Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
1
Paper ID TSF1009
Predicting the thermal performance characteristics of elliptical pin fin heat
sinks under combined natural and forced convection
P. A. Deshmukh
1,*, R. M. Warkhedkar
2
1Assistant Professor, JSPM’s Rajarshi Shahu College of Engineering, Pune (MS), India, 411 033.
2 Associate Professor, Government Engineering College, Karad (MS), India, 415 110.
*Corresponding Author: [email protected], +9120-22934344, +9120-22934084 Abstract
A comprehensive analytical and numerical study is carried out for predicting the thermal
performance of elliptical pin fin heat sink. An analytical model is formulated having capability of
predicting influence of various geometrical, thermal and flow parameters on the thermal resistance of the
heat sink. An experimental technique is developed for measuring the thermal performance of the heat sink
and the overall heat transfer coefficient for the fin bundle. Numerical simulations are carried out for wide
range of geometrical, thermal and flow parameters for pure natural convection and for combined natural
and force convection. The predictive capability of the analytical model is verified by comparison with
simulation data.
Symbol Illustration
a Major axis of elliptical pin fin, mm
b Minor axis of elliptical pin fin, mm
W Width of base plate, mm
L Length of base plate, mm
tb Thickness of base plate, mm
ST Transverse pitch, mm
SL Longitudinal pitch, mm
H Height of pin fin, mm
U∞ Approach velocity, m/s
Tb Surface temperature of pin fin, oC
Tfi Inlet temperature, oC
Tfo Outlet temperature, oC
q Heat flux, W/m2
Re Reynolds Number
Pr Prandtl Number
Gr Grashoff Number
Nu Nusselt Number
α Void Fraction
ϒ Aspect Ratio
1. Introduction
The continuing increase of power densities in
microelectronics and the simultaneous drive to
reduce the size and weight of electronic products
have led to the increased importance of thermal
management issues in this industry. The
temperature at the junction of an electronics
package (chip temperature) has become the
limiting factor determining the lifetime of the
package. The process industries and electronic
industries are taking great amount of efforts over
the years to reduce the size of the devices.
Advanced thermal architectures are required to
meet the future requirements of cooling.
The most common method for cooling
packages is the use of aluminum pin-fin heat
sinks. These heat sinks provide a large surface
area for the dissipation of heat and effectively
reduce the thermal resistance of the package.
They often take less space and contribute less to
the weight and cost of the product. For these
reasons, they are widely used in applications
where heat loads are substantial and/or space is
limited. The overall performance of a pin-fin heat
sink depends on a number of parameters
including the dimensions of the base plate and
pin-fins, thermal joint resistance, location and
concentration of heat sources. These parameters
make the optimal design of a heat sink very
difficult. Traditionally, the performance of heat
sinks is measured experimentally or numerically
and the results are made available in the form of
design graphs in heat sink catalogues. Analytical
and empirical models for the fluid friction and
heat transfer coefficients are used to determine
optimal heat sink design [1]. Several studies are
observed dealing with parametric analysis of heat
sinks with square or circular pin profile. Tahat et
al. [2] has carried out experimental investigation
for heat transfer and pressure drop across
shrouded circular pin fin heat sink arrays
experiencing forced convection. The heat transfer
performance of low aspect ratio pin fin was
investigated experimentally by Lyall et al.[3].
The analytical study of heat transfer and pressure
drop was carried out by Khan et al.[4, 6] with the
help of boundary layer analysis for pin fin heat
sinks experiencing forced convection. In this
study, they had compared circular, plate and
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
2
Paper ID TSF1009
elliptical profiles for enhancement of heat
transfer. Forced convective experimental
investigations for inline and staggered
arrangement of square pin fin heat sink are
reported by Tzer-Mink Jeng et al.[5]. All the
above literature cited is dealing with either
experimental or analytical studies on heat sink
experiencing forced convection.
Very few studies are observed dealing with
mixed convection cooling. Ghosh et al. [7]
analyzed the mixed convection with a classical
approach along the semi-infinite vertical flat plate
by using boundary layer analysis. The effect of
fin density on heat transfer and fluid flow at low
Reynolds number as studied experimentally by
Selvarasu [8]. A comprehensive review of natural
and mixed convection models for electronic
applications was taken by Teertstra [9]. Mixed
convection air cooling of electronic components
is studied numerically by Hamouche [10]. Mixed
convection air cooling in electronic applications
with impinging flow are experimentally
investigated by Bhopte [11] and Kobus [12,13].
Both of these investigations are carried out for
circular pin fin heat sink resulting into a
parametric analysis.
According to the above literature review, no
attempt has been made so far to tackle the
problem of combined natural and forced
convection heat transfer from elliptical pin fin
heat sink either theoretically or experimentally.
