experimental and analytical solution for rayleigh bernard convection · 2017-10-13 · natural...

International Journal of Computation and Applied Sciences IJOCAAS, Volume 3, Issue 2, October 2017, ISSN: 2399-4509

224

Abstract— Natural convection has an undeniable effect

on the thermal-flow processes in engineering practice. The tanks

used in most mobile engineering systems are approximately of

parallelepiped shape. Such tanks may contain all kinds of

hydraulic fluids, so that the research done has chosen water and

air that represent the majority of fluids that can be found in the

given tanks. The paper will show the influence of external effects,

most of all, of temperature changes upon thermal-flow processes

taking place in the given tanks. The obtained results should more

closely show the real flow regimes taking place in the given tanks

as well as their influence upon the deposition of solid particles

that can be found in the given tanks.

Index Terms— Rayleigh-Bernard Convection, laminar

convection, turbulent convection, heat, humidity.

I. INTRODUCTION

he first and the simplest case of the fluid flow which is

described in fluid mechanics is a laminar flow. Such flow

takes place until the flow parameters, such as the

Reynolds number, do not reach a critical value [1]. After that,

the laminar flow becomes unstable under the influence of

small disturbances so that it cannot be maintained as such; so,

it turns into a turbulent one. This flow is extremely unstable

while its mathematical modelling most often extremely

complicated [2].

The most obvious example of the above-mentioned is a

lighted cigarette lying in an ashtray. If we look at the plume of

smoke that arises from the top of the cigarette, one can notice

that in the initial stage it looks relatively smooth and has a

straight flow path. Once it reaches a certain height, the path

suddenly shatters into a spatially and temporally disordered

form. It means that, due to the instability, the laminar flow

switched to the turbulent one [3, 4].

The criterion that determines when the fluid flow

changes or retains its status is called the stability criterion. The

stability criterion plays a central role in fluid mechanics, when

it comes to the fluids that are exposed to disturbance, given

that the instability can cause their transition from the laminar

to the turbulent state [5]. The theory of linear stability in fluid

mechanics implies predicting the critical Reynolds number at

which the fluid flow instability appears [6].

Sadoon K. Ayad is currently a lecturer in the Mechanical Eng. Dept.,

University of Technology, Baghdad, Iraq. E. mail: [email protected]

Predrag Živković is currently an assistant Prof. University of Nis/ Faculty of

Mechanical Engineering, Nis, Serbia. E. mail: [email protected]

Mladen Tomić is currently an assistant Prof. University of Nis/ Faculty of

Mechanical Engineering, Nis, Serbia. E. mail: [email protected]

Natural convection in enclosed spaces has been the

subject of study in energetics for a long time. It appears in a

wide range from the smallest scale (in pipelines, channels,

tanks) to the largest ones (atmosphere, the molten planet core).

The occurring processes depend on geometry and temperature

of respective surfaces, which defines the type of flow that

would occur [7].

A special group of these flows occur when the flow is

performed between the parallel plates of different

temperatures, usually when the temperature of the lower plate

is higher than the upper temperature - well known Rayleigh -

Bénard convection [8, 9]. The flow was experimentally

explained by the French scientist Henri Bénard (Henri Claude

Bénard (1874-1939)) in 1900. Nobel Prize winner for physics,

Lord Rayleigh (John William Strutt, 3rd Baron Rayleigh

(1842-1919)) in 1918 was the first to lay the theoretical

foundations based on the temperature gradient [10]. In this

approach, the boundary conditions at the top and bottom of the

observed domain imply the disappearance of the vertical

velocity component, which is not in accordance with the

Bénard experiment. References [11, 12] have made changes to

the model based on surface tension, which brought the model

into agreement with the experiment, i.e. physical reality.

The given examples of natural convection are still

based on the generalization of the plates between which the

flow takes place being unlimited. In engineering practice, this

is not the case, so that this research will define the influence of

the side walls to the flow, without idealization and within the

real three-dimensional domain [13].

The main objective of the current research is to

determine the real flow parameters in the real tanks exposed to

external influences. As the temperature gradient is the main

cause of a given flow, temperature measurements were

obtained in a real temperature range occurring at the location

where the experiment was be performed, i.e. in the laboratory

of the Faculty of Mechanical Engineering, Niš. The

temperature gradient source is insolation; since it is clear that

the convection intensity, or the occurring velocities, are in

direct proportion to the given temperature difference, what is

to be taken into account are the greatest temperature

differences occurring at respective surfaces.

