Natural convection heat transfer in a partially opened cavity filled with porous media

This paper examines the steady natural convection in a partially opened enclosure filled with porous media using the Brinkman–Forchheimer model. Whilst the part of the left vertical wall of the cavity is heated, the other walls are adiabatic or thermally insulated Based upon numerical predictions, the effects of pertinent parameters such as Grashof number, Darcy number, porosity, length of the heated wall and the location center of the opened cavity are examined. It is found that as the Grashof number increases, due to strengthening buoyancy driven flows, the local Nusselt number from partially heated vertical wall, at a given position on this wall increases. This, in turn, increases the temperature of the heated wall. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Natural convection in a cubical porous cavity with partially active lateral walls

Natural convection in a porous medium filled cubical cavity subjected to differential heating through partially active lateral walls is considered. A finite volume based numerical solution is obtained and the results are analyzed through temperature, velocity and Nusselt number plots. It is found that the heat transfer rate across the cavity increases against S, the heater/cooler size. Three dimensional effects play a significant role when convection becomes strong enough. Moreover the hydrodynamic disturbances caused by the end walls reach the cavity interior for higher values of S and the transverse flow within the cavity gets restricted near the end walls for lower values of S.     

Natural convection in a rectangular cavity with partially active side walls

A numerical study is performed to investigate the effect of aspect ratio on the natural convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature than that of the right side wall. The top and bottom of the cavity and inactive part of the side walls are thermally insulated. Nine different relative positions of the active zones are considered. The equations are discretized by the control volume method with power law scheme and are solved numerically by iterative method together with a successive over relaxation (SOR) technique. The results are obtained for Grashof numbers between 10³ and 10⁵ and the effects of the aspect ratio on the flow and temperature fields and the rate of heat transfer from the walls of the enclosure are presented. The heat transfer rate is high for the bottom–top thermally active location while the heat transfer rate is poor in the top–bottom thermally active location. The heat transfer rate is found to increase with an increase in the aspect ratio.     

Double-diffusive Marangoni convection in a rectangular cavity: Transition to chaos

Transition to chaos in double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the special case when the resultant thermal and solutal Marangoni effects are equal and opposing. Direct numerical simulation is used and some techniques from nonlinear dynamics are adopted to identify the different dynamic regimes. It is found that the supercritical solution branch takes a quasi-periodicity and phase locking route to chaos while the subcritical branch follows the Ruelle–Takens–Newhouse scenario. Transient intermittency in the supercritical branch is observed and physical instability mechanisms of the subcritical branch are identified.     

Natural convection in porous cavity with sinusoidal bottom wall temperature variation

Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20–500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment.     

Transient natural convection with temperature-dependent viscosity in a square partially porous cavity having a heat-generating source

A numerical study is performed on the transient natural convection with a temperature-dependent viscosity inside a square partially porous cavity with a local heat-generating and heat-conducting source. The vertical walls of the cavity are kept at constant cooling temperature while the horizontal walls are adiabatic. The discrete heat-conducting and heat-generating source is located on the bottom wall. A porous layer is located under the clear fluid layer. Governing equations formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions are solved using implicit finite difference schemes of the second order. The control parameters are the Darcy number, Ostrogradsky number, viscosity variation parameter, height of the porous layer, and dimensionless time. The effects of these parameters on the average Nusselt number along the heat source surface, average temperature of the heater, fluid flow rate inside the cavity, as well as on the streamlines and isotherms are analyzed. The results show that porous layer thickness and viscosity of the working fluid are very good control parameters for optimization of the passive cooling system.     

Natural convection in right-angle porous trapezoidal enclosure partially cooled from inclined wall

A numerical study is conducted to investigate the steady free convection flow in a two-dimensional right-angle trapezoidal enclosure filled with a fluid-saturated porous medium. The left vertical wall of the cavity is heated; the inclined wall is partially cooled; and the remaining walls are insulated (adiabatic). Three different cases are considered. While in Case I the cooler wall is located adjacent to the top wall, in Case II it is located in the middle inclined wall. In Case III, it is located adjacent to the bottom wall. Flow and heat transfer characteristics are studied for a range of parameters: the Rayleigh number, Ra, 100 ≤ Ra ≤ 1000; and the aspect ration, AR = 0.25, 0.50 and 0.75. Numerical results indicate that there exist significant changes in the flow and temperature fields as compared with those of a differentially heated square porous cavity. These results lead, in particular, to the prediction of a position of minimum heat transfer across the cavity, which is of interest in the thermal insulation of buildings and other areas of technology.     

