Vibration Effects on Heat Transfer

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 06, June 2019, pp. 266-277, Article ID: IJMET_10_06_022
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=6
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
THE EFFECT OF TRANSVERSE VIBRATION
ON THE NATURAL CONVECTION HEAT
TRANSFER IN A RECTANGULAR ENCLOSURE
Nasrat K. Murad
Assistant Instructor, Sulaimani Polytechnic University, Iraq
Hameed D. Lafta
Assistant Professor, Sulaimani Polytechnic University, Iraq
Sadiq Elis Abdullah
Assistant Professor, Sulaimani Polytechnic University, Iraq
ABSTRACT
The effect of transverse vibration on the natural convection heat transfer in a
rectangular enclosure with an aspect ratio of 0.5 filled with air as a working fluid
aligned horizontally on a mechanical shaker generating a sinusoidal transverse
vibrational displacement was studied experimentally. The study was carried for a
Raghiely number between (3.77 - 10.8)*107
with applied heat flux between (20 - 45)
Watt. The vibrational experimental measurements were carried out for different
frequency ratio (0.87-1.6) and vibrational Rayleigh number ranged between (0.12 -
2.7)*107
. The results of the heat transfer inside the enclosure without vibration show
a very close agreement with the published one. The vibrational heat transfer results
show that the behavior of different heat transfer convection parameters can be
affected by applying a forced vibration condition. It is shown that the high heat
transfer can be achieved at frequencies near to the system natural frequency at
constant heat flux. Also, it is concluded that a careful attention should be given to the
proper selection of heat flux and frequency ratio results in obtaining maximum values
of heat transfer parameters with low cost of power consumption.
Key words: Frequency ratio, Natural convection, Rectangular enclosure, Transverse
vibration.
Cite this Article: Nasrat K. Murad, Hameed D. Lafta, Sadiq Elis Abdullah, The
Effect of Transverse Vibration on the Natural Convection Heat Transfer in a
Rectangular Enclosure. International Journal of Mechanical Engineering and
Technology 10(6), 2019, pp. 266-277.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=6

The Effect of Transverse Vibration on the Natural Convection Heat Transfer in a Rectangular
Enclosure
1. INTRODUCTION
Natural convection heat transfer enhancement has received considerable attention in last
decay due to their increasing engineering applications such as solar energy systems,
electronics cooling equipment, thermal energy storage. Vibration techniques are one of the
enhancement techniques used for these purposes (Kalase 2017). Wu-Shung Fu and Chien-
Ping Huang (2006 ) performed a numerical simulation to study the effects of a vibrational
heat transfer on natural convection in a vertical channel flow. Their results show that for the
same Rayleigh number, natural convection of a vibration heat plate with a certain
combination of frequency and amplitude is possibly smaller than that of stationary state. They
also, derived an expression for the critical frequency in terms of Rayleigh number and
amplitude.
Zena K. kadim and Hadi O. Mery (2016) studied experimentally the effect of vibration on
free convection heat transfer applied to sinusoidal surface, horizontally, vertically and facing
down word. Their studied including implementation of different heat flux subjected to forced
vibration with frequencies (5, 10, 15, 20, 25 Hz). They concluded that the vibrational heat
transfer enhancement depend on vibrational Reynolds number. The mixed convection heat
transfer around a pair of hot and cold horizontal micro tubes under the intensification heat
transfer state applying vibration studied experimentally by (Qiuxiang Wang 2017). They
showed that when the vibrational disturbance is strong, the relative effect on a given natural
convection is strengthened, and, when the vibrational disturbance is weak, the relative effect
on a given natural convection is weakened as well.
Numerical solution of Navier-Stokes equations based on different algorithms was adopted
by many researchers to investing the effect of sidewall vibration on a heat transfer in an
enclosure (Ho Sang Kwak 1998), (Yiqiang 2008), and (Semih 2017). Their results indicated
that the implementations of sidewall vibration have a significant effect on the heat transfer
and the maximum gain of the time-mean Nusselt number occurred at the resonance frequency.
(Hideo 2000) studied the chaotic behavior of vibrational thermal convection in a square
enclosure. A calculation method with features of the average Nusselt number was adopted.
The angular frequency of vibration was changed between 10 and 7680 and the Rayleigh,
Prandtle and Grashof numbers were held constant. Their results clarified that the region where
the hysteresis phenomena were detected corresponded to the one where the variation of the
surface averaged Nusselt Number was irregular and periodic. Also, El-hachemi (2018)
presented a numerical analysis on natural thermosolutal convection in a rectangular enclosure
filled partially and vertically by a porous layer subjected to vertical vibration. The Brinkman-
Extended Darcy equation was used for modeling the fluid flow in the enclosure. They found
that the vibration effect can be used beneficially where the operation is conducted under
restricted permeability and temperature gradient.
The effect of ultrasonic vibration on the melting process of phase change materials (PCM)
inside an enclosure was studied experimentally by (Oh 2002). The experimental results
revealed that the ultrasonic vibration accelerating the melting process as much as 2.5 times
than the melting process without vibration. Also, Hajiyan (2018) reported a novel numerical
work on the melting of phase change material inside a cylindrical enclosure under the
application of vibration. The governing equations of mass conservation, momentum, and
energy were solved by COMSOL Multiphysics software to simulate the melting behavior of
phase change material during vibration conditions. They observed that the vibration affects
the melting behavior significantly.
Adel (2014) investigated experimentally the effect of mechanical vibration on natural
convection in a cubic enclosure filled with air. Mechanical vertical vibration of (2-8) Hz was

