Study of turbulent flow downstream from a linear source of heat

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
INTERNATIONAL JOURNAL OF MECHANICAL
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEME
ENGINEERING AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4 Issue 1 January- February (2013), pp. 08-21
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STUDY OF TURBULENT FLOW DOWNSTREAM FROM A
LINEAR SOURCE OF HEAT PLACED INSIDE THE
CYLINDER WAKE

D. Tcheukam-Toko*1, B. S. Tagne-Kaptue2, A. Kuitche2, R. Mouangue1, P. Paranthoën3
1
Department of Energetic Engineering, IUT, University of Ngaoundere, P. O. Box 455
Ngaoundere, Cameroon
2
Departments of Energetic and Electrical Engineering, ENSAI. P. O. Box 455 Ngaoundere,
Cameroon.
3
CNRS UMR 6614 CORIA, University of Rouen, P. O. Box 12 – 76801 Saint-Etienne du
Rouvray, France.
* Corresponding author. Email: tcheukam_toko@yahoo.fr

ABSTRACT

A turbulent flow downstream from a linear source of heat placed inside the cylinder
wake has been studied numerically in this paper. Special attention has been paid to the
cylinder wake effect on the source of heat diffusion in downstream flow. The turbulent model
has been applied a standard κ-ε two equations model and the two-dimensional Reynolds
Averaged Navier–Stokes (RANS) equations are discretized with the second order upwind
scheme. The SIMPLE algorithm, which is developed using control volumes, is adopted as the
numerical procedure. Calculations were performed for a wide variation of the Reynolds
numbers. The investigations reveal that with increasing Reynolds number, the instabilities
appear in the wake zone, showing an oscillatory flow, also called von Karman Vortex Street.
His geometry has an important influence on the thermal field and the diffusion process.
Comparison of numerical results with the experimental data available in the literature is
satisfactory.

Keywords: Passive scalar, linear source of heat, Cylinder wake, Turbulent flow, CFD.

8


I. INTRODUCTION

The dispersion of passive contaminant generated of locale fashion in a turbulent flow,
is an important phenomenon funded in many problems of heat and mass transfer (Warhaft,
[1]). His industrials applications are the dryer, the heat pump, the boilers, the air
conditioning, the refreshes of electronics components, the reactor conception, etc... The terms
passive and locale means respectively that the contaminant emitted does not modified the
characteristics of main flow and the scale, at which the scalar is injected, is always very lower
than the integral scale of turbulence. In many practices situations, these diffusions
phenomenon’s appeared in some complex turbulent flows which are perturbed by the
obstacles and are characterized by the higher structures.
Many studies carried out in turbulence during these last decade, have showed the existence of
coherent structures inside the stress flows, even at the high Reynolds numbers. Veeravalli and
Warhaft, [2], carried out a study of thermal dispersion from a line source in a shearless
turbulence mixing layer. They did not associate the instabilities phenomenon caused by the
existence of wake. Le Masson, [3], has worked on the control of Bénard Von-Karman
instabilities downstream from a heated obstacle at low Reynolds number, but he does not
defined all the control parameters of instabilities. Brajon-Socolescu, [4], has carried out a
numerical study on the Bénard Von-Karman instabilities behind a heated cylinder. Lecordier
and al. [5], also, who have worked on the transition control downstream from a 2D obstacle
using a source of heat located inside his neared wake. These last two studies were limited
because of lack of critical Reynolds number. Weiss [6], has studied a passive scalar diffusion
inside the neared obstacle wake. He demonstrated that the thermal field is strongly influenced
by the geometry of Vortexes Street, but he worked only with one Reynolds number.
Paranthoën and al. [7], have carried out a dynamic field experimental study of Bénard von-
Karman Street downstream from a heated or not heated 2D obstacle. This study used only
one Reynolds number. Many others recent studies were carried out by Champigny and
Simoneau, [8], on the mixed convection around a wide vertical cylinder. They did not take in
account, the wake effects on the thermal field dispersion and the choice of turbulence model.
Aloui, [9], in the studies carried out on the flow control, does not take in account the choice
of parameters control and the source of heat. However, it is clear that few of these studies
have been dedicated on the influence of structures in the diffusion and transport phenomenon,
with the exception of Crow and al. [10], who have worked on the solids particles dispersion.
The number of studies carried out in this domain is not enough, however, it’s aroused many
interest, because of his responsibility on the existence of counter-gradient zones in these
flows. In this case, the flux of passive contaminant has the same direction and the same way
with the mean temperature gradient (FuIachier and al. [11]; Sreenivasan and al. [12],
Veeravalli and Warhaft, [2]). Corsin [13], has showed that it is not possible to model the heat
transport with the linear model of gradient transport using a turbulent diffusivity.
In order to explain the influence of structures on the thermal transfer phenomenon and
diffusion process, we have carried out a numerical study of turbulent flow downstream from
a linear source of heat placed inside the cylinder wake, by using several Reynolds numbers.
To lead well this study, we are going to analyze the temperature and velocity profiles
respectively inside the cylinder wake and downstream from the linear source of heat. Then,
we will analyze the means temperature gaps profiles, the transversal flux of heat profiles, in
function of transversal gradient of mean temperature. We will end this analyze by doing the
comparison between the numerical and the experimental results.

