on Heat Transfer Process Inside Open and Closed Porous Cavity

Many researchers used different methods in their investigations to enhance the heat transfer coefficient, one of these methods is using porous medium. Heat transfer process inside closed and open cavities filled with a fluid-saturated porous media has a considerable importance in different engineering applications, such as compact heat exchangers, nuclear reactors and solar collectors. So, the present paper comprises a review on natural, forced, and combined convection heat transfer inside a porous cavity with and without driven lid. Most of the researchers on this specific subject studied the effect of many parameters on the heat transfer and fluid field inside a porous cavity, like the angle of inclination, the presence of vibration, magnetic fields, and heat generation. They used different thermal and hydrodynamic boundary conditions, different geometries of cavity, and different saturated-fluids. Results manifested that the fluid and thermal characteristics enhance greatly as porosity increases at a high value of Darcy number. Also, vibrational effects are a dominant factor in the heat transfer process only at high Darcy and Reynolds numbers.


INTRODUCTION
Convective heat transfer is influenced by two modes of energy transfer between a solid wall and the adjacent fluid. The first mode is called natural convection in which the fluid motion is caused by buoyancy forces due to the density differences resulted from the variation of temperature in the fluid. The second mode of fluid motion is known as forced convection which is caused by forcing fluid over the wall surface by using external means, such as fan, compressor, or internal means within the system itself, like rotating cylinder and driven lid. In most practical applications, both modes are presented, this is known as mixed convection. Heat transfer enhancement leads to energy saving by reducing the time of operating as well as reducing the cost of constructing by decreasing the size of equipment. There are several methods to increase the heat transfer performance. One of these efficient methods is increasing the thermal conductivity of the working fluid by using nanofluids and porous media. Porous medium is formed by many closely packed particles containing pores (voids) filled with fluids (Kaviany, 1992), see Fig.1. It is characterized by its porosity. The porosity of a medium represents the fraction of the actual total volume of the porous media filled the void space (Nield and Bejan, 1992). Other important properties of the porous medium (e.g. permeability, electrical conductivity, tensile strength, etc.) can be derived from the respective properties of its basic elements (packed particles and fluid) and the porosity media in addition to pores structure.
The use of porous media in the convective heat transfer applications has received a considerable attention in the last two decades from many researchers because of its importance in many uses of industry (Kakac, et al., 1991), such as heat transfer through an insulator filled with air and heat transfer from pipes buried in a bed of small stones saturated with ground water (Oosthuizen and Naylor, 1999). Other practical applications under different heat transfer processes include crude oil production, building insulation, grain storage, geothermal systems, storage of the nuclear waste material, ground water pollution, and solar collectors.
Heat transfer characteristics in a lid-driven cavity have been an important attention due to its many applications in engineering and science. Applications include cooling of electronic devices, oil extraction, compact heat exchanger devices, etc. Lid-driven cavities filled with a saturated porous medium have a great importance in engineering applications, such as solar power collectors, heat exchangers, packed-bed catalytic reactors, nuclear industrial systems and so on (Nield and Bejan, 1999) and (Vafai, 1984).

LETERATURES DEAL WITH NATURAL CONVECTION
Free convection flow and heat transfer in porous media inside enclosure have been receiving a considerable attention in the literature. Based on these studies, various correlations have been reported for the average Nusselt number for triangular, square, rectangular and tall cavities. (Oosthuizen and Naylor, 1996) studied the laminar natural convection from a cylinder placed inside a porous square enclosure saturated with a fluid. It was found that there is a dimensionless fluid layer thickness that gives a minimum mean Nusselt number for a given situation because of no motion in the fluid layer leading to a decrease in the mean heat transfer rate. (Nithiarasu, et. al., 1997) used both Darcy and non-Darcy flow regimes to study the double-diffusive natural convection in an axisymmetric saturated porous cavity. It was concluded that the predicted heat transfer rate is lower for the generalized model if compared with the existing non-Darcy model, because the generalized model includes inertial, viscous and non-linear drag forces. (Getachew, et. al., 1998) studied the double-diffusive free convection inside a rectangular porous cavity saturated by a non-Newtonian fluid with a constant vertical walls temperature and concentration. Results for flow field, temperature and concentration distributions, and the heat and mass transfer rates agree with those obtained by discrete numerical experiments. (Watit and Phadungsak, 2006) investigated the transient natural convection heat transfer through a fluid-saturated porous medium in a square cavity with insulated vertical and bottom walls and heated top wall. It was found that the flow pattern has a local effect on the heat convection rate. (Hakan, 2007) proved that the inclination angle of a partially cooled rectangular porous enclosure with one hot wall as well as aspect ratio is the dominant factor on the fluid field and heat transfer behavior. The heat transfer process enhances as aspect ratio decreases. inferred that the characteristics of streamlines and isotherms due to free convection in a triangular cavity filled with a fluid saturated porous medium strongly depend on the position of the circular body inside the cavity. The average heat transfer data is significantly worse with increasing both heat generation and size of the circle. (Mansour and Sameh, 2015) debated the free convective heat transfer in a triangular enclosure with different angles of inclination containing Cu-water saturated porous medium and subjecting to heat generation. It was concluded that increasing the value of nanoparticle volume fraction significantly enhances the average Nusselt number. (Chen, et. al, 2016) simulated the free convective in a square porous enclosure using the local thermal equilibrium model and the local thermal non-equilibrium model. It was shown that both models give an excellent agreement. (Saravanan and Brin, 2018) examined the natural convective flow inside closed square cavity filled with a porous medium at nonequilibrium thermal condition between the fluid and solid phases. It was inferred that the maximum overall heat transfer occurs at the isothermal hot vertical walls of the cavity. (Ammar, et. al, 2018) studied the affectivity of aspect ratio in a conjugate porous cavity with partially heated vertical wall, cooled vertical right wall, and insulated horizontal walls. It was concluded that decreasing the wall thickness and aspect ratio leads to improve the rates of heat transfer. (Iman, et. al, 2019) examined experimentally the natural convection inside enclosure with a heated bottom and cooled top walls, filled with large solid spheres. The higher heat transfer rates resulted from the higher Rayleigh number values depend on the packing size and thermal conductivity of the used spheres.
The results were compared with these of the exact solutions and gave a high accuracy.