Nasrat K. Murad, Hameed D. Lafta, Sadiq Elis Abdullah
applied at two different heat fluxes. They found that at high Rayleigh number the thermal
convection dominants and the vibration does not enhance heat transfer remarkably; While, at
low Rayleigh number, the vibration enhances heat transfer rate significantly.
In the present work, an attempt was made to study experimentally the effect of transverse
sinusoidal wall vibration of an air-filled rectangular enclosure on the convection heat transfer.
Different heat fluxes are adopted under resonant, sub-resonant, and over-resonant vibration
frequencies. The temperature measurements and vibrational measurements provided the data
required for determining the Rayleigh number and Nusselt number.
2. MATHEMATICAL FORMULATION
The total heat input to the rectangular enclosure may be calculated from the amount of
electrical power consumed by the electrical heater as follows:-
(1)
Where I represent the current consumed by electrical heater and V is the voltage.
The convection heat transfer can be calculated from the energy balance equation:-
(2)
Where Qcond is the conduction heat transfers r.
The conduction heat transfer can be calculated from the following equation [10] :-
( ) ( ) ( ) ( ) (3)
Where:-
Ah: hot wall surface area.
U: overall heat transfer coefficient.
Tamb : ambient air temperature.
Th : hot wall surface temperature.
Tf : fluid temperature and it is equal to .
Tc : cold wall surface temperature.
K : air thermal conductivity.
T: wall thickness.
W, H, and L are the dimensions of the enclosure.
The convection heat transfer coefficient can be calculated using Newton’s law of cooling
(Holamn 1997), such that:-
( )
(4)
A group of nondimensional numbers may be included in the study of the natural
convection heat transfer. One of the well known dimensionless numbers that is called Nusselt
number, which is defined as:-
(5)
The other dimensionless number it is called Rayleigh number, which is defined as:-
( )
(6)
Where
: is constant given by ( ).

Enclosure
: fluid temperature in Ko
.
g: is the gravity constant.
 : is the thermal diffusivity.
 : is the kinematic viscosity.
Inside enclosures, the transition from laminar to turbulent flow occurs when the Rayleigh
number is greater than one million ( Kwak 1998), (Zidi 2018).
For enclosure under vibration condition, the Nusselt and Rayleigh numbers may be
defined as:-
(7)
( )
(8)
Where suffix v refers to the quantities calculated in vibration condition; x and  are the
amplitude and frequency of vibration respectively.
3. EXPERIMENTAL WORK
The test rig and the experimental measurements are divided into three sections, as given
below:-
3.1. The test enclosure
The rectangular enclosure under investigation had an inner dimension of 30 cm  30 cm  60
cm. The hot and cold surfaces are of 30 cm  30 cm and the other four surfaces are of 30 cm
 60 cm. The hot wall is made of 1.5 mm copper plate backed with a flexible steel heater. The
steel heater is isolated by glass wool backed with aluminum plate and a polystyrene board of
70 mm. The cold wall is made of 1.5 mm thick copper plate over which a water jacket of 30
cm  30 cm  2 cm was backed. The other four walls consisted of MDF wood with a gray
surface. The test cell is insulated with 40 mm polystyrene board to minimize heat losses to the
environment, see Fig. 1, below. Five thermocouples of type k were impeded on the hot wall
surface and two thermocouples at the cold wall surface.
Figure 1 Test enclosure description (tope view).