9


II. MATERIAL AND METHODS

II.1 Mathematical models used
The continuity equation is given by the equation bellow:
డఘ
ሬԦ
൅ ݀݅‫ݒ‬൫ߩ ܸ ൯ ൌ 0 (1)
డ௧
The conservation equations of the average quantity of movement of Navier-Stockes known by the
name RANS are for compressible fluid and Newtonian given by the formula bellow.

డ
ሺߩ‫ݑ‬௜ ሻ
డ
൅ డ௫ ൫ߩ‫ݑ‬௜ ‫ݑ‬௝ ൯ ൌ െ
డ௉ డ డ௨ డ௨ೕ ଶ డ௨ డ തതതതത
൅ డ௫ ൤ߤ ൬డ௫ ೔ ൅ డ௫ െ ଷ ߜ௜௝ డ௫೔ ൰൨ ൅ డ௫ ቀെߩ‫ݑ‬ప ‫ݑ‬ఫ ቁ ൅ ‫ܨ‬௜ (2)
′ ′
డ௧ ᇣᇧೕ ᇧᇤᇧᇧᇥ ด
డ௫೔ ᇣᇧᇧᇧᇧᇧᇧᇧᇧᇤᇧᇧᇧᇧᇧᇧᇧᇧᇥ ᇣᇧ ᇧᇤᇧ ᇧᇥ
ೕ ೕ ೔ ೔ ೕᇧ ᇧ
௖௢௡௩௘௖௧௜௩௘ ௙௢௥௖௘௦ ௩௜௦௖௢௦௜௧௬ ௙௢௥௖௘௦ ௙௢௥௖௘௦
୲୰ୟ୬ୱ୮୭୰୲ ௗ௨௘ ୲୭ ௚ୣ୬ୣ୰ୟ୲ୣୢ ୠ୷
௣௥௘௦௦௜௢௡௦ ௧௨௥௕௨௟௘௡௖௘
തതതതത
െߩ‫ݑ‬ప ‫ݑ‬ఫ are the components of the Reynolds stress. Its expression is bellow as given by the
′ ′

Boussinesq J. (1897), hypothesis:

തതതതത
′ ′ డ௨ డ௨ೕ ଶ డ௨
െߩ‫ݑ‬ప ‫ݑ‬ఫ ൌ ߤ௧ ൬డ௫ ೔ ൅ డ௫ ൰ െ ଷ ൬ߩ݇ ൅ డ௫ ೔ ൰ ߜ௜௝ (3)
ೕ ೔ ೕ
The k- є turbulence models used by the software FLUENT [14] are:
• the k-є standard model
• the k-є RNG model
• the k-є realisable model
We are going to use the k-є realisable model to carry out calculations in the software
FLUENT. The turbulence k-є realisable model proposed by Shih and al., [15], was proposed to make
up for the insufficiency of the other k-є models such as the k- є standard model, the k-є RNG model,
etc..., by adopting a new formula for the turbulent viscosity while implicating a variable Cµ at the
origin (proposed by Reynolds) and a new equation for the disposed based on the dynamic equation of
the vortices fluctuations. The equations of its transporting equations are:
• The turbulent kinetic energy transport equation, which is given by the formula bellow.
•
ࣔ ࣔ ࣔ ࣆ ࣔ࢑
ሺ࣋࢑ሻ ൅ ࣔ࢞ ൫࣋࢑࢛࢐ ൯ ൌ ࣔ࢞ ൤ቀࣆ ൅ ࣌ ࢚ ቁ ࣔ࢞ ൨ ൅ ࡳ࢑ ൅ ࡳ࢈ െ ࣋ࢿ െ ࢅࡹ (4)
࢚ࣔ ࢏ ࢏ ࢑ ࢐
• The transport equation of the dissipation rate of turbulent kinetic energy, which is given by
the formula bellow.

