scholarly journals Nonlinear Double-diffusive Convection in a Low Prandtl Number Fluid

1980 ◽  
Vol 33 (1) ◽  
pp. 59 ◽  
Author(s):  
N Riahi
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Layer Structure ◽  
Solute Concentration ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Solute Fluxes ◽  
Boundary Layer Method ◽  
Double Diffusive

Nonlinear double-diffusive convection is studied using the modal equations of cellular convection. The boundary layer method is used by assuming a large Rayleigh number R for a fluid of low Prandtl number (J, and different ranges of the diffusivity ratio 7: and. the solute Rayleigh number Rs. The heat and solute fluxes are found to increase with R(J and decrease with Rs. The effect of the solute is stabilizing, although the convection in a fluid with large (J is less affected by the solute concentration. The flow is shown to have a solute layer which thickens as (J, R, .-1 or R;l decreases. It is proved that it is only for this layer that the solute affects the boundary layer structure.

Nonlinear Double-diffusive Convection in a Moderate Prandtl Number Fluid

1981 ◽  
Vol 34 (2) ◽  
pp. 185
Author(s):  
N Riahi
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Double Diffusive Convection ◽  
Layer Method ◽  
Diffusive Convection ◽  
Solute Fluxes ◽  
Boundary Layer Method ◽  
Moderate Prandtl Number Fluid ◽  
Large Rayleigh Number ◽  
Double Diffusive

Recent work on nonlinear double-diffusive convection in a low Prandtl number fluid is extended to the case of a moderate Prandtl number G'. The boundary layer method is used by assuming a large Rayleigh number R for different ranges of the diffusivity ratio -c and the solute Rayleigh number R; It is found that the heat and solute fluxes F and F; increase with G', Rand n;', and that F; F- 1 is independent of G'. The flow is shown to have a solute layer of thickness proportional to F-1-2, The horizontal wavenumber which maximizes F is found to be independent of G', but it increases with Rand R;1

scholarly journals Simulations of a double-diffusive interface in the diffusive convection regime

2012 ◽  
Vol 711 ◽  
pp. 411-436 ◽  
Author(s):  
J. R. Carpenter ◽  
T. Sommer ◽  
A. Wüest
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Molecular Diffusion ◽  
Layer Structure ◽  
Previous Theory ◽  
Convection Regime ◽  
Graphic Interface ◽  
Diffusive Convection ◽  
Diffusive Interface ◽  
Double Diffusive

AbstractThree-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A ‘double-boundary-layer’ structure is found in all of the simulations, in which the temperature ($T$) interface has a greater thickness than the salinity ($S$) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The $TS$-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the $TS$-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the $S$-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

Temperature Modulation of Double Diffusive Convection in a Horizontal Fluid Layer

2006 ◽  
Vol 61 (7-8) ◽  
pp. 335-344 ◽  
Author(s):  
Beer Singh Bhadauria
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Thermosolutal Convection ◽  
Periodic Part ◽  
Temperature Modulation ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Horizontal Fluid Layer ◽  
Double Diffusive ◽  
Diffusivity Ratio

Linear stability analysis is performed for the onset of thermosolutal convection in a horizontal fluid layer with rigid-rigid boundaries. The temperature field between the walls of the fluid layer consists of two parts: a steady part and a time-dependent periodic part that oscillates with time. Only infinitesimal disturbances are considered. The effect of temperature modulation on the onset of thermosolutal convection has been studied using the Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of frequency and amplitude of modulation, Prandtl number, diffusivity ratio and solute Rayleigh number. Stabilizing and destabilizing effects of modulation on the onset of double diffusive convection have been obtained. The effects of the diffusivity ratio and solute Rayleigh number on the stability of the system are also discussed.

scholarly journals Double Diffusive Convection in a Layer of Maxwell Viscoelastic Fluid in Porous Medium in the Presence of Soret and Dufour Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Viscoelastic Fluid ◽  
Fluid Layer ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Free Boundaries ◽  
Soret And Dufour Effects ◽  
Diffusive Convection ◽  
Double Diffusive

Double diffusive convection in a horizontal layer of Maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient (Soret effects) and concentration gradient (Dufour effects) is investigated. For the porous medium Darcy model is considered. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the Maxwell viscolastic fluid layer confined between two free-free boundaries. Rayleigh number on the onset of stationary and oscillatory convection has been derived and graphs have been plotted to study the effects of the Dufour parameter, Soret parameter, Lewis number, and solutal Rayleigh number on stationary convection.