Enclosur
e
Vibration
meter
Frequency
controller
The temperature of the hot surface is varied by controlling the input voltage to the steel
heater via a voltage regulator and the cold surface temperature was kept constant and uniform
by water circulation throughout the water jacket.
3.2. The data logger
The data acquisition system consists of three parts. The first part represents the temperature
measurements which is carried out by seven thermocouples connected via 12 channel data
logger which in turns directly transferred the data to the computer. Then, a computer program
was monitored and saved the measured data in a temperature-time dependent form. The five
thermocouples of the hot surface distributed such that four thermocouples equally distributed
at the perimeter of the hot surface and the fifth one at the center. While the cold surface
thermocouples are mounted equally at the center of the cold surface.
The voltage and current measurements are carried out via a digital voltmeter and ampere
meter. The electrical power measurement represents the total amount of heat flux imparted to
the enclosure.
The third part of measurement represents the frequency-amplitude measurements. These
measurements providing the data required to study the effect of vibration implementation on
heat transfer inside the test cavity. For achievement of these measurements, the frequency of
vibration was controlled and measured via a digital frequency controller - meter, while the
amplitude of vibration is measured by an accelerometer magnetically fixed to the shaker table
and integrated with a portable vibration meter.
3.3. The vibration shaker
The sinusoidal transverse vibration is implemented for the enclosure wall by a mechanical
vibration shaker, as shown in Fig. 2. The enclosure is aligned horizontally and it is firmly
fixed to the vibration shaking table by two rectangular fixtures. The frequency of vibration is
controlled by a digital frequency controller and measurement of the amplitude is carried out
by a portable vibration meter. In the present work, the vibrational frequency is applied at sub-
resonance, resonance, and over resonance frequencies. Thus, a frequency-amplitude test is
carried out to determine the system overall natural frequency.
Figure 2 Vibration shaker - enclosure assembly.

Enclosure
3.4. Experimental Procedure
The experiments, in the present work, were conducted in a rectangular enclosure with an
aspect ratio of 0.5 filled with air as a working fluid. The recording of data including seven
temperature measurements, the first two reading represents the temperature of cold walls, and
the other five readings represent the hot wall temperature measurement, and the last one
represents the ambient temperature reading. Firstly all the temperatures measurement are
carried out without vibration, for four sets of heat fluxes of (20, 30, 40, and 45) Watts
respectively. The complete set of temperature measurements is carried out with time and the
final readings are taken when the temperature reaches nearly steady state values and these
experimental measurements are of a long time measurements process. In the second part of
temperatures measurements sets, the transverse vibration displacement is applied by
sinusoidal mechanical vibration shaker. A frequency ratio (applied frequency/system natural
frequency) of different values (0.5 to 2) is applied. All the test procedure carried out such
that, firstly a specific heat flux is imposed on the system until steady state temperature is
gained. The transverse vibration is applied for the system at a specific frequency, and then all
the temperature measurements are recorded when the steady condition is predominant. The
test apparatuses with vibration shaker and data logger system are shown in Fig. 3.
Figure 3 Experimental test setup
4. RESULTS & DISCUSSIONS
4.1. Natural Convection inside Rectangular Enclosure
Fig. 4 shows the variation of the Nusselt numbers of natural convection with the Rayleigh
Number. The result indicates that the relationship between the Nusselt number and Rayleigh
number show a good agreement compared with that published one (Casado 2017). The
empirical relationship between the Nusselt number and Rayleigh number of the present study
may be given by Nu= 0.4189Ra0.2635
, and that presented by (Casado 2017) is given by Nu=
0.433Ra0.276
for an enclosure with aspect ratio of 0.5 and Rayleigh number >107
.

Figure 4 Variation of Nusselt Number versus Rayleigh number.
The relationship between the total heat flux and the absolute temperature ratio (the hot and
cold temperatures are in Kelvin's) is shown in Fig.(5) below. The thermal results show that
the total heat transfer as a function of absolute temperature ratio increases linearly with
increasing the absolute temperature ratio. The heat flux- temperature ratio trend shows a very
good agreement with that presented by [15]. The above two results can be considered as a
verification case study of the present work for the experimental test setup and temperature
measurements. Thus, the subsequent results for the cases with and without vibration can be
trusted on the bases of the agreement of the main two above results of the natural convection
heat transfer in a rectangular enclosure.
Figure 5 Effect of Heat Flux on absolute temperature ratio (Th/Tc).
4.2. Convection Heat Transfer with Transverse Vibration
The effect of transverse vibration on the convection heat transfer in an enclosure is studied in
the present work with a different transverse vibration frequency. The effect of vibration was
presented in terms of what is called the frequency ratio, which represents the ratio of forced
frequency to the system natural frequency. This developed study of the effect of vibration on
the natural convection heat transfer in terms of frequency ratio shows a power full tool in
determining the most critical frequency ratio that controlling the effect of vibration on the
different parameters included in the convection heat transfer inside an enclosure. As well as,

