A review on heat transfer enhancement techniques during natural convection in vertical annular geometry

1. Introduction

In recent years, the world has seen an enormous increase in energy demand due to industrial advancement (Azhar and Siddiqui, 2021). Many applications require waste heat to be removed for them to work efficiently without compromising their desired output, such as cooling of the nuclear reactor core (Yu et al., 2012), electronics cooling (Yilmazer and Kocar, 2014), solar collectors (Nobari et al., 2012), etc. The most widely accepted processes cited for heat removal are forced or natural convection. Forced convection requires either a pump or blower (energy absorbing devices); however, no moving components are needed for heat removal through natural convection. Natural convection seems to be a solid contender as far as energy saving is concerned. The vertical concentric annulus possesses technical importance due to its compact size, simple geometry, robust structure, and wide acceptance in commercial and industrial applications (Husain, 2017).

Natural convection (NC) in vertical annular geometry (VAG) has been a focus of great attention among researchers in recent years as it can potentially be employed in several industrial applications. Researchers worldwide have been exploring different techniques to augment the heat transfer rate through free convection and have investigated their effects in VAG for a couple of decades. These techniques include nanofluids, use of the magnetic field, use of cylinder wall rotation, use of discrete wall heating, use of porous material, use of boiling, etc.

Natural convection in an annular cavity was the starting point of research in this field. A few earlier studies focusing on natural convection in annular cavities were pioneered by de Vahl Davis and Thomas (1969) and Kumar and Kalam (1991). NC in VAG was first investigated by El-Shaarawi and Sarhan (1981). Later, research on NC in VAG was carried out by Mohanty and Dubey (1996), Siddiqui et al., (2010) and many others.

The most recent area of research during NC in VAG is nanofluids as the working fluid. Researchers are trying to explore different types of Nano-fluids to enhance the heat transfer rate. Some of the researchers who carried out studies in this field are Cadena-de la Peña et al. (2017), Khan and Siddiqui (2020), etc.

There are many heat transfer applications in which magnetic field can be utilized, such as nuclear reactor cooling system (Kasaeipoor et al., 2015), pumping and levitation of materials with magnetic properties (Ghasemi et al., 2011). Other magnetic field applications include reducing the fluid flow caused by natural convection (Afrand et al., 2015). Recent trends concerning NC in VAG shows a considerable rise in the interest of exploring the effect of magnetic field on heat transfer. Al-Nimr (1995a) was the first who performed analytical solutions for fully developed natural convection flow under the influence of a magnetic field in an open-ended vertical concentric annulus. Other researchers who have explored this field are Sankar et al. (2006), Afrand (2017), etc.

Heat transfer from a rotating cylinder has a wide range of engineering applications like cooling the rotor of electrical machines, cooling gas bearings, condenser for seawater distillation (Elghnam, 2014), etc. The effect of cylinder rotation on heat transfer was initially studied by (Becker and Kaye, 1962). Other researchers who studied the effect of cylinder rotation on heat transfer in a vertical annulus were Coney and El-Shaarawi (1974), Ball and Farouk (1987), etc.

Many engineering applications involve heating at some discrete locations. Many researchers have studied the effect of discrete heating on NC in VAG, such as Sankar and his coworkers. Many researchers studied the effect of porosity on heat transfer and flow characteristics on NC in VAG viz. Prasad and Kulacki (1984), etc.

Another exciting area cited in the open literature for heat transfer enhancement is allowing the working fluid to boil. The heat transfer coefficient observed during boiling was much higher than that observed in single-phase flow. Due to this reason, several researchers performed studies on NC in VAG during boiling that include Khalid Usmani et al., (2003), Husain and Siddiqui (2017), etc.

Review studies regarding forced, mixed and free convection in horizontal and vertical annular geometries have been carried out by researchers such as Ahmed and Ahmed (2017) & Husain et al., (2021a). However, despite its technical importance in many engineering applications, no review studies have been performed to the best of the authors’ knowledge that focus on the special techniques used for heat transfer enhancement during NC in VAG. This paper is an important step towards fulfilling this research gap and hopefully will provide an extensive review of heat transfer enhancement procedures and techniques in VAG. This paper scanned the most investigations published in heat transfer enhancement during natural convection in a vertical annulus in all the leading publication houses like Elsevier, Taylor & Francis, Begell houses, Wiley, etc. The selected publications in the presented work range from 1962 to 2020.

