Computational Analysis of Heat sink or Extended Surface

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072
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Computational Analysis of Heat sink or Extended Surface
Kamlesh Kumar Sinha1, Pankaj Ahirwar2
1Mechanical Engineering Department, RCET Raipur C.G. India
2Assistant Professor , Department of Mechanical Engineering, RCET Raipur, C.G. India
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Abstract—This paper focuses on comparative natural
convection of an heat sink with vertical and horizontal
configuration. The heat transfer characteristics has been
examined and compared and the obtained results from
finite element approach. The governing equation of heat
sink are solved and simulated by using FEV tool namely
ANSYS Fluent where parametric analysishasbeen carried
out in which effect of various number of fin configuration
has been studied. The validation of heat transfer
characteristics has been done with previous published
work and the results are within acceptable range.
Key Words: Heat Sink, CFD, Heat Transfer.
INTRODUCTION
In the present era, the trend to design electronic products
becomes thinner, lighter, shorter, & smaller. Due to the
actuality that shrinking in the dimension of these electronic
components will consequence in a drastic increase in the
heat generation rate when evaluating with previous
products. For this reason, an efficient cooling system to
remove the high heatgenerationandconsequentlymaintains
the reliability and stability oftheproducts,havegainedmuch
attention.
The heat sink component is the most common heat
exchanger for CPUs and has been extensively exercised in
order to provide cooling utility for electronic components.
The conventional heat sink module utilized the natural as
well as forced convection cooling technique; dissipate heat
from CPUs to the ambient air. The combination of the heat
sink and fan design usually involvedinthisforcedconvection
cooling technique.
Literature Survey
Emrana and Islama 2014 performed a three-dimensional
numerical simulation is in order to investigate the flow
dynamics and heat transfer characteristicsina microchannel
heat sink. A commercial CFD code was employing with finite
element method to numerical simulation.Fortheaccuracyof
results Mesh independence test was performed.
Mehran al. 2014 examines numerically and
experimentally, Steady-state external natural convection
heat transfer from vertically-mounted rectangular
interrupted fins. FLUENT software is employed to develop a
2-D numerical model of fin interruption effects. An
experimental numerical parametric study was performedto
investigate the effects of finspacing,andfindisruption.Anew
compact correlation is proposed for calculatingtheoptimum
interruption length.
Qarnia and Lakhal 2013 using numercail approach
investigate the heattransfer bynatural convectionduring the
melting of a phase change material. A mathematical model
was developed to investigate the thermal performance of
PCM based-heat sink.
Farhad et al.2013solve .Navier–StokesequationsandRNG
based k- turbulent model for array of solid and perforated
fins mounted in vertical flat plates used to predict turbulent
flow parameters. Flow and heat transfer features are
presented for Re. no. from 2×104 - 3.9 × 104.Prandtl
numbers was taken as 0.71. Numerical simulation is
validated by compare with experimental results.
Mateusz al.2013 used water and copper oxide nano fluids
for cooling heat sink of PC Processor. The commercial
package ANSYS Fluent 13 was employed to generate a CFD
heat transfer simulation.The experimental resultswereused
to validate the numerical model of the analyzed system.
Ayla dogan et al. 2012 perform numerical investigation to
find out the natural convection heattransferfromanannular
fin on a horizontal cylinder and present correlation for the
optimum fin spacing depending on Rayleigh number and fin
diameter.
Fahiminia et al. 2011investigate the laminar natural
convection on vertical surfaces computationally. The CFD
simulations are carried out using fluent software. Governing
equations are solvedusinga finitevolumeapproach.Relation
between the velocity and pressure is made with SIMPLE
algorithm
Cheng-Hung al. 2011 develops a three-dimensional heat
sink design to estimate the optimum design variables.
Levenberg–Marquardt Method (LMM) was used and
commercial code CFD-ACE+ was developed. Temperature
distributions are dignified by using thermal camera for the
optimal heat sink modulesandresultsarecomparedwiththe
numerical solutions to validate the design
Mahmoud et al. 2011 conduct anexperimenttoinvestigate
the effects of micro fin height and spacing on heat transfer
coefficient for a horizontallymountedheatsink understeady
state natural convection conditions, fin height ranging from
0.25-1.0 mm and fin spacing from 0.5 to 1.0 mm was taken.
C.J. Kobus, T. Oshio 2005 investigate the the effect of
thermal radiation on the thermal performance of heat sink