ࣔ ࣔ ࣔ ࣆ ࣔࢿ ࢿ૛ ࢿ
ሺ࣋ࢿሻ ൅ ࣔ࢞ ൫࣋ࢿ࢛࢐ ൯ ൌ ࣔ࢞ ൤ቀࣆ ൅ ࣌ ࢚ ቁ ࣔ࢞ ൨ ൅ ࣋࡯૚ ࡿࢿ െ ࣋࡯૛ ࢑ା ൅ ࡯૚ࢿ ࢑ ࡯૜ࢿ (5)
࢚ࣔ ࢐ ࢐ ࢿ ࢐ √࣏ࢿ
Where:

ఎ ௞
‫ܥ‬ଵ ൌ ݉ܽ‫ ݔ‬ቂ0.43, ቃ, with, ߟ ൌ ܵ (6)
ఎାହ ఌ
Gk represent the turbulent kinetic energy due to the average gradient of velocity. Gb represent the
generation of kinetic energy due to floating. YM represent the contribution of the fluctuating
dilatation. C2 and C1ε are the constants; σk and σε are the numbers of turbulent Prandtl relative to k
and ε.
The values of constants are represented on the table 1 below.

Table 1: The constants of model
C1ε ‫ܥ‬ଶ ߪ௞ ߪఌ
1.44 1.9 1.0 1.2

10


The turbulent transport of heat is modelled by the usage of the analogy concepts of Reynolds to the
turbulent transfer. The energy equation is given as:

డ డ డ డ்
ሺߩ‫ܧ‬ሻ ൅ ሾ‫ݑ‬௜ ሺߩ‫ܧ‬ ൅ ܲሻሿ ൌ డ௫ ൬݇௘௙௙ డ௫ ൅ ‫ݑ‬௜ ൫߬௜௝ ൯௘௙௙ ൰ ൅ ܵ௛ (7)
డ௧ డ௫೔ ೕ ೕ
E is the total energy, its expression is:
మ
௉ ௎೔
‫ ܧ‬ൌ݄െఘ൅ ଶ
(8)
Keff, the coefficient of effective thermal conductivity and K, the coefficient of laminar thermal
conductivity, expressed as:
஼೛ ఓ೟
݇௘௙௙ ൌ ݇ ൅ (9)
௉௥೟
൫߬௜௝ ൯௘௙௙ is the Tension Newtonian effective of vicious stress. Its expression is given by the formula
below:

డఓ డ௨ ଶ డ௨
൫߬௜௝ ൯௘௙௙ ൌ ߤ௘௙௙ ൬ డ௫ ൅ డ௫ ೔ ൰ െ ଷ ߤ௘௙௙ డ௫೔ ߜ௜௝
ೕ
(10)
೔ ೕ ೔

II.2 Boundaries conditions
We have based our study on the experimental study of Paranthoën and al. [16],
carried out inside the air by choosing as first value of Reynolds number (Re = 15). The
figure 1 bellow shows the configuration of that experiment. The Reynolds number is
obtained from the following relation, Re = UD/ν, where D represented the cylinder
diameter, and U, the air longitudinal velocity. The value of Re, at which the vortexes
street appears is 48, and it is considered as the critical Reynolds number (Rec ). The
electric power by length unity (P/L), supply to linear source is about 10W/m, which is
corresponding to a temperature of 393K, higher than the temperature of the upstream
flow. For this threshold difference (Re - Rec), for this level of heating P/L, for these
positions inside the vortexes street (Xs + = 7 ; Ys+ = 0), and for this ratio D/d = 100, the
linear source do not modified the instability as shown in Lecordier and al.[5], d is the
linear source of heat diameter.

Figure 1: Experimental configuration of Paranthoën and al. [16].

