Numerical study of heat transfer by natural convection in concentric

hexagonal cylinders charged with a nanofluid

TALOUB DJEDID1

, BOURAS ABDELKRIM2, ZIED DRISS3

(0≤ Ø ≤0.12) on fluid flow and heat transfer performance. It is found that in high thermal Rayleigh numbers, a

thin thermal boundary layer is illustrated at the flow that heavily strikes the ceiling and lower from the outer

cylinder. In addition, the local and mean Nusselt number from a nanofluid are enhanced by enhancing the volume

fraction of the nanoparticles.The results are shown within the figure of isocurrents, isotherms, and mean and local

Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable

agreement.

Key-Words: - Natural convection, hexagon, thermal Rayleigh numbers, nanofluid, volume fraction.

Received: May 28, 2021. Revised: November 26, 2021. Accepted: December 19, 2021. Published: January 6, 2022.

enhance the thermal transfers of fluids has presented

rise to the generation of a new class, called

nanofluids. Holding nanoparticles suspended these

solutions within a basis fluid. Gratitude to their

thermic performance-enhancing properties,

nanofluids can be applied in many fields such as the

environment, production, cooling of electronic

components, biology, medical diagnostics, water

treatment, cooling in a heat engine Tzeng et al. [1],

and energy storage. However, the main difficulty

electrical, and into the attendance of a magnetic

domain, two-volume forces control the nanofluid

the triangular cavity. Moghari et al. [5] have studied

numerically the pressure loss and thermal properties

of the flow of nanofluid Al2O3 water in horizontal

rings. Each single-phase fluid method was selected

for the modeling of nanofluids. The effects of some

important parameters studied and discussed in detail.

They have observed that there are significant

increases in pressure loss and in elevating energy,

which is not acceptable. Izadi et al. [6] examined

numerically the influence from the ratio of the

by natural convection under uniform heat flow into

an annular enclosure loaded by nanofluids. They used

the finite element approach based on the control

volume. To evaluate the impact of thermic

conductivity and viscidity from the nanofluid they

used the Maxwell-Garnetts (MG) and Brinkman

models. These results explicate that increasing the

aspect report raises the values of the mean Nusselt

number. Dawood et al. [8] published a numerical

simulation of increasing heat transfer employing

numerical research at the heat transfer by natural

convection from nanofluid inside a rectangular cavity

including different pairs from heaters and icehouse.

The surfaces from the cavity are protected and many

pairs of heating and cooling devices with isothermal

surfaces are placed inside the cavity. The influences

of many parameters about the heat transfer flow and

the dispersion of nanoparticles are investigated.

These results designate that the location of the

coolers has several important impacts on the heat

in a ring-shaped enclosure, which formed within a

heated triangular internal surface and a circular

external surface. The impact of the volume fraction

from nanoparticles on improving heat transfer has

been tested at various thermal Rayleigh numbers. In

addition, the influence concerning diagonal,

horizontal, and vertical eccentricities in different

from a cylinder in the circular cylinder. The two-

phase representation is utilized within the event of

nanoliquids. They noticed that the heat transportation

is highest in the event from a cylindrical ring

accompanied on such cylindrical and square

enclosures. Mebarek et al. [16] numerically studied

the convective heat transfer of Titania nanofluids

with various basis fluids into a cylindrical ring by a

discrete warmth source. A computer code is a

developed basis on the finite volume approach

various heat fount locations alongside the internal

cylinder from the ring. Their goal is to recognize the

optimal location from the warmth fount to maximize

or minimize heat transportation to many Rayleigh

number valors and various volume fractions from the

nanoparticle. These results show that the position

from the heat fount has a deep influence on the flow

motif. The volume fraction from nanoparticles more

commands heat transportation into the ring geometry.

Lakshmi et al. [18-21] examined analytically the

shallow rings present the most suitable heat

transportation and high rings present the most critical

production. The appearance concerning a dilute

concentration from nanoparticles significantly

improves the warmth transportation within the

system. They concluded that a simple cylindrical ring

soaked by water and AA7075 lamellar mixture

nanoparticles is properly satisfied to heat transfer due

to its large efficient thermic conductivity compared

to other formed nanoparticles and that a large

the bicellular flow model to the two non-uniform

thermic states across any Rayleigh number ranges.