II. MATHEMATICAL MODEL

Despite the complex mathematical model, under certain

conditions, we can predict how the instability is affecting the

structure of the turbulent flow. A typical example is the

Rayleigh - Bénard convection in which a thin layer of fluid,

limited by two parallel plates is heated from below. Due to the

temperature differences in the fluid layers, the flow under the

impact of the buoyancy forces occurs in the fluid. Depending

Experimental and Analytical Solution for

Rayleigh-Bernard Convection

Sadoon K. Ayed, Predrag Živković, Mladen Tomić

T


225

on the flow parameters, different cell structures are formed in

the temperature, velocity and vorticity fields. In the case of 3D

flow, so-called rolls are formed [14].

Therefore, the Rayleigh-Bénard's problem in its

simplest form and in the way it was treated in its earliest

study, is the case of the so-called infinite layer. In such a case,

the fluid layer is limited by two infinite horizontal plates. The

surface is heated from below, i.e. it is at a higher temperature

than the upper plate [15]. The upward heating has a negative

temperature gradient since the fluid is denser on the top than

on the bottom; such a formation, with the denser fluid at the

top, is potentially unstable. When the temperature gradient is

below a certain value, the natural tendency of a fluid to be

moving due to the buoyancy forces will be disrupted due to

the viscosity of the fluid, and heat dissipation. Thermal

instability occurs when the negative temperature gradient

exceeds a certain critical value [16].

The thermal convection phenomenon caused by the

negative thermal gradient is known as the Rayleigh-Bénard

convection. As for the physicality of the phenomenon,

however, combining both names into a single expression adds

confusion in understanding of the convection mechanism,

which is still not fully resolved: Bénard observed phenomenon

in which instability due to the temperature dependence on the

surface tension coefficient played an important part, while

Rayleigh studied the convection caused by other types of

instability, namely by non-uniformity of temperature (and

density) of the fluid layer. The term Rayleigh-Bénard

convection is usually attributed to the convection resulting

from the Rayleigh mechanism, while the term Bénard-

Marangoni convection refers to thermo-capillar convection

[17, 18].

There are numerous examples of the Rayleigh-Bénard

convection such as electro-convection (where the fluid is a

liquid crystal and there is a time-varying potential along the

cell), the binary fluids (with two different fluids within a cell)

and the Bénard-Marangoni convection (where the top plate

does not exist so that the surface tension acts as an additional

driving force). This case plays a major role in the development

of stability theory in hydrodynamics [19].

Other systems showing the properties of model forming

are the Taylor-Couette flow (between concentric rotating

cylinders), the Faraday waves (which occur in the fluid cell

with vertical disorders) and reaction-diffusion systems

(oscillating chemical reactions) [20].

Cell formation is a characteristic of the systems which

are far from equilibrium. They can be thrown out of balance

by different physical mechanisms. Some of them are:

temperature difference in the fluid, electrical potential

difference or chemical reactions. For each of the driving

forces there is a dissipation mechanism, such as viscosity,

which opposes the unbalancing of the system. The balance

between the driving force and the dissipation mechanism

results in the cell formation that can have different shapes

(circular, square, hexagonal, spiral, stripes...) [21, 22].

Mass conservation equation

𝜕𝜌

𝜕𝑡+𝜕(𝜌𝑢𝑖)

𝜕𝑥𝑖= 0,

(1)

Momentum conservation equations – Navier-Stokes

equations

𝜕(𝜌𝑢𝑖)

𝜕𝑡+𝜕(𝜌𝑢𝑖𝑢𝑗)

𝜕𝑥𝑗

=𝜕(𝜏𝑖𝑗)

𝜕𝑥𝑗−𝜕𝑝

𝜕𝑥𝑖

+ 𝑓𝑖 ,

(2)

Energy conservation equation

𝜕(𝜌ℎ)

𝜕𝑡+𝜕(𝜌𝑢𝑖ℎ)

𝜕𝑥𝑖

=𝜕(𝑗𝑖ℎ)

𝜕𝑥𝑖+ 𝜇𝛷 + 𝑆ℎ ,

(3)

where are: ρ density, ui velocity components, p pressure, fi

source terms of the equations of conservation of momentum

(volume, Coriolis, buoyancy forces, etc.) that can be ignored,

h entalphy, Sh production/destruction of energy, jih fluxes of

diffusive energy transport. In all the equations, we can notice,

on the left hand side, unsteady and convective terms, while

those that are diffuse and source can be noticed on the right

hand side [23].