This paper aims to provide a clear picture of research performed using different techniques in the field of NC in VAG and how it has progressed over the last few decades. The areas which require particular attention and need to be addressed in the future are identified. In addition, future research ideas have been discussed that may help researchers conduct high-quality research in the field of NC in VAG. The authors believe that this paper can serve as a valuable asset for those who want to explore this exciting field of NC in VAG.

2. Use of nano-fluids

Recently, nanofluids are being used for the enhancement of heat transfer in many applications. The implementation of this technique can be easily done by replacing the working fluid with nanofluids. The enhancement in heat transfer using nanofluids needs the proper selection of optimum volume fraction. A wrong volume fraction can deteriorate the heat transfer. The challenge in implementing this technique is to prepare the nanofluids and keep them stable for longer durations. The biggest drawback of nanofluids is their instability and adverse effects on the surface. A lot of research work in this area has been performed and is still going on worldwide. Some of the work related to NC in VAG are as follows.

Abouali and Falahatpisheh (2009) computationally studied the heat transfer during NC in VAG of Al2O3 + water nanofluids. They use finite volume technique to numerically investigate convection heat transfer over a wide range of aspect ratios, Grashof number and nanoparticle volume fraction. Fig. 1 shows the Nusselt number for GrL = 104, K = 2 and different particle fractions as a function of aspect ratio in the vertical annulus. They revealed that Nusselt number (Nu) drops monotonically with an increase of particle volume fraction and found deterioration of heat transfer rate during NC in VAG. They also developed a correlation of Nusselt number of nanofluids in annuli in terms of aspect ratio, Rayleigh number, radius ratio and particle fraction. They conclude that researchers find a contradiction in natural convection heat transfer available in the literature because of uncertainty in the calculation of thermophysical properties of nanofluids.

The conjugate heat transfer during NC in VAG is numerically studied by Shahi et al., (2011). The geometry consists of a heated inner cylindrical rod and outer walls are kept isothermal. They presented their numerical results for a range of Rayleigh number with water copper Nanofluid and reported enhancement of Nusselt number with a concentration of nanoparticles and effects are more pronounced at higher Rayleigh numbers. They stated that the orientation of the tube greatly affects the flow and heat transfer and found that the maximum average Nusselt number is obtained at an inclination angle of zero degrees.

Abouali and Ahmadi (2012) performed theoretical and numerical investigations of natural convection heat transfer for Cuo nanofluids and compared results with empirical correlation available in the literature. Their results show that the heat transfer rate was maximum at a volume fraction of 0.5% and 0.6%, respectively, for Ra = 104 and 105. They conclude that there is no such appreciable enhancement in HTC, even for an extreme case of less than 1%.

Cadena-de la Peña et al., (2017) performed an experimental study for NC in VAG using TiO2 and AlN nanoparticles dispersed in mineral oil-based nanofluids with three different concentrations, i.e. 0.01, 0.1 & 0.5 wt%. Nusselt number increased only in the case when the concentration of nanofluids was 0.01 wt % and decreases in the other higher concentrations. The deterioration in heat transfer at higher concentrations was mainly due to the sedimentation of nanoparticles and higher viscosity. But in general higher enhancement was found at a low aspect ratio. Highest HTC was found for AlN treated with oleic acid (added surfactant). Fig. 2 shows the experimental set-up, location of thermocouples and top view of the cavity used in the analysis.

Khan and Siddiqui (2020) carried numerical modelling of NC in VAG that was partially heated using nanofluids (Alumina and water) having a high aspect ratio of 352. Four different models have been solved using the combination of two famous thermal conductivity models and viscosity models, and the concentration of the nanofluids was varied (1–4 vol %) for heat flux range 3–12 kW/m2. Table 1 shows the material properties of fluids and nanoparticles with the temperature used in the analysis. Results show augmentation in heat transfer with volume fraction nanofluids. Maximum enhancement in heat transfer was found at 14.17% and the lowest at 7.27%. A generalized correlation was developed for the Nusselt number inside the annulus for nanofluids in terms of Rayleigh number (Ra), Reynolds number (Re), volume fraction (α), Richardson number (Ri) and Prandtl number (Pr).