Melting heat transfer in the stagnation-point flow of Maxwell fluid with double-diffusive convection

2014 ◽  
Vol 24 (3) ◽  
pp. 760-774 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Farooq ◽  
Ahmad Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Stagnation Point ◽  
Boundary Layer Thickness ◽  
Double Diffusive Convection ◽  
Content Type ◽  
Diffusive Convection ◽  
Double Diffusive

Purpose – The purpose of this paper is to analyze the melting heat transfer in the stagnation-point flow with double-diffusive convection. Design/methodology/approach – Series solutions for velocity, temperature and concentration are constructed via homotopy analysis method. Findings – The authors observed that the behaviors of N, ?2 and M on the velocity and boundary layer thickness are qualitatively similar. Further, for A<1 the velocity profile and boundary layer thickness increase with the increase of A. However, when A>1 then the velocity profile increases but the boundary layer thickness decreases when A is increased. Originality/value – This analysis has not been discussed in the literature previously.

Onset of Double Diffusive Convection in a Thermally Modulated Fluid-Saturated Porous Medium

2008 ◽  
Vol 63 (5-6) ◽  
pp. 291-300 ◽  
Author(s):  
Beer S. Bhadauria ◽  
Aalam Sherani
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Periodic Part ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Fluid Saturated Porous Medium ◽  
The Galerkin Method ◽  
Double Diffusive

The onset of double diffusive convection in a sparsely packed porous medium was studied under modulated temperature at the boundaries, and a linear stability analysis has been made. The primary temperature field between the walls of the porous layer consisted of a steady part and a timedependent periodic part and the Galerkin method and the Floquet were used. The critical Rayleigh number was found to be a function of frequency and amplitude of modulation, Prandtl number, porous parameter, diffusivity ratio and solute Rayleigh number.

scholarly journals Linear and Nonlinear Stability Analysis of Double Diffusive Convection in a Maxwell Fluid Saturated Porous Layer with Internal Heat Source

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Moli Zhao ◽  
Qiangyong Zhang ◽  
Shaowei Wang
Keyword(s):  
Rayleigh Number ◽  
Heat Source ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Maxwell Fluid ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Linear And Nonlinear ◽  
Double Diffusive

The onset of double diffusive convection is investigated in a Maxwell fluid saturated porous layer with internal heat source. The modified Darcy law for the Maxwell fluid is used to model the momentum equation of the system, and the criterion for the onset of the convection is established through the linear and nonlinear stability analyses. The linear analysis is obtained using the normal mode technique, and the nonlinear analysis of the system is studied with the help of truncated representation of Fourier series. The effects of internal Rayleigh number, stress relaxation parameter, normalized porosity, Lewis number, Vadasz number and solute Rayleigh number on the stationary, and oscillatory and weak nonlinear convection of the system are shown numerically and graphically. The effects of various parameters on transient heat and mass transfer are also discussed and presented analytically and graphically.

scholarly journals Numerical Simulations of Melt-Driven Double-Diffusive Fluxes in a Turbulent Boundary Layer beneath an Ice Shelf

2020 ◽  
Author(s):  
Leo Middleton ◽  
Catherine A. Vreugdenhil ◽  
Paul R. Holland ◽  
John R. Taylor
Keyword(s):  
Boundary Layer ◽  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Small Scale ◽  
Relevant Parameter ◽  
Double Diffusive Convection ◽  
Ice Shelf ◽  
Diffusive Convection ◽  
Forced Turbulence ◽  
Double Diffusive

AbstractThe transport of heat and salt through turbulent ice shelf-ocean boundary layers is a large source of uncertainty within ocean models of ice shelf cavities. This study uses small-scale, high resolution, 3D numerical simulations to model an idealised boundary layer beneath a melting ice shelf to investigate the influence of ambient turbulence on double-diffusive convection (i.e. convection driven by the difference in diffusivities between salinity and temperature). Isotropic turbulence is forced throughout the simulations and the temperature and salinity are initialised with homogeneous values similar to observations. The initial temperature and the strength of forced turbulence are varied as controlling parameters within an oceanographically relevant parameter space. Two contrasting regimes are identified. In one regime double-diffusive convection dominates, and in the other convection is inhibited by the forced turbulence. The convective regime occurs for high temperatures and low turbulence levels, where it is long-lived and affects the flow, melt rate and melt pattern. A criterion for identifying convection in terms of the temperature and salinity profiles, and the turbulent dissipation rate, is proposed. This criterion may be applied to observations and theoretical models to quantify the effect of double-diffusive convection on ice shelf melt rates.

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