having pin fin array by theoretical and experimental
approach. In order to investigate the ability of influence of
thermal radiation on the thermal performance a new
coefficient effective radiation heat transfer is collaborated.
For validation of theoretical model it is matched with
experimental data.
Hung-Yi Li et al. 2007 donethereinvestigationon plate-fin
heat sinks by numerically and experimental. Impingement
cooling is used by amending, the Reynolds number (Re), the
impingement distance(Y/D), and the fin dimensions. The
results appearance that heat transfer is enhance by the heat
sink with increasing the impinging Reynolds number
G. Hetsroni et al. 2008, Natural convection heat transferin
metal foam strips with two porosities examined
experimentaly. Image processing of the thermal maps was
used to evaluation of non-equilibrium temperature
distribution for surface along with inner area of the metal
foam. Augmentation in heat transfer at natural convection
was found 18–20 times with respect to the flat plate.
Goshayeshi and Ampofo 2009 conduct numerical studies
on vertical fins, attached with the surface.Natural convective
heat transfer find out from heated plane which is kept into
air with horizontal and vertical surface. Results show that
vertical plate with dimensionless form delivers best
performance for the natural cooling.
Dong-Kwon Kimet al. (2009) compared the thermal
performances of two types of heat sinks i.e.: plate-finandthe
second is pin-fin. By their investigation results theypropose,
a volume averaging approachbasedmodel for envisaging the
pressure drop and the thermal resistance.
Burak and Hafit 2009 developed expressionforprediction
of the optimal fin spacing for vertical rectangular fins with
rectangular base. The correlation for predicted on the basis
of experimental data.
Li and Chao 2009 investigate the performance of plate-fin
heat sinks with cross flow. The effect of different parameters
like the fin width, fin height, Re. number of cooling air on the
thermal resistance and the pressure drop of heat sinks were
studied.
Naidu et al.2010 investigates by both experimentally and
theoretically to find the outcome of inclination of the base of
the fin array on heat transfer rate.
Sable et al. 2010 investigate the natural convection of a
vertical heated plate with a multiple v- type fins having
ambient air surrounding. The mica gladded Nichrome
element is inserted between two base plates.
Younghwan and Kim 2015investigateanalyticallythermal
performance of optimized plate-fin and pin-fin heat sinks
with a vertically oriented base plate. A new correlationofthe
heat transfer coefficient is proposed and validated
experimentally to optimize pin-fin heat sinks.
Mathematical Modelling
The governing equations for heat sink this problem are
those of Navier-Stokes along with the energy equation. The
Navier-Stokes equations are applied toincompressibleflows
and Newtonian fluids, including the continuity equation and
the equations of conservation of momentum on the x and y
According to equations
2 1 1
1 2
1 2
2 2
1 1
2 2
2 1 2
1
( )
u u u
u u
t x x
u u
g T T
x x x

 

  
  
  
   
      
   
1
* *
2
* *
1 2
0
u u
x x
 
 
 
x1 momentum equation
1
* * * * *
* *1 1 1 1 1
1 2* * * * *
1 2 1 2
*
Pr
*
u u u u up
u u
t x x x x x
     
      
      
x2 momentum equation
1
2
** * * *
* *2 2 2 2
1 2* * * * *
1 2 1 2
2
*
Pr
*
Pr *
uu u u up
u u
t x x x x x
Gr T
     
      
      

Energy equation
* * * 2 * 2 *
* *
1 2* * *2 *2
1 2 1 2*
T T T T T
u u
t x x x x
     
         
Where Gr is the Grashof number given as
3
2
g TL
Gr




Often, another non-dimensional number called the
Rayleigh number is used in the calculations. This is given as
3
Pr
g TL
Ra Gr



  hl
Nu
k

Methodology
The ANSYS 14.5 finite element program was used natural
convection in differentially heated enclosures. For this
purpose, the key points were first created and then line
segments were formed. The lines were combined to create a
surface. Finally, this surface is provided thickness model is
made. We modelled 6 different geometrical configurationsof

the heat sink with different number of fin and spacing
configuration. The heat sink was discretized into 21788
elements with 44520 nodes. Heat sink boundary conditions
can also be (provided in the mesh section through naming
the portion of modeled sink i.e Base, Base Top, Fins, Interior.
20 Fins
13 Fins
8 Fins
7 Fins
4 Fins
5 Fins
Figure 1 Geometrical and Mesh Model