The purpose of this work is to formulate a simple
theoretical model capable of predicting the
thermal performance characteristics of a pin fin
heat sink with elliptical profile under combined
natural and forced convection conditions, in terms
of various design parameters. Further, to develop
an experiential measurement technique that can
be used to indirectly measure the effective
thermal resistance of the heat sink and the
average convective heat transfer coefficient for
the fin array. The value of the simple model,
coupled with the heat transfer correlations for the
fin array, will be its ability to provide design
insight; including the existence of optimum fin
spacing.
2. Formulation of a theoretical model
A theoretical model for predicting the thermal
performance of a pin-fin array heat sink is
formulated by considering the heat sink to be
made up of a number of individual pin-fins
operating in parallel.
2.1 Assumptions:
This study assumes the following design
considerations:
1. Each pin is of uniform cross section and
height, H, with elliptical cross section.
2. The fin tips are adiabatic.
3. There is no airflow bypass, i.e. the heat
sink is fully ducted.
4. The airflow is normal to the pin-axis.
5. The approach velocity is uniform for each
row in a heat sink.
6. Flow is steady, laminar.
7. Radiation heat transfer is negligible.
8. There is no slip at the base plate and the
fin surface.
2.2 Mass Constraints
The shape of the elliptical pin fin is selected in
such a way that the mass of the elliptical and
circular fin is same. Assuming the material and
volume same for both the fins:
(a) (b)
Fig. 1 (a) Circular pin, (b) Elliptical pin
√ (1)
Equation (1) represents the equivalent diameter of
elliptical pin fin.
The aspect ratio (ϒ) and axis ratio (ϵ) for the
elliptical pin fin can be defined as:
(2)
Elliptical pins provide more general geometrical
configuration than circular pins. In the limiting
cases, they represent a horizontal plate fin
when , and a circular pin fin when .
Thus a systematic analytical investigation of
elliptical geometries can provide not only heat
transfer characteristics from elliptical fins but
also from circular fins and finite plate fins.
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
3
Paper ID TSF1009
2.3 Theoretical Model
The well-known one-dimensional differential
equation governing the temperature distribution
for such a fin, covered in most introductory heat
transfer textbooks [1-2], is given by:
(
) ( ) (3)
(4)
where
√
(5)
The boundary conditions are,
and
(6)
Fig. 2 Single elliptical pin fin in an infinite flow
Solving the resulting differential equation,
subjected to appropriate boundary conditions,
yields the axial temperature distribution in the
representative fin as represented in “Eq. (7)”.
(7)
Using this temperature distribution, along
with Fourier model for conduction, the rate of
heat transfer from a single elliptical pin fin, ,
can be modeled as,
( ) (8)
Also in terms of the convective heat
transfer coefficient, the rate of heat transfer from
the part of heat sink base not occupied by fins,
can be expressed as,
(9)
where
Therefore, the total rate of heat transfer from
the heat sink, , which contains n fins, can be
expressed as,
(10)
Using “Eqs. (8)-(10)”, the effective thermal
resistance of the heat sink, , can be modeled
as ,
(11)
( ) ( ) (12)
(13)
Further “Eq. (13)” can be modified in least
number of parameters by considerable algebraic
manipulations as,
√ (14)
(√ ) (15)
where
is the efficiency of each pin
fin assuming negligible tip heat loss.
(16)
(17)
where
, is an important parameter
coefficient for a fin bundle and can be called as
the fin bundle void fraction. The void fraction, ,
of a fin bundle is that fraction of a cross sectional
area of the fin bundle that is occupied by air.
(a) Inline (b) Staggered
Fig. 3 Schematics of elliptical pin fin array.
The fin bundle void fraction, , in terms of
longitudinal pitch, SL, and transverse pitch, ST,
can be defined as,
.
“Eq. (17)” represents a theoretical model for
predicting the effective thermal resistance of heat
sink, , in terms of area of fin heat sink
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
4
Paper ID TSF1009
base, , fin bundle void fraction, , number of
pin fins, n, efficiency of pin fin, , perimeter of
pin fin, P, height of pin fin, H, and the
convective heat transfer coefficient, h, between
the fins and flowing air. It is assumed in this
model that the convective heat transfer coefficient,
h, is the same for each fin and also for the base.
All the above physical and thermal parameters
are readily available, except one. The exception
being the convective heat transfer coefficient, h.
The convective heat transfer coefficient is the
result of a combination of a number of complex
physical mechanisms involving fin geometry, fin
spacing, free stream air velocity and direction,
buoyancy forces, fluid properties and the bundle
effect. The complexity of the physical mechanism
governing this particular parameter is such that
they can only partially be modeled. Therefore in
order to determine the required convective heat
transfer coefficient, h, there will be the need for
indirect measurement.