Table 1. Thermophysical properties of base fluid and nanoparticles (Khan et al., 2020)

S. No.	Thermophysical properties	Base Fluid (Water)	Nanoparticle (Al2O3)
1	Thermal Conductivity (W/mK)	0.6	42.64
2	Specific heat, J/Kg.k	4182	765
4	Density, kg/m3	999.02	3880
5	Volumetric expansion coeff. (1/K)	0.000168	0.00000846
6	Viscosity (Ns/m2)	0.001123	0.489

Mebarek-Oudina (2019) carried out a numerical analysis to investigate Titania nanofluids thermal and hydrodynamic characteristics filling a cylindrical annulus. Engine oil, water and ethylene glycol were used as base fluids. At the same time, the Maxwell model for convective heat transfer was incorporated to capture the effects of nanoparticle volume fraction distribution on the governing equations. The results were presented in isotherms and streamlines for varying Rayleigh number, base fluid type, and nanoparticle volume fraction. Also, the study showed the effects of different parameters on the local Nusselt number as it seems to vary with the type of the base fluid.

Usmani et al., (2021) carried out 2D numerical analysis of NC in VAG with Al2O3 – MWCNT/water as working fluid. They observed a 73.6% enhancement in heat transfer at a concentration of 4%.

Khan et al., (2020) performed a numerical analysis of NC in VAG with Al2O3 nanofluid. They observed a 10.86% enhancement in heat transfer with the Brinkman model and a 3.91% enhancement with the Buongiorno model.

In recent years, nanofluids have caught the attention of researchers in almost all research areas. Most of the research work with nanofluids is numerical. The reason might be the time for nanoparticle settlement in the base fluid. Also, if the volume required is high, preparing a large quantity of nano-fluids and maintaining their stability is quite tricky and a tedious task. Most of the researchers observed heat transfer enhancement with the increase in the volume fraction of nanoparticles.

3. Use of magnetic field

This technique can be easily implemented by applying a magnetic field perpendicular to the flow. The working fluid should have magnetic properties. This technique can help in the reduction of natural convection. The heat transfer and fluid flow can be easily controlled by changing the applied magnetic field. Many researchers have studied the effect of the magnetic field during NC in VAG.

Al-Nimr and Alkam (1999) presented an analytical solution for the effect of the magnetic field during NC in VAG filled with porous material and studied four fundamental boundary conditions. They developed expressions for volumetric flow rate, local Nusselt number and mixing-cup temperature. Sankar et al., (2006) studied the influence of magnetic field on NC in VAG of fluid with low Prandtl number (0.054) numerically. An axial magnetic field curbed the flow and heat transfer in shallow cavities. However, the radial magnetic field seems to be most effective in taller cavities. The flow oscillations were found to be suppressed when an external magnetic field was impressed. The Nusselt number (average) shows an increasing trend with the radii ratio but a decreasing trend with the Hartmann number (Hr).

Kakarantzas et al., (2007) numerically studied the influence of magnetic field imposed on electrically conducting fluid during NC in VAG. They used 3-D DNS for large ranges of Rayleigh and Hartmann numbers (0–100) to assess the flow. They observed turbulent flow in the absence of a magnetic field and which loses its turbulent behaviour at the high magnetic field, even becomes laminar at large Hartmann Number (Hr > 75). They reported the reduction of convection heat transfer with magnetic field and flow loses its axisymmetry due to the development of Hartmann and Robert layers. Fig. 3 shows the 3D distribution of isotherms, vertical velocity, electric potential and electric current for Ra = 105 and Ha = 100.