Table 1 the boundary Condition of Heat Sink
Boundary Condition Value
Heat Sink Base Temperature, K
350, 375,
400, 430
Ambient Temperature, K 300
kinematic viscosity, ν(m2/s) 1.81E-05
Thermal Conductivity, k(w/mK) 0.02816
Dynamic viscosity, μ(kg/ms) 1.96E-05
Specific heat capacity, Cp(j/kgK) 1006.3
Prandtl Number, Pr 0.701122
Coefficient of Thermal Expansion, β 0.003077
Density, ρ 1.086
Diffusivity, α 2.56E-05
Density Module
Boussinesq
Model
Results and Discussion
Validation
The governing equations of the problem were solved,
numerically, using a Element method, and finite Volume
method (FVM) usedinorder tocalculatetheThermodynamic
characteristics of a Heat sink. As a result of a grid
independence study, a grid size of 105 was found to model
accurately the Thermodynamic performance characteristics
are described in the corresponding results. The accuracy of
the computational model was verified by comparing results
from the present study with those obtained by Fahiminia
[10], Goshayeshi [6], Analytical and FVM results.
Table 2 Grid Independence Test at ΔT=130K for different Heat sink
configuration
Total Convective Heat Transfer in (W)
Number of Fin and Fin
Spacing in mm
Mesh
Element
Present
(FEV)
20, 2.1mm
44520 29.57845
36520 29.56967
16640 29.42761
13, 3.9mm
43750 47.35242
31752 47.34912
11328 47.21461
4, 18.6mm
12636 30.51392
10528 30.50927
4416 30.48760
Table 3 Comparative Optimum Fin Spacing at different Temperature
Gradient
Temperature
difference (ΔT)
Optimum Fin Spacing in (mm)
Ref.[10] Present (FEV)
50 6.42 6.40
75 6.19 6.15
100 6.04 6.00
130 5.84 5.50
Figure 2 Variation of convective rate with base-to-ambient temperature
difference at H = 29.2 mm and L = 80 mm Ref. [10]
In table 2 shows the Grid independence result of FVM
result obtained from the ANSYS tool.Ithasbeenseenthatthe
obtained result for different mesh element shows good
convergence for difrrent number of fins and fin spacing.
figure 2 and 3 shows the Comparative Optimum Fin
Spacing at different Temperature difference. It has been
observed that the obtained result shows the same trend so
that the results are suitably verified and the minute
variation in result is due to grid sizing, operating condition,
geometrica paramters, etc.

Figure 3 Variation of convective rate with base-to-ambient temperature
difference at H = 29.2 mm and L = 80 mm
Figure 4 Natural convection heat transfer coefficients for different heat
sinks Ref. [10]
Figure 5 Variation of Convective heat transfer coefficient for different fin
Spacing
Figure 5 shows the Variation of Convective heat transfer
coefficient for different fin Spacing. It hasbeenobservedthat
on increasing fin spacing as well as temperature gradient
convective heat transfer coefficient remarkably increases.
This is due to mixing of the boundary layer occurs (the fills
up with warm air). However, the obtainedresultsshowsame
trends with the available literature Fahiminia [10] and form
the figure 6.3 also.
Therefore, from this it can be concluded that at high
temperature difference between base-to-ambient, leads to
higher rates of convective heat transfer coefficient.
Figure 6Variation of Nusselt Number for different fin spacing
Figure 6 shows the variation of Nusselt Number for
different fin spacing. It has been observed that on increasing
fin spacing nusselt number noteworthy increases and
monotonous at lower temperature difference. Therefore,
widely spaced fins have higher heat transfer coefficient but
smaller surface area.
A Case study has been considered in which a heat sink
with vertical as well horizontal configuration show in figure
7 is simulated at same boundary condition and it has been
observed that Vertical plate with vertical fins gives the best
performance for natural cooling in comparison with a
horizontal one this is due to air enters the channel from the
lower end, rises as it is heated under the effect of buoyancy,
and the heated fluid leaves the channel from the upper end,
however this effect can be visualized from the figure 8 to 11
in which closely packed and widely spaced fin are simulated
for different temperature difference.And theconvectiveheat
transfer is significant for vertical configuration at higher
temperature difference which is clear from figure 12

