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 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.

Boundary-layer solutions of single-mode convection equations

1981 ◽  
Vol 102 ◽  
pp. 211-219 ◽  
Author(s):  
N. Riahi
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Single Mode ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Inertial Terms ◽  
Large Rayleigh Number

Nonlinear thermal convection between two stress-free horizontal boundaries is studied using the modal equations for cellular convection. Assuming a large Rayleigh number R the boundary-layer method is used for different ranges of the Prandtl number σ. The heat flux F is determined for the values of the horizontal wavenumber a which maximizes F. For a large Prandtl number, σ [Gt ] R⅙(log R)−1, inertial terms are insignificant, a is either of order one (for $\sigma \geqslant R^{\frac{2}{3}}$) or proportional to $R^{\frac{1}{3}}\sigma^{-\frac{1}{2}}$ (for $\sigma \ll R^{\frac{2}{3}}$) and F is proportional to $R^{\frac{1}{3}}$. For a moderate Prandtl number, \[ (R^{-1}\log R)^{\frac{1}{9}} \ll \sigma \ll R^{\frac{1}{6}}(\log R)^{-1}, \] inertial terms first become significant in an inertial layer adjacent to the viscous buoyancy-dominated interior, and a and F are proportional to R¼ and \[ R^{\frac{3}{10}}\sigma^{\frac{1}{5}} (\log\sigma R^{\frac{1}{4}})^{\frac{1}{10}}, \] respectively. For a small Prandtl number, $R^{-1} \ll \sigma \ll (R^{-1} \log R)^{\frac{1}{9}}$, inertial terms are significant both in the interior and the boundary layers, and a and F are proportional to ($R \sigma)^{\frac{9}{32}} (\log R\sigma)^{-\frac{1}{32}}$ and ($R \sigma)^{\frac{5}{16}} (\log R \sigma)^{\frac{3}{16}}$, respectively.

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.

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.

Oscillatory double-diffusive instabilities in a vertical slot

2001 ◽  
Vol 426 ◽  
pp. 347-354 ◽  
Author(s):  
OLIVER S. KERR
Keyword(s):  
Prandtl Number ◽  
Linear Stability ◽  
Salinity Gradient ◽  
Double Diffusive Convection ◽  
Salinity Gradients ◽  
Vertical Slot ◽  
Diffusive Convection ◽  
Prandtl Numbers ◽  
Double Diffusive ◽  
Oscillatory Instabilities

Recent linear stability analyses of double-diffusive convection in a laterally heated vertical slot containing water have shown that for very weak (or no) vertical salinity gradient the initial instabilities are steady, but as the salinity gradient is increased there is a transition to oscillatory instabilities. For higher Prandtl number fluids the initial instabilities in a slot with no stratification can be oscillatory or wave-like. We show that the oscillatory instabilities in water are linked to these higher Prandtl number oscillatory instabilities. The salinity gradient has a destabilizing effect on these oscillations, making them appear for Prandtl numbers where oscillatory instabilities are not possible in the absence of salinity gradients. We derive an asymptotic description for this mode of instability.

scholarly journals On the Onset of Double-diffusive Convection in a Couple Stress Nanofluid in a Porous Medium

2018 ◽  
Vol 62 (3) ◽  
pp. 233-240
Author(s):  
Gian C. Rana ◽  
Ramesh Chand
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Stationary Convection ◽  
Stress Parameter ◽  
Diffusive Convection ◽  
Double Diffusive ◽  
Solutal Rayleigh Number

Double-diffusive convection in a horizontal layer of nanofluid in a porous medium is studied. The couple-stress fluid model is considered to describe the rheological behavior of the nanofluid and for porous medium Darcy model is employed. The model applied for couple stress nanofluid incorporates the effect of Brownian motion and thermophoresis. We have assumed that the nanoparticle concentration flux is zero on the boundaries which neutralizes the possibility of oscillatory convection and only stationary convection occurs. The dispersion relation describing the effect of various parameters is derived by applying perturbation theory, normal mode analysis method and linear stability theory. The impact of various physical parameters, like the couple stress parameter, medium porosity, solutal Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have been examined on the stationary convection. It is observed that the couple stress parameter, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effects on the stationary convection whereas the solutal Rayleigh number and Dufour parameter have very small effect on the system.

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