same effects. These analytic results are confirmed numerically and the effects of various parameters are depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, magnetic field, porous medium and Hall currents which were non- existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

1214 Double diffusive convection during the unsteady solidification process around a vertical cylinder

2013 ◽  
Vol 2013.50 (0) ◽  
pp. 121401-121402
Author(s):  
Hiroyasu MIYAKAWA ◽  
Shigeo KIMURA ◽  
Takahiro KIWATA ◽  
Nobuyoshi KOMATU ◽  
Takaaki KONO
Keyword(s):  
Vertical Cylinder ◽  
Solidification Process ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Double Diffusive

scholarly journals Maxwell–Cattaneo double-diffusive convection: limiting cases

2021 ◽  
Vol 927 ◽  
Author(s):  
D.W. Hughes ◽  
M.R.E. Proctor ◽  
I.A. Eltayeb
Keyword(s):  
Fluid Layer ◽  
Double Diffusion ◽  
Stellar Atmospheres ◽  
Fickian Diffusion ◽  
Double Diffusive Convection ◽  
Oscillatory Convection ◽  
Future Paper ◽  
Diffusive Convection ◽  
Very High ◽  
Double Diffusive

Double-diffusive convection, in which a fluid is acted upon by two fields (such as temperature and salinity) that affect the density, has been widely studied in areas as diverse as the oceans and stellar atmospheres. Assuming classical Fickian diffusion for both heat and salt, the evolution of temperature and salinity are governed by parabolic advection–diffusion equations. In reality, there are small extra terms in these equations that render the equations hyperbolic (the Maxwell–Cattaneo effect). Although these corrections are nominally small, they represent a singular perturbation and hence can lead to significant effects when the underlying differences of salinity and temperature are large. In this paper, we investigate the linear stability of a double-diffusive fluid layer and show that amending Fick's law for the temperature, or the salinity, alone can lead to new modes of oscillation and to very large changes in the preferred wavelength of oscillatory convection at onset. In particular, the salt finger regime of classical double diffusion is here replaced by Maxwell–Cattaneo oscillations when the salt concentration is very high. The more complicated case when both laws are amended is left to a future paper, now in preparation.

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