Sankar et al. [24] examined the effects from heat

transport conjugated into nanofluids by many

nanoparticles so as alumina, titanium oxide, or

copper within a closed annular geometry and formed

by an internal cylinder having a regular large

(Cu- water). The nanofluid is considered

incompressible and Newtonian by negligible viscous

diffusion and pressure working. The thermophysical

properties of the nanofluid are assumed constant with

the exception of the density, which changes

according to the Boussinesq approximation. The

Boussinesq approximation is applied to model the

buoyancy effect. The acceleration due to gravity acts

in the negative y-direction.

Fig. 1 Physical and computational field

2.2. Mathematical model

The treatment of the considered physical problem

These different boundary conditions in dimensional

form can be recapitulated as:

The initial conditions are:

U=V=0 (22)

External cylinder (six sides of hexagon)

U=V=0 (26)

2.6 Meshing choice

The impact of the size and number from nodes at the

resolution represented on the warmth transfer to the

"heated" active party from the cylinder explained

with the average Nusselt number in figure 2. An

irregular mesh close to the walls was utilized to

(figure 2). In this paper, eight combinations (64 ×

110, 74 × 130, 84 × 150, 94 × 170, 104 × 190, 114 ×

210, and 124 × 230) of check volumes are utilized to

examine the influence of grill size at the precision of

foretold results. Figure 2 presents the convergence

from the mean Nusselt number, in the heated inner

cylinder level by grill refinement. It is remarked that

mesh independence is reached by combining control

volumes (114 × 210) in which the mean Nusselt

number does not vary importantly with the finer mesh

which controlled at uniform imposed temperatures.

that the isotherms and the streamlines are

symmetrical with respect to the fictitious vertical

median plane. This figure show that the flow regime

the external cylinder).

At Rat = 105, the isotherms grow and ultimately take

on the form of a mushroom. The temperature

distribution decreases from hot cylinder to cold

heat is transported by conduction. At Rat (= 105 and

enhance extra confusing, and the vortex intensity

raises while the Rayleigh number rises. In that case,

the flow highly strikes the ceiling from the exterior

cylinder conducts the production of a thin thermic

layer. The form of the rotating spirals increases, the

isotherms go up, and heat is transferred by

convection.

Rat=2.5x105

Fig. 5 Isotherms (right) and isocurrents (left) for several

values about the thermal Rayleigh number, Rat at Ø=0

The evolution from the average Nusselt numbers by

the nanoparticle volume fraction for various thermal

Rayleigh number is presented in figure (6). It is noted

that as an adjusted value concerning the thermal

Fig. 6 Evolution of the mean Nusselt number by the

Rayleigh number

local Nusselt number values for the nanofluid are

higher than those for pure water. This is due to the i

to pure water, which increases heat transfer by

diffusion through the inner wall. In the thermal

values of the local Nusselt number increase due to the

significant influence of thermal convection and

volume fraction values of the nanoparticles. Let us

examine figure (8). It starts from the highest value

gradually rises and reductions until it arrival position

Co and Do. Then, the local Nusselt number leaps

directly from the area of point Do to point Eo, where

the values are almost zero it is the lower part of the

enclosure where the fluid is practically stationary.

Fig. 8 Evolution of the local Nusselt number alongside

enclosure at diverse values from the volume fraction

about the nanoparticles for Rat = 105 .

Figure (9) illustrates the distribution of the local

Nusselt number on the internal polygon sides (Ai-Bi,

lower part of the internal polygon where the fluid is

practically immobile.

isotherms are symmetrical to the

perpendicular line for all situations.

thermal boundary layer is illustrated at the

flow that heavily strikes the ceiling and

lower from the outer cylinder.

nanofluid are enhanced by enhancing the

volume fraction of the nanoparticles.

conduction process essentially controls the

heat transport within the annulus. During the

convection becomes dominant. The

isotherms grow more confounded and

thermal convection is commanding.

The research sheds light on this domain and indicates

the need for more investigations in the future by

examining

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