In Newtonian fluid viscous stresses are proportional to

the deformation so that tensor τij has the following form

𝜏𝑖𝑗 = 𝜇 (

𝜕𝑢𝑖𝜕𝑥𝑗

+𝜕𝑢𝑗𝜕𝑥𝑖

)−𝜇2

3

𝜕𝑢𝑘𝜕𝑥𝑘

𝛿𝑖𝑗 , (4)

where are: μ dynamic viscosity of the fluid, δij Kronecker delta

operator (δij=1 for i=j and δij=0 for i≠j).

In equation (4) diffusive flux of energy transport jih

includes energy transport by conduction and viscous

dissipation. This can be expressed in the form:

𝑗𝑖ℎ = 𝛤𝑇

𝜕𝑇

𝜕𝑥𝑖, (5)

where

𝛷 =

1

2(𝜕𝑢𝑖𝜕𝑥𝑗


)

2

−2

3

𝜕𝑢𝑘𝜕𝑥𝑘

𝜕𝑢𝑙𝜕𝑥𝑙

, (6)

and

ℎ = 𝑐𝑝𝑇 (7)


226

where ΓT = λ is diffusion coefficient of enthalpy, or in this case

thermal conductivity [24].

The change of density as a function of temperature for

incompressible fluids can be assumed in the linear form

𝜌 = 𝜌0(1 − 𝛽(𝑇 − 𝑇0)) (8)

where β is compressibility factor of dimension K-1.

For the Navier-Stokes equations, where ρ is constant, we

obtain

𝜌𝜕𝑢𝑖𝜕𝑡

+ 𝜌𝜕(𝑢𝑖𝑢𝑗)

𝜕𝑥𝑗

= 𝜇𝜕

𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗


) −𝜕𝑝

𝜕𝑥𝑖+ 𝜌𝑔𝑖 ,

(9)

respectively

𝜌 (

𝜕𝑢𝑖𝜕𝑡

+𝜕(𝑢𝑖𝑢𝑗)

𝜕𝑥𝑗)

= 𝜇𝜕



)

−𝜕𝑝

𝜕𝑥𝑖+ 𝜌𝑔𝑖,

(10)

where body forces fi are replaced by ρgi.

(𝜌0 + 𝜌′) (𝜕𝑢𝑖𝜕𝑡


𝜕𝑥𝑗) = 𝜇

𝜕



)

−𝜕𝑝0𝜕𝑥𝑖

−𝜕𝑝′

𝜕𝑥𝑖+ 𝜌0gi + 𝜌′gi,

and noting that in the hydrostatics

𝜕𝑝0𝜕𝑥𝑖

= 𝜌0gi (11)

we finally obtain

(𝜌0 + 𝜌′) (



𝜕𝑥𝑗)

= μ𝜕



) − 𝜌0𝑔𝑖

−𝜕𝑝′

𝜕𝑥𝑖+ 𝜌gi.

(12)

Dividing the whole expression with ρ0, we obtain

(1 +

𝜌′

𝜌0)(



𝜕𝑥𝑗)

= ν𝜕



) −1

𝜌0

𝜕𝑝′

𝜕𝑥𝑖

+𝜌′

𝜌0gi.

(13)

For small values of density variation the following is obtained



𝜕𝑥𝑗= ν

𝜕



)

−1

𝜌0

𝜕𝑝′

𝜕𝑥𝑖+𝜌′

𝜌0gi.

(14)

A member of the right-hand side with ρ' remains in the

expression, because the size of gi is large enough to affect the

expression. Finally, taking into account density dependence on

temperature, we obtain



𝜕𝑥𝑗= 𝜈

𝜕



) −1

𝜌0

𝜕𝑝′

𝜕𝑥𝑖− gi𝛽𝛥𝑇.

