Effects of Nonuniform Thermal Gradient and Adiabatic Boundaries on Convection in Porous Media

1980 ◽  
Vol 102 (2) ◽  
pp. 254-260 ◽  
Author(s):  
N. Rudraiah ◽  
B. Veerappa ◽  
S. Balachandra Rao
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heat Source ◽  
Thermal Gradient ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Single Term ◽  
Special Cases ◽  
Basic Temperature ◽  
Bounding Surfaces

The effects of different combinations of thermally insulated boundaries and nonuniform thermal gradient caused by either sudden heating or cooling at the boundaries or by distributed heat sources on convective stability in a fluid saturated porous medium are investigated using linear theory by considering the Brinkman model. In the case of sudden heating or cooling, solutions are obtained using single-term Galerkin expansion and attention is focused on the situation where the critical Rayleigh number is less than that for uniform temperature gradient and the convection is not maintained. Numerical values are obtained for various basic temperature profiles and some general conclusions about their destabilizing effects are presented. In particular, it is shown that the results of viscous fluid (σ = 0) and the usual Darcy porous medium (σ → ∞) emerge from our analysis as special cases. In the case of convection caused by heat source, since the effect of heat source is not brought out by the single-term Galerkin expansion, the critical internal Rayleigh number is determined using higher order expansion by specifying the external Rayleigh number. It is shown that, for values of σ2 ≥ 2.45 × 105, the different combinations of bounding surfaces give almost the same Rayleigh number and an explanation, following Lapwood, for this surprising behavior is given. It is found that the heat source’s effect on convection decreases for wave numbers up to the value 2.2 and drops suddenly around the critical value of 2.4 and then increases up to 2.5.

Thermal Convective Instabilities in a Porous Medium

1984 ◽  
Vol 106 (1) ◽  
pp. 137-142 ◽  
Author(s):  
M. Kaviany
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Temperature Distribution ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Onset Of Convection ◽  
Long Time ◽  
Nonlinear Temperature

The onset of convection due to a nonlinear and time-dependent temperature stratification in a saturated porous medium with upper and lower free surfaces is considered. The initial parabolic temperature distribution is due to uniform internal heating. The medium is then cooled by decreasing the upper surface temperature linearly with time. Linear stability theory is applied to the more formally developed governing equations. In order to obtain an asymptotic solution for transient problems involving very long time scales, the critical Rayleigh number for steady-state, nonlinear temperature distribution is also obtained. The effects of porosity, permeability, and Prandtl number on the time of the onset of convection are examined. The steady-state results show that the critical Rayleigh number depends only on the ratio of porosity to permeability and when this ratio exceeds a value of one thousand, the critical Rayleigh number is directly proportional to this ratio.

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.

Interacting convection modes in a saturated porous medium of nearly square planform: four modes

2017 ◽  
Vol 82 (3) ◽  
pp. 526-547 ◽  
Author(s):  
Brendan J. Florio ◽  
Andrew P. Bassom ◽  
Konstantinos Sakellariou ◽  
Thomas Stemler
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Critical Value ◽  
Basins Of Attraction ◽  
Stable States ◽  
Pitchfork Bifurcations ◽  
Multiple Stable States ◽  
Box Dimensions

Abstract Convection can occur in a confined saturated porous box when the associated Rayleigh number exceeds a threshold critical value: the identity of the preferred onset convection mode depends sensitively on the geometry of the box. Here we discuss examples for which the box dimensions are such that four modes share a common critical Rayleigh number. Perturbation theory is used to derive a system of coupled ordinary differential equations that governs the nonlinear interaction of the four modes and an analysis of this set is undertaken. In particular, it is demonstrated that as the Rayleigh number is increased beyond critical so a series of pitchfork bifurcations occur and multiple stable states are identified that correspond to the survival of just one of the four modes. The basins of attraction for each mode in the 4D phase space are described by a reduction to a suitable 3D counterpart.

Finite Amplitude Convection in a Rotating Porous Medium

1987 ◽  
Vol 42 (1) ◽  
pp. 13-20
Author(s):  
B. S. Dandapat
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Interstitial Fluid ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Onset Of Convection

The onset of convection in a horizontal layer of a saturated porous medium heated from below and rotating about a vertical axis with uniform angular velocity is investigated. It is shown that when S ∈ σ >1, overstability cannot occur, where ε is the porosity, σ the Prandtl number and S is related to the heat capacities of the solid and the interstitial fluid. It is also shown that for small values of the rotation parameter T1, finite amplitude motion with subcritical values of Rayleigh number R (i.e. R < Re, where Re is the critical Rayleigh number according to linear stability theory) is possible. For large values of T1, overstability is the preferred mode.