Shivashankar (2010) numerically studied the influence of magnetic field on the natural convective flow in the double annuli packed through porous-medium. They found the radial magnetic field to be most effective in suppressing the convection in taller cavities compared to the shallow cavities. Venkatachalappa et al., (2011) study the effect of magnetic field on the double-diffusive NC in VAG. Their results show that the magnetic field subdues the double-diffusive convective flow only for lesser buoyancy ratios. While, for higher buoyancy ratios, the magnetic field suppresses the thermal convective flow.Jha et al., (2018) theoretically studies the influence of magnetic field during NC in VAG of electrically conducting fluid having geometry in micro dimensions. They obtained the exact solution of governing equations in the presence of the radial magnetic field. They analyzed the impact of various factors like Hartmann Number, radius ratio, refraction parameter etc., on flow conditions like fluid velocity and volume flow rate. The results show that an increase in radius ratio enhances volume flow rate and reduces slip induced by fluid wall interaction, while Hartmann Number has a negative effect on volume flow rate.

Afrand (2017) showed a three-dimensional numerical simulation of NC in VAG with molten gallium as a working fluid. The magnetic field was applied in the perpendicular direction of the annulus mould. The outer and inner wall has been maintained at constant and distinct temperature. The bottom and top being considered adiabatic and filled with electrically conducting fluids. Results reveal that the magnetic field suppresses natural convection in the thin annulus more than in the thick annulus. The magnetic field has generated the electric potential that results in a fall in Lorentz force in the opposite direction to buoyancy force. Low Rayleigh number (Ra) was found desirable to suppress the convection. To cast the high Prandtl number liquid metal, a higher magnetic field should be applied for superior quality products. Fig. 4 shows induced electric field and distribution of Lorentz force in the horizontal plane (Z = 0.5) (Ra = 105, A = 1 and Pr = 0.072). Afrand et al., (2017) performed numerical work to study the effect of electric field on magneto NC in VAG with electrical conducting liquid potassium as working fluid. They found that the presence of magnetic and electric fields changes the axisymmetry of the flow and reduces Lorentz forces, respectively.

Marzougui et al., (2020) performed the numerical analysis inside a magnetized porous channel for the study of fluid flow. The principle of thermodynamic irreversibility has been applied to study Poisoille-Rayleigh-Benard mixed convection inside a channel of the aspect ratio of (A = 5). The study is also accompanied by a uniform transverse magnetic field. The various properties of fluid flow are extensively studied with the change in several parameters like Hartmann number (Ha), Darcy number (Da), Brinkmann number (Br), and porosity. Studies revealed that the entropy generation declines with Darcy number and surges with the magnetic effect. Also, Brinkman number variance has a significant impact on entropy production.

The effect of magnetic field on NC in VAG has been observed numerically since 1995. All of them reported a decrease in natural convection heat transfer with the increase in Hartmann number. Considerable changes in the flow axisymmetry have also been observed.

4. Use of cylinder wall rotation

This technique is a bit difficult to implement as a complete set-up is required to rotate the cylinders. However, in many applications, a rotating cylinder is encountered. The convection improves with the rotational speed of the cylinder. Some of the works related to rotating cylinder during free convective flow are.

Experimental and numerical studies during NC in VAG with a rotating inner cylinder were performed by Becker and Kaye (1962a & 1962b). Their results show that the rotation of the inner cylinder stabilizes the flow while outer cylinder rotation destabilizes the flow. The apparatus used for studying the effect of the cylinder rotation is shown in Fig. 5. Their experimental results reveal the existence of three flow regimes, i.e. purely laminar flow for a wide range of Reynolds number and Taylor number, Laminar-plus-Taylor-vortexes flow and turbulent flow.

El-Shaarawi and Khamis (1987) performed the numerical analysis of laminar NC in VAG (open-ended). The inner cylinder was rotating and uniformly heated, while the outer was adiabatic. Kodah and EI-Shaarawi (1995) studied NC in VAG with two rotating boundaries. Their results show the features of the induced flow caused by the isothermally heated boundaries. The influence of the rotation of the outer cylinder on the fluid heat absorption and adiabatic wall temperature was presented.