(15)

If p=p0+p', then dp=dp', followed by



𝜕𝑥𝑗= ν

𝜕



) −1

ρ0

𝜕𝑝

𝜕𝑥𝑖− gi𝛽Δ𝑇,

(16)

By introducing the dimensionless quantities for

velocity U, time τ, pressure and temperature �̅� and �̅�, and

length �̅� we obtain equation in the following form:

1

𝑃𝑟(𝜕𝑈𝑖

𝜕𝜏+𝜕(𝑈𝑖𝑈𝑗)

𝜕�̅�𝑗) =

𝜕2𝑈𝑖

𝜕�̅�𝑗2 −

𝜕�̅�

𝜕�̅�𝑖+ 𝑅𝑎�̅�,

(17))

In this expression, Pr represents the Prandtl number,

while the Rayleigh number Ra, analogously to the Reynolds

number, is the ratio of the buoyancy and the viscous forces,

that is

𝑅𝑎 =

g𝛽𝛥𝑇𝐿3

𝜈𝑎.

(18))

Further interest is to determine the stability limit of the

Rayleigh-Bénard convection, and the effect of the disturbance,

or perturbation on the fluid state.

In practice, there are three types of the tank - spherical,

cylindrical and prismatic. The first two types are mainly

storage tanks of large volume, and therefore stationary. As

most of the reservoirs in mobile systems are approximately of

parallelepiped shape (for vehicles, in the airplanes wings and

fuselage...), this research will focus on this type [25].

Since it is known that the intensities of the velocities

that occur at such convection are quite low, the study is based

on the numerical experiment. For the purpose of validation of

the numerical experiment, an experimental installation is

formed with respective dimensions H×W×L of 1×2×4

(500×250×125mm, in x, y and z directions, respectively) [26].

The experiment comprised the measurement of the

temperature profiles in several sections, both vertical and

horizontal.


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III. EXPERIMENTAL SETUP

As there are many types of hydraulic fluids we can find

in real tanks, the real as well as the practical experiments were

carried out with five different working fluids - water, diesel

fuel, motor oil, alcohol and air (the case of an "empty" tank).

One can, with sufficient accuracy, assume that the chosen

fluids faithfully represent the majority of fluids that can be

found in the real tanks.

Since the impacts of the Rayleigh-Bénard convection

on real tanks are not extensively explored in the available

literature, the aim of this study is to show the real thermal-

flow processes in the case of the aforementioned

parallelepiped tank. Better knowledge of these processes can

increase the safety and reliability of the whole systems of

which they are component parts, which is of exceptional

importance, especially for tanks in various hydraulic systems

of an aircraft.

Fig. 1: Scheme of experimental installation

In order to confirm the results of the experiment, in the

premises of the Laboratory for Thermal Engineering, the

experimental installation was formed in which the temperature

was measured at 16 points in the chamber, in several sections,

both vertical and horizontal, using a special construction of

PT100 temperature sensors that enabled chamber sealing in

respective positions. The chamber is insulated on the sides by

sponge and Styrofoam. Additional check-up of the results is

done by thermal imaging camera.

As can be seen in the diagram of Fig. 2, above the

chamber there is a water area, 50mm high, in which there is a

heater, which is through the variable resistor (Variac) can

accurately heat the water. In this chamber there is a mixer, for

equalization of the temperature of the water, and thus the hot

plate, which is located on the opposite side of the heater. The

chamber is equipped with the trestles which enable its turning

so that the hot plate can be either at the top or the bottom of

the chamber. External influences are simulated by heating the

upper plate (insolation). The following Fig. shows the

temperature field at the appropriate layers of insulation,

obtained by thermal imaging camera Flir E30.


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Fig. 2 Checking the temperature field by thermal imaging camera for the

gradual removal of insulation in case of air as the working medium

Fig. 3 Structure and parameters of temperature probes TS-05 with PT100

temperature sensor

A. Measuring system

The measurement system was developed in cooperation with

firm Nigos, Nis [27]. It consists of two eight-channel data

loggers for collecting data on temperatures in respective

chamber locations. This approach gives temperature profiles

in three vertical sections, on either side of the chamber, in

order to determine the temperature deviation from the "front"

(sunny) and "rear" side of the chamber. In order to determine

the uniformity of temperature distribution of hot plate, close to

it a set of 5 temperature sensors was located at one lateral side

and two on the other.