Figure 13 Variation of Nusselt Number in vertical Configuration for
different Temperature Gradient
Figure 13 illustrate the Variation of Nusselt number in
Vertical configuration for different Temperature Gradient. It
has observed that on increasing Temperature difference
(Gradient) nusselt number significantly increases and it is
monotonous at lower number of fins. This is due to
significant spacing between the fins which yields high
convective coefficient at high temperature gradient.
Figure 14 Variation of Nusselt Number in Horizontal Configuration for
different Temperature Gradient
Figure14 illustrate the Variation of Nusselt number in
Horizontal configurationfor differentTemperatureGradient.
It has been observed that the graph shows same trend for
Horizontal one but in lower limit as compared with vertical
configuration. From it can be conclude that convective
coefficient is a strong function of nusselt number.
Conclusion
For Optimization and analysis of a heat sink following
conclusion has been drawn which significantly affects the
performance of heat sink
On increasing fin spacing convective heat transfer first
increases up to optimum spacing and then starts decreasing.
This is due to higher heat transfer coefficient but lesser
surface area.
As temperature difference increases convective heat
transfer coefficient increases noteworthy.
Widely spaced heat have high heat transfer coefficient at
corresponding higher temperature difference.
Vertical configuration heatsink hasbetterperformanceon
comparison with horizontal one.
Nusselt number linearly increases has temperature
difference increases.
Increasing fin spacing Nusselt number increases
Convective heat transfer coefficient is a strong function of
nusselt number.
At a specified temperature difference and fin height, the
convective heat transfer rate increases with increasing fin
spacing till it reaches optimum spacingandthenwithfurther
increasing fin spacing heat transfer rate decreases.

Figure 7 Fin configurations for natural (Free) cooling
Figure 8 Variation of temperature contour of the heat sink s=8.8 and ΔT=50

Figure 11 Variation of temperature contour of the heat sink s=8.8 and ΔT=75
Figure 12 Variation of temperature contour of the heat sink 20 Fins and ΔT=130

On increasing fin height by employing longer fins, but
with a fixed volumetric flow rate performance may
actually decrease with fin height.
REFERENCES
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characteristics of staggered vertical pin fin array heat sinks under
combined mode radiation and mixed convection with impinging
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2696
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sinks under confinedimpingingjetconditions”InternationalJournalof
Heat and Mass Transfer 50 (2007) 1963–1970
[3] G. Hetsroni, M. Gurevich, R. Rozenblit, “Natural convection in metal
foam strips with internal heat generation” Experimental Thermal and
Fluid Science 32 (2008) 1740–1747
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a Vertical and Horizontal Surfaces Using Vertical Fins”Energy and
Power Engineering, 2009, 85-89
[5] BurakYAZICIOĞLUandHafitYÜNCÜ,”ACORRELATIONFOROPTIMUM
FIN SPACING OF VERTICALLY-BASED RECTANGULAR FIN ARRAYS
SUBJECTED TO NATURAL CONVECTION HEAT TRANSFER”Isı
BilimiveTekniği Dergisi, 29, 1, 99-105, 2009 J. of Thermal Science and
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fin heat sinks withcross flow cooling”InternationalJournalofHeatand
Mass Transfer 52 (2009) 2949–2955
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(2009) 3510–3517
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Nomenclature
g Acceleration due to gravity, m
s−2
k Thermal conductivity, W m−1
K−1
L Side of the Wall, m
N Normal direction on a wall
Nu Local Nusselt number
P Dimensionless fluid pressure
Pr Prandtl number
Ra Rayleigh number
Re Reynolds number
Gr Grashof number
T Fluid temperature, K
u x component of velocity
U x component of dimensionless
velocity
v y component of velocity
V y component of dimensionless
velocity
X Dimensionless distance along
x coordinate
Y Dimensionless distance along
y coordinate
τ stress
τp non-dimensional ramp time
ε Emissivity

z AxialCoordinate
Greek Symbols
α Thermal diffusivity, m2 / s
β Thermal expansion coefficient
at constant pressure, K−1
ρ Density, kg m−3
cp Specific heat coefficient
cv Specific heat coefficient
Λ Thermal Conductivity
φ Angle

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