Venkatachalappa et al., (2001) conducted a numerical analysis to know the rotational effects on the axisymmetric free convective flow in annuli. They maintained both the vertical walls at constant temperatures while the horizontal walls as adiabatic. Their results show that for moderate Grashof number and when only the outer cylinder was in rotation, the outward bound flow was restricted to a thin region alongside the bottom surface. In contrast, the return flow covers the entire cavity. At a higher Grashof number and moderate speed of rotation of cylinders, thermal convection was dominant, and a rise in the heat transfer was observed. Table 2 depicts the influence of rotation on the Nusselt number.

Table 2. The effect of rotation on the average Nusselt number (Pr = 1.0) Venkatachalappa et al. (2001).

A	Gr	$Ω_{i}$	$Ω_{o}$	$\overline{Nu}$
1	104	0	0	2.4787
		0	500	1.7949
		500	0	2.6494
	105	0	500	4.5505
		0	2000	2.2547
		500	0	4.8462
		2000	0	4.9958
	106	0	0	8.3568
		0	500	8.3242
		0	2000	8.1099
		500	0	9.2351
		2000	0	9.3145
	104	500	500	2.2021
		2000	500	4.0454
		−2000	2000	2.2513
		−1500	1000	2.4963
2	105	2000	0	4.5499
		0	2000	2.7812
	106	1000	2000	7.3038
		1500	500	7.5388
		−2000	2000	3.0629
		−1500	1000	3.9740

The effect of wall rotation has been studied by researchers both numerically and experimentally. Results reveal that the rotation of the inner cylinder helps the flow; however, the outer cylinder rotation destabilizes it. Also, thermal convection was dominant at a higher Grashof number with moderate rotational speeds, and a considerable rise in the heat transfer was observed.

5. Use of discrete wall heating

This situation arises in many engineering applications that involve heating at some discrete locations. Thus analysis of discrete wall heating is critical. To implement it, heating elements have to be positioned at some discrete locations. The location of the heater should be to maximize heat transfer. Many researchers have studied the effect of discrete heating on NC in VAG.

Sankar (2010) numerically solved four boundary conditions on both boundaries during double-diffusive free convective flow in vertical annuli. The annulus walls at entry & exit were not heated. Extreme influence of the unheated entry and exit on the flow was observed. Sankar and Do (2010) examined the influence of discrete heating on NC in VAG. In their study, the inner wall has two discrete heat sources while the outer wall was isothermally cooled. They used the physical configuration and coordinate system. The results reveal higher heat transfer rates at the bottom heater that rises with radii ratio and drops with aspect ratio. Fig. 6 shows the effect of the heater length ratio on the average Nusselt number for different values of Ra at aspect ratio = 5.

Lopez et al., (2012) did a numerical analysis of NC in VAG having a separate heat source on the inner cylinder. They observed very weak flow for low heat flux, and heat transfer was mainly via conduction. They observed that after the end of the conduction controlled regime, the flow was divided into three separate regions. Sankar et al., (2015) studied the effects of size and location of two discrete heaters on NC in VAG. It was found that the average Nusselt number drops with the aspect ratio, although maximum temperature shows a reverse trend. At the bottom heater, greater heat transfer was observed in comparision to the top heater for most of the cases. Generally, the maxima of temperature were at the top heater.

Mebarek-Oudina (2017) performed simulations to solve free convection in cylindrical annuli having discrete isoflux heat zones of various lengths, and heat transfer stability was also seen. The distinct heat sources were fixed on the inner wall. Interestingly they observed that HTC was higher for smaller heater length and also the rate of HTC drops on decreasing the heater length. Fig. 7 shows the influence of the heater length ratio on the local Nusselt number for different parameters. On increasing the critical Rayleigh number, the natural convection process enhances and consequences in decreasing heat source temperature. However, the critical Rayleigh number falls on increasing the heater length. Fig. 7 depicts streamlines and isotherms for Ra = 108 and various dimensionless sizes of heater (ε).