The temperature measurement and acquisition were

done by 2 eight-channel loggers VT08 and 16 PT100 probes

type TS05, 0.1ºC accuracy, enabling the necessary chamber

sealing (Fig. 5). Calibration of PT100 probes using a reference

thermocouple (TP) is shown in the following Fig.

Microprocessor logger VT08, in addition to

temperature measurement is comparing the measured values

with the set limit values. If some measured value of the

measuring point exceeds the permitted limit, one of the relay

outputs, serving as alarms, is activated. The limit values are

widely adjustable. There is a possibility of adjusting the

temperature offset for each input. The upper display shows the

measured current value of the temperature measuring points,

and the bottom shows the number of the measuring point.

Changing the display can be automatic or manual. In

automatic change, the display for a limited time alternates

measured points for which the measured temperature values

are displayed. In the case of manual changes, permanent

display of the desired measuring point can be set.

B. System for data acquisition – NIGOS Manager Acquisition

Software

NIGOS Manager is a PC application that enables

monitoring and management of all the measuring and control

devices that have embedded communication interface [28].

The application allows communication with devices over a

serial or USB port and the appropriate adapter. It is possible to

work and in a LAN network using a communication server to

remote computers.

The user with administrator access rights defines the

network of devices the application communicates with. He has


229

the ability to choose the parameters of the device monitored

(diagram with current values is generated) and archive them in

a database. Based on the data collected, reports can be

generated afterwards in a graphical or table form, or the data

can be exported to a file for processing in other applications

for table calculations such as Excel, Calc, etc.

There is also the possibility of entry of data from the

report to a file. Data is written to the .csv (comma-separated

values) format. This file can be opened in any text editor, as in

Microsoft Office Excel. Report generation can be a time-

consuming operation, depending on the number of data to be

displayed (depending on the time period for the report and the

period of entry in the database). For faster generation a shorter

period should be chosen or lower frequency of entries in the

database.

NIGOS Manager can be used to adjust the device,

because through communication interface can access their

parameters. Current setting can be saved to a file (setting all

parameters). It is possible to enter previously recorded settings

to other devices of the same type.

C. 4.4 Thermal imaging camera Flir E30

For comparison of data measured on the PT100

temperature probes, parallel periodical measuring of the

temperature field is executed with thermal camera Flir E30

[29]. Cameras specifications are given in Table 4.1. The

camera data shows that the reading accuracy of temperature

field is ±2°C or ±2% of reading, however, since the

temperature was up to a level of 50°C, it follows that the

accuracy level is ±1°C, which is an order of magnitude smaller

than the accuracy of the used probe PT100. The use of thermal

camera was limited to a comparison with the measured

temperature fields and visualization, but not really measuring.

However, the obtained results are consistent with the

measured, and as comparative values they can be taken into

account within the specified accuracy.

TABLE 1 Thermal imaging camera flir E30 technical data [30]

Model FLIR E30

Optical performance

Resolution 160 × 120 pixels

Global resolution 19,200 pixels

Temperature sensitivity < 0.10°C

Accuracy ±2°C or ±2% reading

Temperature range -4°F to 662°F (-20°C to

350°C)

Video camera w/lamp 2.0 MP

Video output Composite

Sampling frequency 60 Hz

IV. RESULTS AND DISCUSSIONS

The aim of the experiment was to determine the

influence of external conditions on the fluid contained in the

parallelepiped tank. In order to facilitate the comparison of

results, the same heat flux is brought to the water in the

chamber, and the surrounding air is left to the influences of the

atmosphere. The chamber is tested with air as the working

fluid. Fig. 4 shows the preliminary results of the

measurements for a period of 5 days.

Fig. 4 The five-day temperature changes of air as the working fluid

Fig. 5 shows a typical daily temperature change. It can be

concluded that all the temperatures show similar behaviour in

relation to environment temperature change.