The calculation domain is a cobbled of length 300 mm, and of height 32 mm. On this domain,
the linear source of heat is located at 14 mm behind the cylinder, at the same axis. The
principal flow is emitted longitudinally across a rectangular section of width 64 mm and of
height 32 mm. The cylinder diameter is 2 mm, and the linear source of heat diameter is 0.02
mm, which is well satisfied by the ratio D/d = 100. In this study, the sign “+” in quote,

11


indicates a normalised quantity. The heights are normalised by D and the temperature gaps
are normalised by the reference temperature gap ∆Tref. The molecular effects being negligible
in front of the turbulence, the relationship ∆T/∆Tref can be assimilated to a concentration C,
which will vary between 1 at emission and 0 at the infinity. ∆T is the difference between the
initial temperature of the principal flow and the temperature of the linear source of heat at an
instant t. The velocities are normalized by the sound velocity at 300K, when air is assimilated
as a perfect gas. This domain of calculation represented on figure 2 bellow, is meshed with
the Gambit program. It is a regular grid type with its cells in the quadrilateral form, with
185,054 cells. The principal flow is introduced longitudinally through the left of the cylinder.
Air comes out at 300 mm from the input.
a)

b) c)

Figure 2: Mesh of calculation domain:
a): Calculation domain, b): Zoom around the
cylinder wake, c): Zoom around the linear
source of heat

We have imposed the atmospheric pressure conditions at the output. The different values of
Reynolds number applied at the input are: Re = 63, 126, 252, 504, 700 and 900. The wall
cylinder temperature and the ambient temperature chosen are 300K.

III. RESULTS AND DISCUSSION
III.1 Dynamic field
The figures 3a, 3b, 3c, 3d, 3e and 3f, represented the fields of dimensionless velocities
iso-value, respectively for the following Reynolds number 63, 126, 252, 504, 700 and 900.
For a low Reynolds number (Re = 63), we observe the formations of turbulent boundaries
layers around of cylinder. Inside the cylinder wake, the velocities remains weak and the flow
is propagated progressively to the linear source of heat direction, located at the position X+ =
7. This propagation has a spherical wave form which appear in upstream and downstream

12


from this linear source of heat. When the flow velocities increase (Re = 126), the vortexes
tables appears inside the cylinder wake and becomes slightly oscillatory in downstream from
the linear source of heat, where the smalls vortexes street are beginning to appear.
For the middle velocities (Re = 252, and Re = 504), the vortexes numbers are increasing, and
these small vortexes alternated are more than more periodicals. The vortexes tables are
increasing along the longitudinal axis, showing the formation of the Bénard von-Karman
vortex street.

a) b)

c) d)

e) f)

Figure 3: Dimensionless velocities iso-values.
a) Re = 63, b): Re = 126, c): Re = 252, d): Re = 504, e): Re = 700, f): Re = 900.

When the flow velocities are increased (Re = 700 and Re = 900), the coherent structures are
becoming more than more periodicals, because of the concave angle of the boundary layer
around the cylinder walls which decreases. For Re = 700, the periodical removing model of
vortex is changing. The wake symmetry is decreasing with a production of a secondary

13


periodical removing of vortex. For Re = 900, the secondary periodical removing does not
appear again inside the vortexes twins. For these two Reynolds numbers, there is a strong
apparition of instabilities generating also an oscillatory flow which evolved as small alternate
vortexes called Bénard Von-Karman Vortex Street. The thickness of these alternate vortexes
is decreasing with their longitudinal propagation. We also noted a net adherence between the
cylinder lateral wall and the fluid, because of low values of velocities (blue color zone, U+ =
0.0625).
The figures 4a and 4b represented the longitudinal variation of dimensionless velocities (U+),
near the cylinder, respectively at the positions Y+ = -1, and Y+ = +1, for the different
Reynolds number (Re = 63, 126, 252, 504, 700 and 900). We observed a strong augmentation
of the velocity which decreased suddenly in the neared cylinder wake. This strong gradient of
velocity approved the presence of turbulent boundaries layers around the cylinder. These
profiles show that the cylinder is an obstacle which generated the instabilities in the flow
when the velocities are increasing.

a) b)

Figure 4: Dimensionless longitudinal velocity profiles : a) Y+ = -1.5, b) Y+ = +1.5.

III.2 Thermal field
The figures 5a, 5b, 5c, 5d, 5e and 5f, represented the flow thermal field, principally the area
of the linear source of heat, for the different Reynolds numbers. When the Reynolds number
is increasing, the heat propagation is decreasing. The heat reached the position (X+, Y+) =
(+9, ± 0.25), for Re = 63, while it’s reached a position less than (X+, Y+) = (+8, 0.02), for Re
= 900. This give a difference of (∆X+, ∆Y+) = (+1, 0.23), on the thickness of the thermal
field. This strongly diminution shows the incapacity of thermal field to have more resistance
when the flow becomes more than more turbulent. This means that the Reynolds numbers
increased the passive scalar dispersion in the turbulent flow (Tcheukam-Toko and al., [19]).
The figures 6 bellow represented the longitudinal temperature profiles for different Reynolds
number at a certain positions around of cylinder. Theses profiles reveals the existence of
symmetry between the temperatures evolutions with the origin axis Y+ = 0. For the low
Reynolds number (Re < 504), the temperature of linear source of heat remains higher along a
large distance, then his value decreased from the position X+ = 16, where it’s not changing,
and evolve longitudinally to his minima value. For the higher Reynolds numbers, the
temperature of linear source of heat remains weak and stays minima as from the position X+
= 18, where it’s longitudinally evolve. This shows that the passive scalar total dispersion is
developing between the position X+ = 7 (linear source of heat position), and the position X+ =
20 (from 40 mm of cylinder and from 26 mm of the linear source of heat). For the higher
Reynolds number, the longitudinal flow is predominating and the linear source of heat
remains weak.