Natural convection in a square porous annulus

The current study is focused to investigate the natural convective heat transfer characteristics in a porous square annulus. Finite element method is used as a tool to simplify the partial differential equations that govern the heat and fluid flow characteristics inside the porous medium. A simple three noded triangular element is used to divide the porous domain into smaller segments known as elements. The algebraic set of equations resulting from the finite element equation are assembled into a global matrix and then solved iteratively to get the solution variables. Thermal equilibrium as well as non equilibrium in porous domain is considered. The effect of various geometric and physical parameters are investigated. The boundary conditions are such that the inner walls of the annulus are heated isothermally to temperature T_h, and the outer surfaces are exposed to cool temperature T_c. The width ratio defined as the ratio of hollow portion to the length of the cavity is varied from 0.125 to 0.875. Results are discussed with respect to width ratio, Rayleigh number, radiation parameter and viscous dissipation parameter.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Natural convection in a thin horizontal porous annulus

The possible modes of time-dependent natural convection in a horizontal annulus of finite length are considered. The annulus is filled with porous material and the annular thickness is assumed small in comparison with the mean radius. All boundaries are impermeable and adiabatic; heating is through a circumferentially distributed volumetric heat source. The governing equations reduce to a set of two non-linear ordinary differential equations. Steady non-linear oscillations exist for the special case of infinite Rayleigh number and symmetric heating about the vertical. For lower Rayleigh numbers, damped oscillations are obtained, the degree of damping increasing with the inclination of the line of symmetry and with decreasing Rayleigh number. Multiple stable steady states are obtained for small inclinations. Chaotic motions do not develop for non-inertial Darcy flows.     

Natural convection along a vertical porous surface

This paper describes an experimental study on natural convection along a vertical porous surface consisting of a bank of parallel plates with constant gaps. Compared with a smooth surface, the heat transfer for a porous surface with streamwise gaps is somewhat enhanced owing to enthalpy transport due to flow within the gaps and that with spanwise gaps is enhanced due to the leading- and trailing-edge effects of solid-phase micro surfaces. Observations show that no clear transition to turbulent flow occurs at a critical Rayleigh number for a smooth surface and that the boundary layer oscillates with a dominant frequency at higher Rayleigh numbers. The dominant frequency for a porous surface is nearly the same as that for a smooth surface. This fact obviously indicates that the oscillations of natural convection are almost independent of the porous structure of the heating surface and are mainly dependent on the behavior of the outer boundary layer. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 385–397, 1997     

Oscillatory natural convection of water-glycerin mixture in a tall rectangular cavity: Transition to the chaos

This paper presents results of a numerical investigation involving bifurcation sequence leading to chaos in natural convection inside a vertically tall rectangular cavity having an aspect ratio equal to 15 and a Prandtl number equal to 125, corresponding to water-glycerin mixture. The flow is characterized by a vertical stratification of the temperature field for Grashof numbers greater than or equal to 200 that is outside the conduction regime and it is stationary monocellular up to a critical value Gr_c = 2800 where a periodic oscillatory regime appears. As Grashof number is increased, a transition from a steady periodic bicellular flow to an oscillatory multicellular flow, with 2 main central cells and 2 secondary cells, occurs. The regime remains periodic until Gr = 3100 where there is a first appearance of the chaotic regime which extends over a narrow interval of the Grashof number delimited by Gr = 3200.     

Natural convection and its fractal for liquid freezing in a vertical cavity filled with porous medium

The numerical simulation for a freezing liquid-saturated porous media in a vertical cylindrical cavity under the third kind of thermal boundary condition is reported in this paper. It shows that the effect of natural convection in the liquid phase decreases the freezing layer thickness and the freezing front has a wave shape instead of a stable plane, with one or more pair of eddy cells. This indicates a fractal existence. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 165–171, 1999     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

Natural convection in a partially open square cavity with internal heat source: An analysis of the opening mass flow

A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra_e = 10³–10⁵, while the influence of the heat source was evaluated through the relation R = Ra_i/Ra_e, investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra_e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra_e whereas these features are absent at higher Ra_e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.