Fig. 5: Typical daily temperature change

Fig. 6 shows the hourly change in temperature during the

parallel measurements with the IC camera. Period of 30

minutes before and 30 minutes after the measurement with

thermal camera (results shown in Figs. 7 & 8). Measurement

with the thermal camera lasted for 4 minutes, during which

layer after layer of insulation was removed. As the probes

located in the chamber showed no noticeable temperature

differences (other than those along the cold plates, which

show a very slight increase in the level of up to 0.4° C), it can

be concluded that this is due to increased convective heat


230

exchange caused by increased room air velocity (opening the

door, the movement during the measurement, removing and

restoring the insulation, etc.)

Fig. 6 Typical hourly changes in temperature (during the thermal camera

measurement)

The chamber used in the experiment has shown great

flexibility. The probes are placed at appropriate locations so

that there are 3 or 4 probes that measure temperature in 3

different vertical sections. This arrangement allows

measurement with various hydraulic fluids at different

temperature regimes and positions of the warmer and cooler

plates. The experiment has shown that the relative stability of

the surrounding air has allowed the cooler plate to be directly

exposed to external conditions. The measuring system has

shown an appropriate response to external conditions,

enabling a variety of experiments. Selected Probe TS-05, due

to the massive threaded part somewhat increased measurement

inertia; yet this has allowed control measurements with the

thermal camera. Thermal camera measurements have shown

no significant heat loss in the insulated part of the chamber.

Fig. 7: The temperature profile in the left, middle and right vertical cross-

section of the chamber with air in case of RBC (left) for temperatures

TS01=41.3°C and TS16=30.3°C

As at this time for technical reasons it was not possible

to perform measurement of velocity field in the experimental

chamber (although it same is equipped with transparent

openings to allow the possible application of laser-Doppler

anemometry), the measurement of temperature profiles was

carried out in multiple cross sections, both horizontal and

vertical for all of the working fluids (air). For comparison,

there was a series of measurements with the warmer plate

positioned on the upper side (which simulated the impact of

solar radiation as a source of the temperature gradient in the

fluid) – the RRBC case, and then to a warmer plate positioned

on the lower side (a classic setting for Rayleigh-Bénard

convection) – the RBC case.

0

25

50

75

100

125

30 32 34 36 38 40

Hei

gh

t [m

m]

Temperature [°C]

0

25

50

75

100

125

30 32 34 36 38 40

Hei

ght

[mm

]

Temperature [°C]

0

25

50

75

100

125

30 32 34 36 38 40

Hei

ght

[mm

]

Temperature [°C]

0

25

50

75

100

125

34 36 38 40 42 44 46 48

He

igh

t [m

m]

Temperature [°C]


231

Fig. 8 The temperature profile in the left, middle and right vertical cross-

section of the chamber with air in case of RRBC (right) for temperatures

TS01=51°C and TS16=33°C

The natural convection in enclosed spaces has been

studied for a long time in energetics. It emerges in a wide

range from the smallest scales (in various vessels and devices)

to the largest ones (atmosphere, molten planet core). The

occurring processes depend on geometric relations and

temperature of respective surfaces, which defines the type of

flow that would occur.

A special group of these flows occurs when the flow

takes place between two parallel plates with different

temperatures, most often when the lower plate temperature is

higher than that of the upper – a well-known case is that of the

Rayleigh-Bénard convection. This case was first experim-

entally investigated by Henry Bénard in 1900, while the Nobel

Prize winner for physics, Lord Rayleigh (John William Strutt,

3rd Baron Rayleigh) was the first to lay the theoretical

foundations based on the temperature gradient. In the later

studies this problem was theoretically better described,

especially after the introduction of the model based on surface

tension. These studies are mainly based on the study of flow

between 2 infinite parallel plates, which left space for the

study of the impact of the real side walls in real tanks, without

process idealization and in the real three-dimensional

domains.

V. CONCLUSIONS

All the research results can be summarized in the form

of several characteristic findings:

- The chamber used in the experiment has shown great

flexibility. The probes are placed at appropriate locations

so that there are 3 or 4 probes that measure the

temperatures in 3 different vertical cross sections. This

arrangement allows measurement with various hydraulic

fluids with different temperature regimes and warm and

cool plate positions.

- The experimental results have indicated that the relative

stability of the surrounding air allows the cooler plate to

be directly exposed to external conditions.

- Measuring system showed an appropriate response to

external conditions, enabling a variety of experiments.