14


a) b)

c) d)

e) f)

Figure 5: Dimensionless Temperature Iso-value.
a) Re = 63, b): Re = 126, c): Re = 252, d): Re = 504, e): Re = 700, f): Re = 900.

15


a) b)

c) d)

Figure 6: Dimensionless longitudinal temperature profiles.
a): Y+= -1, b) Y+= +1. c) Y+= -1.5, d) Y+= +1.5

III.3 Comparison of numerical and experimental results
To valid our results, we compared the dimensionless mean temperature gaps profiles
( T+), and transversal velocity – temperature correlation profiles (<v’T’>+), with the experimental
results.
The figure 7 bellow, shows that the dimensionless mean temperature gaps profiles are in
accordance with the experimental result when Re = 63. These accordance are more important for
∆X+ = 1. The figure 8 shows a similar accordance for the positions ∆X+ = 2, and ∆X+ = 4.
The figure 9 shows that the comparison of transversal velocity – temperature correlation profiles
(<v’T’>+), with experimental data, is also satisfactory.
a) b)

Figure 7: Comparison of dimensionless mean temperature gaps profiles numerical and
experimental for Re = 63. a): at ∆X+ = 1, b): at ∆X+ = 16.

16

)

Figure 8: Comparison of dimensionless mean temperature gaps profiles.
Numerical (multicolor) and Experimental (black)
umerical

Figure 9: Comparison of transversal velocity – temperature correlation profiles (<v’T’> +)
for Re = 63: numerical (multi color) and experimental (black on white).
:

Figure 10: Comparison of transversal flux of heat profiles in function of transversal gradient of mean
temperature. –v’+T’+ = f((dT/dY)+), at the position X+ = 9

17


The Richardson number is very low for our all simulations Ri << 1. This means that, the
forced convection predominated. Moreover, the dynamic perturbation and the gravity effects
are very low, because of linear source Reynolds number and Ri which are respectively less
than 1 and 10-3, as approved by Lecordier and al., [5], and Godard and al., [17]. The
calculated value of Peclet number confirmed that, the heat exchanges are only by convection
(Pe >> 1), as in the studies carried out by par Husson, [18].
Until present, the existence of counter-gradient zones was, observed in the heated flows,
showing the dissymmetry of the velocity and temperature profiles, characterized by a
minimum or a maximum (FuIachier and al. [11], Sreenivasan and al. [12], Veeravalli and
Warhaft, [2]). The counter-gradient observed when the linear source is placed on the
central line of the vortex street, shows that, the dissymmetry of the velocity and mean
temperature profiles is not his necessary condition of existence. This last is depending at
the same time, of the fluctuations form v/u, of the location of the source of heat, and of
the thickness of the linear source (Paranthoën and al., [16]). In these conditions, the heat
emitted by the source of much localized fashion, undergo a preferential convection in
these two corresponding directions. These shows the presence of a maxima, observed on
the mean temperature profiles which has a symmetry position with the central line. This
could not be the same case if the prevision density of dynamic field parameters were
Gaussian.
The counter-gradient is coming out from a simply situation where the small dimensions
of heated fluid zones (relatively at velocity field scale), are carrying preferentially in
some directions different to the principal flow. In this case, the heat flux created
downstream from a linear source and the mean temperature profiles are not still
compatible with the transit by gradient. This variation can be dissymmetric as in the
experimental works carried out by Veeravalli & Warhaft, [2], or can be symmetry as in
this present numerical work. The necessary condition is that, this variation must be
maximal for one or many values different of zero at the position of air injection.