(Saravanan and Brin, 2018)
Ra=10 7 -10 11 Da=10 −6 −10 −10 Applying the nonequilibrium thermal conditions on convection inside a porous enclosure Bifurcation of the existing cellular pattern when the system moves towards thermal equilibrium. They used different sizes and thermal conductivities of sphere with a high range of Ra (10 7 -10 9 ).
At high Ra, the convective contribution of the total heat transfer for all sphere conductivities, sizes, and packing types is similar to the case of pure Rayleigh-Bénard convection.  Irwan, et al., 2010) found that the porosity of media affects the velocity of boundary layer and the strength of vortex through porous media inside lid-driven square cavity. (Gazy, et al., 2012) studied the effects of solid boundaries, inertia forces, and thermal dispersion on the transient forced convection from a nonequilibrium heated cylinder embedded in a packed bed of spherical particles. It was elucidated that the porous particles prevents the appearance of wakes behind the cylinder and improves significantly the process of heat transfer. (Gazy, et al., 2012) compared in another study between the two-phase energy model (local thermal non-equilibrium between the solid medium and the fluid) and the local thermal equilibrium model to study the influence of the particle diameter of a packed bed of spherical particles on the forced convection about an embedded circular cylinder. It was concluded that using the porous media with large particles around the heated cylinder improves considerably the average Nusselt number and decreases significantly the increasing of the unfavorable pressure drop in the bed if small particles are used. (Gazy and Mark, 2013) found that using porous media enhances the heat transfer rate from the cylinder placed in either an empty or a porous medium filled channel much higher than that promoted by using non-zero mean sinusoidal varying the pulsating forced convective flow, particularly at higher Reynolds number. (Manal and Salman, 2014) investigated the forced convection heat transfer by clean or dusty air in a two-dimensional annulus enclosure filled with porous media (glass beads) between two vertical concentric cylinders with a uniformly heated inner cylinder and a cooled outer cylinder. The results evinced that the clean air flow decreases the wall temperature as Reynolds number increases, while the reverse behavior takes place for the dusty air flow. (Abdelraheem and Sameh, 2014) used a non-Darcy model to study the heat transfer by natural and mixed convection in a saturated cavity. It was concluded the heat transfer rate and the flow regime are affected by porosity, permeability ratio, Darcy number, and the angle of inclination. (Mouwaffaq and Amir, 2015) proved that the rate of heat transfer increases as the distance between semicircular sections increases and the separation is prevented by porous media. (Luma, 2015) showed that the heat transfer process enhances with increase of aspect ratio and Re and decrease of porosity ratio. Table  2. Represents a summary of researches concerning with forced and mixed convection inside porous cavity. Using of metal foam

LETERATURE DEAL WITH FORCED AND MIXED CONVECTION
The heat transfer enhances with increase aspect ratio and Re and decrease of porosity ratio.

CONCLUSIONS
Increasing of heat transfer coefficient is an important factor in the industrial and engineering applications to save energy and reduce the constructing and operation costs. There are several methods to increase this coefficient. One of these efficient methods is using porous-fluid media as working fluid to increase the fluid thermal conductivity. Most of the researchers carried out as theoretical investigations in this field because of spending much money and time in the experimental work. So, the present paper has introduced the available theoretical literature concerning with the steady and unsteady, two-and three-dimensional free, forced and combined convection heat transfer inside different geometries of cavity and different hydrodynamic and thermal boundary conditions. As can be shown above, many factors play a significant role in the heat transfer process, such as the shape of cavity, the type of porous-fluid media, the angle of inclination, vibration, magnetic field, heat generation, etc. The most important conclusions have been given in Table 1 & 2. Finally, as can be revealed from Tables 1 & 2., there are no researches dealing with the natural convection heat transfer for compound nanofluids inside porous spherical enclosure or porous corrugated annulus. Also, the periodic heat flux boundary condition can be applied to all cases studied in the above literature. So, my suggestion to researchers is studying these cases.