Probes carriers have somewhat increased measurement

inertia, but allowed the control measuring with the

thermal camera. Thermal camera measurements showed

no significant loss of heat on the insulated part of the

chamber

- This chamber construction, through transparent

openings, enables the use of non-contact methods for

temperature and velocity field measurement, such as

laser-Doppler anemometry, various optical methods, etc.

- On the basis of experimental data numerical experiment

was performed. Validation is done through the

temperature field in several sections. The values of

Rayleigh number are in accordance with the obtained

velocity field.

REFERENCES

[1] M. T. Chaichan, D. S. M. Al-Zubaidi, "Control of hydraulic

transients in the water piping system in Badra–pumping station

No.5," Al-Nahrain University, College of Engineering Journal

(NUCEJ), vol. 18, No. 2, pp. 229-239, 2015.

[2] M. T. Chaichan, "Enhancing productivity of concentrating solar

distillating system accompanied with PCM at hot climate,"

Wulevina, vol. 23, No. 5, pp. 1-18, 2016.

[3] H. A. Kazem, S. Q. Ali, A. H. A. Alwaeli, K. Mani and M. T.

Chaichan, "Life-cycle cost analysis and optimization of health

clinic PV system for a rural area in Oman," Proceedings of the

World Congress on Engineering 2013, vol. II, WCE 2013,

London, U.K., July 3 - 5, 2013.

[4] M. T. Chaichan & K. I. Abaas, "Productivity amelioration of

solar water distillator linked with salt gradient pond," Tikrit

Journal of Engineering Sciences, vol. 19, No. 4, pp. 24-34,

2012.

[5] M. T. Chaichan, K. I. Abaas & H. A. Kazem, "The effect of

variable designs of the central receiver to improve the solar

tower efficiency," International J of Engineering and Science,

vol. 1, No. 7, pp. 56-61, 2012.

[6] M. T. Chaichan & K. I. Abaas, "Practical investigation for

improving concentrating solar power stations efficiency in Iraqi

weathers," Anbar J for Engineering Science, vol.5, No. 1, pp.

76-87, 2012.

[7] M. T. Chaichan, K. I. Abaas, "Performance amelioration of a

Trombe wall by using phase change material (PCM),"

International Advanced Research Journal in Science,

Engineering and Technology, vol. 2, No. 4, pp. 1-6, 2015.

[8] S. T. Ahmed & M. T. Chaichan, "A study of free convection in

a solar chimney sample," Engineering and Technology J, vol.

29, No. 14, pp. 2986-2997, 2011.

[9] A. H. A. Al-Waeli, M. T. Chaichan, H. A. Kazem, K. Sopian,

"Comparative study to use nano-(Al2O3, CuO, and SiC) with

water to enhance photovoltaic thermal PV/T collectors," Energy

Conversion and Management, vol.148, No. 15, pp. 963-973,

2017. https://doi.org/10.1016/j.enconman.2017.06.072

[10] A. H. A. Al-Waeli, K. Sopian, M. T. Chaichan and H. A.

Kazem, H. A. Hasan, A.N. Al-Shamani, "An experimental

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investigation on using of nano-SiC-water as base-fluid for

photovoltaic thermal system," Energy Conservation and

Management, vol. 142, pp. 547-558, 2017. [11] M. J. Block, "Surface tension as the cause of Benard cells and

surface deformation film," Nature (London), pp. 650-651, 1956.

[12] J. R. A. Pearson, "On convection cells induced by surface

tension," Journal of Fluid Mechanics, vol. 4, No. 5, pp. 489-

500, 1958.

[13] S. Ayed, "Experimental study of temperature distribution for

turbulent Rayleigh – Benard convection in rectangular tank,"

Annals of Faculty Engineering Hunedoara – International

Journal of Engineering, vol. 12, No. 1, pp. 117-120, 2014.

[14] M. M. Jovanović, D. S. Živković, J. D. Nikodijević, "Rayleigh-

Benard Convective instability in the presence of temperature

variation at the lower wall," Thermal science, vol. 16, No. S2,

pp. 281-294, 2012.

[15] S. Ayed, et al., "Instability of Rayleigh-Benard convection

affected by inclined temperature variation," 12th International

conference on accomplishments in electrical and mechanical

engineering and information technology - DEMI 2015, pp. 373-

378, 2015.