Jha and Oni (2018) analytically studied NC in VAG based on mathematical equations and boundary conditions as the time-periodic thermal wall. Modified Bessel's function of 1st and 2nd type was developed using suitable transformation for obtaining periodic temperature, velocity, skin friction and HTC as a function of Nusselt number using proper boundary conditions. They took Prandtl number, Strouhal number and radius ratio as the independent variable. The results show that periodic velocity, temperature and skin friction decrease with Prandtl no, Strouhal number and radius ratio. For small Strouhal numbers, the distribution of temperature is independent of the geometry.

Alsabery et al., (2017) studied the effects of non-uniform heating and a finite wall thickness on natural convection numerically using the finite difference method based on the local thermal non-equilibrium (LTNE) model. The results revealed that increasing the thickness of the solid wall reduces the overall heat transfer affected by the solid wall's resistance, mainly when Rayleigh numbers are high. Heat transport in porous media is inhibited by thicker walls or walls with poor thermal conductivity. Moreover, the results graphically depicted the effects of different parameters on streamlines, isotherms, and weighted average heat transfer.

Many researchers have studied the effect of discrete and periodic heating of the wall. The influence of the unheated entry and exit, location, and heater length on the heat transfer rate was reported. The heat transfer rate was sensitive with the heater length - higher for smaller heater lengths. However, to the best of the authors’ knowledge, no experimental work has been reported to date to support the results.

6. Use of porous media

This technique can be easily implemented by filling the annular gap with a porous material. However, the selection of porous material needs a thorough investigation. The drawback of this technique is that it cannot be used in all applications. In many engineering applications, porous media is used. Researchers have studied natural convection heat transfer filled with the porous medium in VAG.

Prasad and Kulacki (1984) numerically solved steady-state natural convective flow in vertical annuli. A saturated porous medium was filled in the annuli. Their results show the significant effect of curvature on temperature and velocity fields. They presented a generalized form of empirical relation (equation (1)) for the overall Nusselt number in terms of average Rayleigh number, aspect ratio and radius ratio as given below. $N u = c o n s t . R a^{m} A^{n} κ^{p}$

Analytical solution of completely developed flow in vertical porous annuli for four fundamental BCs was performed by Al-Nimr (1995b). Their results reveal that a rise in annulus height does not affect the volumetric flow rate when the flow becomes fully developed. Prasad et al., (1986) conducted experiments on vertical annular geometry to study convection heat transfer for geometrical parameters. The inside wall was heated electrically heated while the outside wall was kept isothermal and a saturated porous medium was filled in the annular space. They found that curvature effects and solid-fluid combinations have a strong influence on temperature fields and observed reduction in Nusselt number with increases thermal conductivity ratio (solid to fluid) of the matrix.

Thansekhar et al., (2009) investigated NC in VAG numerically, which was filled with a porous material. The inside wall was isothermally heated while the outward wall was isothermally cooled while other walls were insulated. The study was performed for 0.1 ≤ λ ≤ 10, 1 ≤ A ≤ 20, 2 ≤ Rr ≤ 20, 0.1 ≤ k* ≤ 10 and Ra ≤ 10000. Results reveal that the Nusselt number at the inward wall rises with the Rayleigh number or radius ratio, while it drops with the aspect & permeability ratio. Correlations for HTC were obtained in terms of other non-dimensional parameters.

Sivasankaran et al., (2010) analyzed the influence of discrete heating in a porous enclosure having heat-generating stuff during natural convective flow. The left wall has two heat sources, and the right wall was isothermally cooled at a lesser temperature. The rest of the walls and unheated portions were kept adiabatic. The rate of heat transfer rises with modified Rayleigh & Darcy number (Da). Though, it drops with aspect ratio.

Sankar et al., (2011) solved the natural convective flow numerically in vertical annuli packed with fluid and wet porous material. They examine the comparative effect of discrete heating on convective flow using the Brinkman-extended Darcy equation. They considered broad range Darcy and modified Rayleigh numbers for heat sources of various lengths and at different locations. Their results show an increase in heat transfer with radius ratio, Darcy number and modified Rayleigh number, whereas it drops with heater length.

