scholarly journals Transient Natural Convection in Porous Square Cavity Heated and Cooled on Adjacent Walls

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. S. Selamat ◽  
I. Hashim ◽  
M. K. Hasan
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Transient State ◽  
Governing Equations ◽  
Square Cavity ◽  
Transient Natural Convection ◽  
Temperature Distributions ◽  
Rayleigh Numbers

Transient natural convection in a square cavity filled with a porous medium is studied numerically. The cavity is assumed heated from one vertical wall and cooled at the top, while the other walls are kept adiabatic. The governing equations are solved numerically by a finite difference method. The effects of Rayleigh number on the initial transient state up to the steady state are investigated for Rayleigh number ranging from 10 to2×102. The evolutions of flow patterns and temperature distributions were presented for Rayleigh numbers,Ra=102and103. It is observed that the time taken to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

Unsteady Darcian Natural Convection within Porous Media of Square Enclosure at Various Rayleigh Numbers

2013 ◽  
Vol 390 ◽  
pp. 18-22
Author(s):  
Ali Hooshyar Faghiri ◽  
Hikmet Şeli Aybar ◽  
Mehrdad Khamooshi
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Constant Temperature ◽  
Transient State ◽  
Left Wall ◽  
Square Enclosure ◽  
Transient Period ◽  
The Right ◽  
Rayleigh Numbers

Transient natural convection within a 2D square cavity filled with a porous medium is numerically investigated. The left wall is suddenly heated to a constant temperature Th, while the right wall is suddenly cooled to a constant temperature Tc. Both the horizontal walls are insulated. The Finite Volume numerical method is used to solve the dimensionless governing equations. The results are obtained for the initial transient state assuaging to the steady state, and for Rayleigh number values of 102–104. It is indicated that the average Nusselt number showing an undershoot during the transient period and that the time needed to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

Transient Natural Convection Experiments in Shallow Enclosures

1982 ◽  
Vol 104 (3) ◽  
pp. 533-538 ◽  
Author(s):  
R. Yewell ◽  
D. Poulikakos ◽  
A. Bejan
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Theoretical Prediction ◽  
Thermal Stratification ◽  
Wave Motion ◽  
The Core ◽  
Transient Natural Convection ◽  
Aspect Ratios ◽  
Approach To Steady State ◽  
Rayleigh Numbers

This paper reports experimental observations on transient natural convection in enclosures at high Rayleigh numbers (1.28×109, 1.49×109) and low aspect ratios (0.0625, 0.112). The phenomenon consists of the establishment of thin intrusion layers along the horizontal adiabatic surfaces; in time, the intrusion layers exchange heat with the isothermal core of the cavity, leading to the thermal stratification of the core. The approach to steady state is gradual, contrary to the theoretical prediction of Brunt-Vaisala wave motion (Patterson and Imberger [6]). The measured durations of the observed transients agree very well with theoretical estimates.

Scaling of the Turbulent Natural Convection Flow in a Heated Square Cavity

1994 ◽  
Vol 116 (2) ◽  
pp. 400-408 ◽  
Author(s):  
R. A. W. M. Henkes ◽  
C. J. Hoogendoorn
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection ◽  
Convection Boundary ◽  
Vertical Walls ◽  
Rayleigh Numbers

By numerically solving the Reynolds equations for air and water in a square cavity, with differentially heated vertical walls, at Rayleigh numbers up to 1020 the scalings of the turbulent natural convection flow are derived. Turbulence is modeled by the standard k–ε model and by the low-Reynolds-number k–ε models of Chien and of Jones and Launder. Both the scalings with respect to the Rayleigh number (based on the cavity size H) and with respect to the local height (y/H) are considered. The scalings are derived for the inner layer, outer layer, and core region. The Rayleigh number scalings are almost the same as the scalings for the natural convection boundary layer along a hot vertical plate. The scalings found are almost independent of the k–ε model used.

A Numerical Study of Natural Convection in a Cavity With Two Fins Attached to Its Vertical Walls

2007 ◽  
Author(s):  
G. A. Sheikhzadeh ◽  
M. Pirmohammadi ◽  
M. Ghassemi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Rayleigh Numbers

Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.

Transient Natural Convection in Enclosures at High Rayleigh Number

1991 ◽  
Vol 113 (3) ◽  
pp. 635-642 ◽  
Author(s):  
D. A. Olson ◽  
L. R. Glicksman
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Transient Behavior ◽  
Full Scale ◽  
Scale Model ◽  
Mixed Gas ◽  
Transient Natural Convection ◽  
Physical Scale ◽  
Rayleigh Numbers

Transient natural convection at Rayleigh numbers of 1010 was studied experimentally in two enclosures of aspect ratio 1/3, one a 1:5.5 physical scale model containing the dense refrigerant gas R114, and the second a full-scale room containing air. In one type of transient the vertical endwall temperature was suddenly changed, while in a second type of transient the isothermal, well-mixed gas was suddenly exposed to hot and cold vertical endwalls. The experiments indicated that the dominant time constant was a convective one. Comparisons between the scale model and full scale show that R114 gas can simulate the transient behavior of air-filled enclosures.