Stability and Convection in Impulsively Heated Porous Layers

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
M. J. Kohl ◽  
M. Kristoffersen ◽  
F. A. Kulacki
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Axisymmetric Flow ◽  
Temperature Fluctuations ◽  
Lower Surface ◽  
Onset Of Convection ◽  
Upward Moving ◽  
The Stability

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η−0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

Solar Radiation Effect on a Magneto Nanofluid Flow in a Porous Medium with Chemically Reactive Species

2018 ◽  
Vol 16 (9) ◽  
Author(s):  
Mohamed R. Eid ◽  
O.D. Makinde
Keyword(s):  
Porous Medium ◽  
Solar Radiation ◽  
Saturated Porous Medium ◽  
Surface Concentration ◽  
Radiation Absorption ◽  
Physical Parameters ◽  
Radiation Chemical ◽  
Electrically Conducting ◽  
Special Cases ◽  
Chemically Reactive Species

Abstract The combined impact of solar radiation, chemical reaction, Joule heating, viscous dissipation and magnetic field on flow of an electrically conducting nanofluid over a convectively heated stretching sheet embedded in a saturated porous medium is simulated. By using appropriate similarity transformation, the governing nonlinear equations are converted into ODEs and numerical shooting technique with (RK45) method is employed to tackle the problem. The effects of various thermo-physical parameters on the entire flow structure with heat and mass transfer are presented graphically and discussed quantitatively. Special cases of our results are benchmarked with some of those obtained earlier in the literature and are found to be in excellent agreement. It is found that both the temperature and surface concentration gradients are increasing functions of the non-Darcy porous medium parameter. One describing result is the incident solar radiation absorption and its transmission into the working nanofluid by convection.

Natural convective heat transfer in a hemispherical cavity filled with ZnO–H2O nanofluid saturated porous medium

2018 ◽  
Vol 29 (10) ◽  
pp. 1850097 ◽  
Author(s):  
Abderrahmane Baïri ◽  
Najib Laraqi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Physical Parameters ◽  
Numerical Work

This three-dimensional (3D) numerical work based on the volume control method quantifies the convective heat transfer occurring in a hemispherical cavity filled with a ZnO–H2O nanofluid saturated porous medium. Its main objective is to improve the cooling of an electronic component contained in this enclosure. The volume fraction of the considered monophasic nanofluid varies between 0% (pure water) and 10%, while the cupola is maintained isothermal at cold temperature. During operation, the active device generates a heat flux leading to high Rayleigh number reaching [Formula: see text] and may be inclined with respect to the horizontal plane at an angle ranging from 0[Formula: see text] to 180[Formula: see text] (horizontal position with cupola facing upwards and downwards, respectively) by steps of 15[Formula: see text]. The natural convective heat transfer represented by the average Nusselt number has been quantified for many configurations obtained by combining the tilt angle, the Rayleigh number, the nanofluid volume fraction and the ratio between the thermal conductivity of the porous medium’s solid matrix and that of the base fluid. This ratio has a significant influence on the free convective heat transfer and ranges from 0 (without porous media) to 70 in this work. The influence of the four physical parameters is analyzed and commented. An empirical correlation between the Nusselt number and these parameters is proposed, allowing determination of the average natural convective heat transfer occurring in the hemispherical cavity.

scholarly journals Mixed Convection Flow over an Unsteady Stretching Surface in a Porous Medium with Heat Source

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Syed Muhammad Imran ◽  
Saleem Asghar ◽  
Muhammad Mushtaq
Keyword(s):  
Porous Medium ◽  
Heat Source ◽  
Mixed Convection ◽  
Numerical Solutions ◽  
Saturated Porous Medium ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Continuous Increase ◽  
Unsteady Mixed Convection ◽  
Unsteady Stretching Surface

This paper deals with the analysis of an unsteady mixed convection flow of a fluid saturated porous medium adjacent to heated/cooled semi-infinite stretching vertical sheet in the presence of heat source. The unsteadiness in the flow is caused by continuous stretching of the sheet and continuous increase in the surface temperature. We present the analytical and numerical solutions of the problem. The effects of emerging parameters on field quantities are examined and discussed.

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