Wang et al., (2019) studied NC in VAG, taking the inner wall as the porous media, and the problem was being numerically solved by the multiple-relaxation-time Boltzmann scheme. In this paper, they considered the Effect of Darcy number, Rayleigh number, the thickness of the porous layer and thermal diffusivity ratio on overall HTC. On increasing the Darcy number, the average Nusselt number increases, which was more prominent at a higher Darcy number. Heat transfer intensifies above a critical value of thermal diffusivity for the porous layer, and decreases below this critical value. Also, the critical value decreases with a rise in the Rayleigh number. Higher HTC were estimated at higher Darcy number and thermal diffusivity ratio. Fig. 8 shows the streamlines and isotherms at different Darcy numbers.

Girish et al., (2018) carried numerical studies for free convective flow in a vertical porous annulus. It was made up of three concentric cylinders. The middle wall was completely thin and conductive, called baffles. The inner and outer wall was constantly heated while other walls are insulated as the boundary condition. Temperature and velocity fields were depicted for a different range of parameters. Results revealed that both geometrical and physical parameters have a substantial effect on velocity and thermal profiles. Fig. 9 shows the configuration and coordinate system of double passage porous annuli.

Kasaeian et al., (2017) performed an exhaustive review on the most recent advances in nanofluid flow in various geometries saturated with or embedded in a porous medium. Using Nanofluids with a higher thermal conductivity than typical working fluids like water offer the possibility of increasing heat transfer rates. Using porous media increases the surface contact area between the working liquid and the porous structure, resulting in greater heat transfer. Most previous papers on nanofluid flow in porous media have focused on nanoparticle volume fraction and nanoparticle sort effects on the Nusselt number as the heat transfer rate index and Sherwood number as the mass transfer parameter.

Badruddin et al., (2020) reviewed recent studies on heat transfer in porous media. The analysis focuses on heat transfer in porous media with various geometrical shapes, such as vertical plates, cavities, and cylindrical shapes. The study considered various heat transfer phenomena such as natural convection, mixed convection, thermal equilibrium, and thermal non-equilibrium. The heat transfer rate from the hot surface to the porous medium is slowed when viscous dissipation is present. Although porous media analysis has been ongoing for over a century, many discoveries still improve our simple understanding of the topic.

Most of the research on NC in VAG filled with porous material is numerical, with a few reported experiments. It was cited that a porous layer of high Darcy number is desirable for better thermal/heat transfer performance.

7. Use of boiling

Heat removal via boiling involves latent heat that is much greater than sensible heat. This results in much higher heat transfer coefficients in comparison to single-phase flow. Although, both the modelling and experimentation during boiling flow are much more complex than single-phase flow. This technique can be implemented by increasing the heat flux applied or selecting a working fluid that boils at a lower temperature. However, extra care should be taken to avoid the critical heat flux that can damage the experimental set-up. Additionally, a condenser is needed to condense the working fluid. Many researchers have performed studies during natural convective boiling flow in a vertical annulus.

Chun et al., (2000) carried out experiments during NC in VAG covering a wide range of parameters. They observed that the critical heat flux (CHF) happens when the flow changes from annular to annular-mist in the pressure range of 3–10 MPa for low mass-flux values. While for high mass fluxes values, the CHFs had maxima at a pressure of 2–3 MPa.

Khalid Usmani et al., (2003) carried experimental work on convective boiling of water during NC in VAG. At a particular submergence level, they found an increase in HTC and liquid mass flow rate with heat input. With a drop-in submergence level, HTC shows improvement, although the mass flow rate of liquid decreases. Siddiqui et al., (2010) determined the conditions of boiling incipience concerning associated parameters heat input, submergence level of liquid and properties of boiling fluid. They observed that the maxima of the wall superheat was near the point of boiling incipience.

Husain and Siddiqui (2017) performed experiments on convective boiling of water in a vertical annulus. The annulus was heated internally by a low voltage high current. The liquid was circulating through a cold leg, creating a closed-loop. The radius ratio and aspect ratio were fixed at 1.184 and 352, respectively. The heat flux on the inner wall has been varied from 15 to 35 kW/m2. Somehow the quasi-steady state condition is achieved for a short time. Heat transfer coefficient decreases sharply at the entrance region and remains constant in subcooled and again rises in the saturated boiling region. Different correlations were developed and validated.