[16] M. Jovanović, "Simulacija velikih vrtloga trubulentnog strujanja

nestišljivog, viskoznog fluida u kanalu promenljivog poprečnog

preseka," PhD thesis, Univerzitet u Nišu – Mašinski fakultet,

2007.

[17] G. Ilić, N. Radojković, M. Vukić P. Živković, I. Stojanović,

"Termodinamika II," Univerzitet u Nišu, Mašinski fakultet, Niš,

2014.

[18] Ž. Stevanović, "Numerički aspekti turbulentnog prenosa

impulsa i toplote," Univerzitet u Nišu, Niš, 2008.

[19] S. Ayed, M. Tomić, P. Živković, "Specific approach for traffic

induced pollution estimation in the city of NIŠ," Polish Journal

of Environmental Studies, vol. 24, No. 6, 2015.

DOI: 10.15244/pjoes/58763,

[20] S. Pavlovic, D. Vasiljevic, V. Stefanovic, Z. Stamenkovic, S.

Ayed, "Optical model and numerical simulation of the new

offset type parabolic concentrator with two types of solar

receivers," Facta Universitatis, Series: Mechanical Engineering,

vol. 13, No. 2, pp. 169-180, 2015.

[21] M. Tomić, P. Živković, M. Vukić, V. Stefanović, S. Ayed, The

analysis of the matrix heat exchanger effectiveness," Advanced

Technologies, vol. 4, No. 1, pp. 89-93, 2015.

[22] S. Ayed, M. Jovanović, G. Ilić, P. Živković, M. Vukic, M.

Dobrnjac, S. Kljecanin, "Experimental study of tempreture

disribution for turbulent rayleigh –bernard convection in

rectangular tank," International journal ANNALS of Faculty

engineering Hunedoara, pp117-120, 2016.

[23] S. Ayad, F Hameed, A. L. Ekaid, "Mixed convection in porous

media heated from below," Association of Arab Universities

Journal of Engineering, vol. 14, No. 1, pp. 87-96, 2007.

[24] S. Ayed, M. Jovanović, G. Ilić, P. Živković, M. Vukic, M.

Dobrnjac, S. Kljecanin, "Experimental study of tempreture

disribution for turbulent rayleigh –bernard convection in

rectangular tank," 11th International Conference on

Accomplishments in Electrical Mechanical Engineering and

Information Technology, University of Banja Luka, Faculty of

Mechanical Engineering, DEMI 2013, pp. 665-672,

2015.

[25] M. A. Tomić, P. M. Živković, M. V. Vukić, S. K. Ayed, The

methodology for determination of perforated plate heat transfer

coefficient," Powerplants 2014, Zlatibor, Serbia.

[26] S. R. Pavlovic, V. P. Stefanović, P. Rajković, E. P. Petrovic, S.

Ayed, "Ray tracing study to determine the characteristics of the

solar image in the receiver for a thermal solar concentration

system," 7th International Symposium on Exploitation of

Renewable Energy Sources and Efficiency, EXPRESS, pp. 35-

39, 2015.

[27] S. Ayed, M. Jovanović, S. R. Pavlovic, E. Petrovic, "Instability

of rayleigh-bernard convection affected by lower wall

temperature variation," KGH 2014, pp. 13.

[28] S. Ayed, P. Živković, M. Tomic, A. Rashid, "Direct numerical

simulation of Navier -Stokes equation for the forced Rayleigh-

Bernard convection of temperature variation at the lower wall,"

7th International Symposium on Exploitation of Renewable

Energy Sources and Efficiency, EXPRESS, pp. 18-22, 2015.

[29] A. Al-Sammarraie, D. Milcic, S. Ayed, "Study behaviour of the

coefficient of friction and wear rate of the brass alloy CuZn30

on counterface material conversely," 14th International

Conference of Tribology-Serbia, Treb15, pp. 49-55, 2015.

[30] S. Ayed, M. Jovanović, M. Tomić, G. Ilić, P. Živković, M.

Vukić, M. Dobrnjac, "Instability of rayleigh-bernard convection

affected by inclined temperature variation," 12th International

Conference on Accomplishments in Electrical and Mechanical

Engineering and Information Technology - DEMI 2015, pp.

373-378, 2015.

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