Natural Convection in a Cavity With a Wavy Wall Heated From Below and Uniformly Cooled From the Top and Both Sides

2006 ◽  
Vol 128 (7) ◽  
pp. 717-725 ◽  
Author(s):  
Amaresh Dalal ◽  
Manab Kumar Das
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Wavy Wall ◽  
Governing Equations ◽  
Integral Forms ◽  
Nusselt Number Distribution ◽  
Lower Temperature ◽  
Volume Method ◽  
Spatially Varying

In this paper, natural convection inside a two-dimensional cavity with a wavy right vertical wall has been carried out. The bottom wall is heated by a spatially varying temperature and other three walls are kept at constant lower temperature. The integral forms of the governing equations are solved numerically using finite-volume method in the non-orthogonal body-fitted coordinate system. The semi-implicit method for pressure linked equation algorithm with higher-order upwinding scheme are used. The streamlines and isothermal lines are presented for three different undulations (1, 2 and 3) with different Rayleigh number and a fluid having Prandtl number 0.71. Results are presented in the form of local and average Nusselt number distribution for a selected range of Rayleigh number (100-106).

Study on the Route to Chaos of Natural Convection in Cylindrical Envelope With an Internal Concentric Cylinder With Slots

2010 ◽  
Author(s):  
Kun Zhang ◽  
Mo Yang ◽  
Yu Wen Zhang ◽  
Mei Lu
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Heat Transfer ◽  
Period Doubling ◽  
Simple Algorithm ◽  
Concentric Cylinder ◽  
Initial Field ◽  
Volume Method ◽  
Rayleigh Numbers

Natural convection heat transfer was investigated numerically in a cylindrical envelope with an internal concentric cylinder with slots. Governing equations are discretized using finite volume method and solved using SIMPLE algorithm with QUICK scheme. Calculations were performed on certain parameters with a Rayleigh number varying from 700 to 20000. The effect of the Rayleigh number on the route to the chaos of the system was analyzed by the phase space of velocity at the sample point. The results show that the system can reach to steady state and symmetric when the Rayleigh number is below 700, and to steady state and asymmetric when the Rayleigh number is equal to 1000. For a Rayleigh number ranged between 1500 and 3000, an asymmetric periodical solution is obtained although the initial field and boundary conditions were symmetric. As the Rayleigh numbers increase further, a quasi-periodic solution of the system is achieved at Ra = 2000. There is one more bifurcation and period doubling at successive critical values of Rayleigh numbers from to. It is ascertained that periodicity is lost at Ra = 20000. The results show that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow.

Natural Convection in Inclined Two Dimensional Rectangular Cavities

2009 ◽  
Author(s):  
Lyes Khezzar ◽  
Dennis Siginer
Keyword(s):  
Natural Convection ◽  
Two Dimensional ◽  
Square Cavity ◽  
Transfer Rates ◽  
Aspect Ratios ◽  
Temperature Distributions ◽  
Start Up ◽  
Side Walls ◽  
Boussinesq Fluid ◽  
Rayleigh Numbers

Steady two-dimensional natural convection in fluid filled cavities has been investigated numerically. The conservation equations of mass, momentum and energy governing the motion of a Newtonian Boussinesq fluid have been numerically solved using the finite volume technique. The computations were performed for three cavity height based Rayleigh numbers 104, 105 and 106. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for several aspect ratios. For the case of the square cavity the calculated values are in excellent agreement with previously published benchmark results. The effects of the inclination of the cavity to the horizontal, with the angle varying from 0 to 180° and the initial start up conditions were investigated in turn for each aspect ratio. The inclination and the “initial” assumed conditions have a significant effect on the flow patterns, temperature distributions and the heat transfer rates. In particular it is found that the average Nusselt number exhibits discontinuities for rectangular cavities and that the occurrence of the discontinuity with angle of inclination is strongly influenced by the assumed start up field in the steady calculations in much the same way as the hysteresis effect that was identified by other workers.

scholarly journals Numerical Study of Three- Dimensional Natural Convection in a Differentially Heated Cubical Enclosure

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Numerical Study ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Cubical Enclosure ◽  
Side Walls ◽  
The Right ◽  
Rayleigh Numbers

—A high-resolution, finite difference numerical studyis reported on three-dimensional steady-state natural convectionof air, for two Rayleigh numbers, in a cubical enclosure, which isheated differentially at one side walls. The temperature of thewall is TC except for the right vertical wall, in which is TH.Thedetails of the three-dimensional flow and thermal characteristicsare described.

Natural convection in an infinite porous medium with a concentrated heat source

1978 ◽  
Vol 89 (1) ◽  
pp. 97-107 ◽  
Author(s):  
Adrian Bejan
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Flow Pattern ◽  
Transient Flow ◽  
Steady State Solution ◽  
Upward Flow ◽  
Rayleigh Numbers

The phenomenon of buoyancy-induced convection in an infinite porous medium with a concentrated heat source is studied analytically. The transient and steady-state temperature distribution and flow pattern around the source are determined using a perturbation analysis in the Rayleigh number based on the heat generation rate at the source. The first-order transient solution derived in the paper is valid for Rayleigh numbers less than 10. The transient flow pattern consists of an expanding vortex ring situated in the horizontal plane containing the source. The steady-state solution, valid for Rayleigh numbers of the order of 20 or less, reveals an upward flow pattern which becomes very intense near the source. The upward flow extends throughout the medium. Both solutions show that as the Rayleigh number increases the region situated above the source is effectively heated by natural convection in addition to direct heat conduction from the source.

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