VI. CONCLUSIONS

These results reveal that, the stability of wake zone is influenced by the behavior of
the physicals properties in function of temperature and of the geometry configuration
considered. In fact, these show that, the thermal field is strongly influenced by the vortex
street. The diffusion process seems to be in two phases connected to the filling time of
Vortexes Street. Moreover, in this case where the mean temperature profiles is generated by
the thermal transfer; we could rather name these counter-gradient zones by “counter-flux
mean temperature profiles”. The different comparisons makes between the numerical and
experimental profiles are satisfactory, but the difference observed, is located at the maximal
level. In perspectives, it would be interesting to associate the heated air jets to this present
study, in order to analyze their influence on the stability of thermal and dynamic fields.

ACKNOWLEDGEMENT

The authors acknowledge the CORIA UMR 6614 CNRS University of Rouen-France,
and The University of Ngaoundere, Cameroon.

18


NOMENCLATURE
Small letters
x longitudinal coordinate (m)
y vertical coordinates (m)

Capital letters
D Cylinder diameter (m)
d source of hat diameter (m)
P Pressure (Pa)
T Temperature (K)
u,v velocities components (m/s)
∆Tréf Temperature difference between heat source and the ambient domain (K)
0x longitudinal axis
0y vertical axis

Greek symbols
ν Kinetic viscosity of air (m2.s-1)
ߤ Dynamic viscosity of air (Pa.s)
ߝ Dissipation ratio of the turbulent kinetic energy
K Turbulent kinetic energy (J.kg-1)
ߩ Volume mass (m3.s-1)

No Dimensional numbers
Re Reynolds number
ܲ‫ݎ‬௧ Turbulent Prandtl number
Res Reynolds number of the linear source
Grs Grashof number of the heat linear source
Gr Grashof number
σk and σε Turbulent Prandtl number relative to k and ߝ

Exponents, indices and specials characters
+ Dimensionless values (with D for the lengths) and (with ∆Tréf for the Temperatures)
Cp Thermal capacity at constant pressure
ߤ௧ Turbulent viscosity
‫ܭ‬ Thermal conductivity
‫ܭ‬௘௙௙ Effective thermal conductivity
൫߬௜௝ ൯ Effective Newtonians tensor of viscous constraints
௘௙௙
x relative to the longitudinal component
y relative to the vertical component
eff effective
ܵ௜௝ Stress ratio of mean Tensor
ߤ௧ Turbulent kinematic viscosity
‫ܦ‬௧ Turbulent dynamic viscosity
ߥ௥௘௙ Referenciel turbulent dynamic viscosity
σij Stress tensor

19


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20


[20] Ashok Tukaram Pise and Umesh Vandeorao Awasarmol, “Investigation Of
Enhancement Of Natural Convection Heat Transfer From Engine Cylinder With Permeable
Fins” International Journal of Mechanical Engineering & Technology (IJMET), Volume1,
Issue1, 2010, pp. 238 - 247, Published by IAEME
[21] Cherian Paul and Parvathy Venugopal, “Modelling Of Interfacial Heat Transfer
Coefficient And Experimental Verification For Gravity Die Casting Of Aluminium Alloys”
International Journal of Mechanical Engineering & Technology (IJMET), Volume1, Issue1,
2010, pp. 253 - 274, Published by IAEME
[22] Kavitha T , Rajendran A , Durairajan A and Shanmugam A, “Heat Transfer
Enhancement Using Nano Fluids And Innovative Methods - An Overview” International
Journal of Mechanical Engineering & Technology (IJMET), Volume3, Issue 2, 2012,
pp. 769 - 782, Published by IAEME
[23] Er. Pardeep Kumar, Manoj Sain and Shweta Tripathi, “Enhancement Of Heat Transfer
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[24] Sunil Jamra, Pravin Kumar Singh and Pankaj Dubey, “Experimental Analysis Of Heat
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Journal of Mechanical Engineering & Technology (IJMET), Volume3, Issue 3, 2012,
pp. 306 - 314, Published by IAEME
[25] Manikandapirapu P.K, Srinivasa G.R, Sudhakar K.G and Madhu D., “Comparative
Analysis Of Pressure Measurements In Ducted Axial Fan” International Journal of
Mechanical Engineering & Technology (IJMET), Volume3, Issue 2, 2012, pp. 85 - 91,
Published by IAEME
[26] Ashok Tukaram Pise and Umesh Vandeorao Awasarmol, “Investigation Of
Enhancement Of Natural Convection Heat Transfer From Engine Cylinder With Permeable
Fins” International Journal of Mechanical Engineering & Technology (IJMET), Volume1,
Issue1, 2010, pp. 238 - 247, Published by IAEME

21

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