Enclosure
the study of the effect of vibration in terms of frequency ratio shows two indices. Firstly the
study provided a result for the real thermal system compared with its near real applications,
and secondly, the applied range of the frequency can be determined according to the sizes
(mass and mounting) of the actual thermal application.
The effect of the transverse vibration with different frequency ratio and different heat flux
on the Nusselt number, convection heat transfer, and the heat transfer coefficient are shown in
Fig. 6, Fig. 7, and Fig. 8 respectively. The results indicated that all the natural heat transfer
parameters can be controlled with controlling of the frequency ratio and they have the hill
trend of behavior. Consequently, this indicated that the same magnitude of the different
parameters can be obtained with a low-frequency ratio of vibration which in turn indicates
low power for inducing the required frequency forced vibration. Respectively, when a thermal
system undergoes an avoidable forced vibration with high forced frequency, then, by
controlling the mounting setup of the system the same results can be satisfied at low forced
frequency with the same magnitude of the natural thermal heat transfer. In other words, for
example, the same values of heat transfer coefficient, see Fig. 8, can be satisfied at two
different frequency ratios (low and high-frequency ratios). So that, from the power consumed
point of view the one with low-frequency ratio can be adapted to obtain the same magnitude
of the heat transfer coefficient.
Figure 6 Effect of transverse vibration frequency ratio on a Nusselt number (Nu) at different heat flux.
Figure 7 Effect of transverse vibration frequency ratio on a heat transfer coefficient (h) at different heat flux.

Figure 8 Effect of transverse vibration frequency ratio on a convection heat transfer at different heat flux.
The effect of different heat flux on a Nusselt number, convection heat transfer and the
heat transfer coefficient at different frequency ratios are shown in Figs (9, 10, and 11)
respectively. The results indicated that the heat flux effect on a natural heat transfer can be
altered and controlled with the application of transverse vibration. In other words, the same
Nusselt number, for example, can be obtained at different low and high heat flux, so that from
point of view of power heat consumption the one with low power can be applied. Also, the
results show that as the frequency ratio being near the resonant one, all the heat transfer
parameters get their maximum values. This can be attributed to the fact that when the forced
frequency near to the system natural frequency, a high disturbance in the fluid inside the
enclosure is achieved and this results in increasing the natural heat transfer in an enclosure.
As well as, it can be seen that at certain frequency ratio an increase in the applied heat flux
, results in an appreciated increase in the Nusselt number and the heat transfer coefficient.
For example, at frequency ratio of 1.6, with an increase in the applied heat flux of (55 %)
results in an increase in the Nusselt number of (47%) and (47 %) increase in the heat transfer
coefficient. While an increase of (55%) in applied heat flux results in an increase of (27 %)
and (28 %) increase in the Nusselt number and heat transfer coefficient. Accordingly, it
means that a very careful attention should be given to the proper selection of the heat flux
with the applied frequency. In other words, the proper selection of applied frequency and heat
flux results in an appreciated increase in the values of natural convection heat transfer of the
thermal systems.
Figure 9 Effect of heat flux on a Nusselt number (Nu) at different excitation frequency.

Enclosure
Figure 10 Effect of heat flux on a heat transfer coefficient (h) at different frequency ratio
Figure 11 Effect of heat flux on a convection heat transfer at different frequency ratio.
5. CONCLUSIONS
In the present work the effect of transverse vibration on the natural heat transfer in a
rectangular enclosure with aspect ratio 0.5 filled with air as a working fluid was studied
experimentally, and, the effect of different heat flux and frequency ratio on the thermal heat
transfer parameters were presented. Finally the following conclusions can be drawn:-
 The experimental results of the Nusselt number and Rayleigh number with heat flux show a
very close agreement with the published one
 The highest heat transfer can be achieved with a forced frequency close to the system natural
frequency.
 At constant heat flux, the same values of heat transfer parameters can be obtained at two
different frequency ratios.
 At a constant frequency ratio, the same values of heat transfer parameters can be obtained at
two different values of applied heat flux.
 A carefully choose of heat flux and frequency ratio results in obtaining maximum values of
heat transfer parameters with low power consumption

AKNOWLEDEMENT
The authors would like to thanks Eng. Aso Abdullah responsible of the Theory of Machines
and Vibration Laboratory for his support and the technician team at workshops, for setting up
the equipments at Mechanical engineering department/College of Engineering/ Sulaimani
Polytechnic University (SPU).
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[3] Kadim, Z. K. and Mery, H. O., 2016. Influence of Vibration on Free Convection Ceat
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Enclosure
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Vibration Effects on Heat Transfer

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