2.4 Indirect measurement of convective heat
transfer coefficient
In order to experimentally measure the
thermal performance of the finned heat sink, it is
essential that the rate of heat transfer between the
heat sink and the flowing air be accurately
measured. Also it should serve for indirect
measurement of convective heat transfer
coefficient, h, between the fins and flowing air.
Fig. 4 Schematic representation of experimental
set up with assisting flow
“Fig. 4” is representing the schematic of
experimental set up. It is divided in three different
sections namely:
1. Wind tunnel,
2. Test section,
3. Measurement and Control panel section
The main body of the rectangular cross-
section wind tunnel duct is manufactured from
wooden sheet and is 2 m high with a constant
internal width of 180 mm. However, the depth of
the duct, and hence the duct’s cross-sectional area,
can be varied by means of adjustable shroud.
Approximately half-way along the height of
the wind tunnel duct is the test section. A
transparent polycarbonate enclosure is used to
enable the pin fin array. Air straightener with
proper meshing is chosen to straighten the air.
The air with controlled velocity and properly
straightened is then passed on test section. Air
velocities are measured with Lutron make AM-
4204 hot wire anemometer. The test section
consists of aluminum elliptical pin fin heat sink.
Pin fins are mounted on the square base plate of
164 mm x 164 mm with 12 mm thickness. Each
elliptical pin fin has 12 mm major axis and 8 mm
minor axis.
The base of the heat sink is heated by a patch
heater with 400 W electrical-resistor strips as the
main heater. The assembly was firmly bolted
together to the bottom surface of the square base.
The lower horizontal surface and the sides of
main heater block are insulated thermally with 50
mm mineral wool blanket. A horizontal guard
heater, rated at 50 W, is positioned parallel to the
main heater, below the mineral wool blanket,
with yet another 20 mm thick layer of mineral
wool placed below it. The whole system of heat
sink base, main and guard heaters, with
associated thermal insulation, is located in a well
fitting open topped asbestos sheet box lined with
wooden sheets. Patch heater is sandwiched
between the base plate and supporting aluminum
plate. The thickness and bottom side of heater
arrangement is completely insulated by using
asbestos sheet insulation to avoid the heat loss.
The power supplied to the main heater could be
adjusted by altering the Variac setting and can be
measured by an in-line voltmeter and ammeter.
The heat input to the guard heater is to be
adjusted until the steady state temperature
difference, across the layer of insulant,
sandwiched between two heaters, is zero. Then,
in all test conditions employed, more than 98% of
the heat generated in the main heater, dissipated
to the air of the surrounding environment,
through the pin fin heat sink. The similar kind of
arrangement of heater assembly was used by
Tahat [2].
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
5
Paper ID TSF1009
The steady state temperature at the base of the
fin array is to be measured by an appropriately
distributed set of five J-type (Iron-Constantan)
thermo-junctions, embedded within the base.
Each thermo junction is screwed in position, so
as to ensure a good thermal contact. The average
value obtained from this thermo-junction is
regarded as the mean overall base temperature.
The inlet and outlet air stream temperatures
across the test section in the wind tunnel are to be
measured by eight thermo-junctions: four are
located immediacy prior to the entrance to the pin
fin assembly and another four just downstream of
the array. All the thermocouples are connected to
the digital temperature indicator through a banana
socket. At a half hourly interval, observations are
to be recorded. When consecutive values are
identical, it is assumed that steady state
conditions are attained.
It is highly desirable to be able to indirectly
obtain an accurate measurement of the rate of
heat transfer from the heat sink to the flowing air,
by simply measuring the electrical power input to
the patch heater assuming a negligible heat loss
off the back side and the edges of the patch heater
assembly.
In order to verify the reliability of this
measurement technique, the independent
measurement of both the electrical power input to
the patch heater, P, and the actual rate of heat
transfer, Q, to the air by the heat sink are done.
The actual rate of heat transfer, Q, to the air by
the heat sink is done by doing the energy balance
on the air as it flows past the heat sink as,
(18)
The mass flow rate, , based on mean flow
velocity, ∞, of air in wind tunnel is defined as:
∞ (19)
Where
(20)
For
,
expression for specific heat of air at atmospheric
pressure [2] is,
[ (
)]
(21)
Due to some heat loss in polycarbonate
enclosure and in heater assembly, the Q value
will be slightly less than P value. The importance
of verifying this is that it provides confidence that
the power input, P, to the main heater is, for all
practical purposes, equal to the rate of heat
transfer, Qs, from the finned heat sink to the
flowing air; thus confirming the reliability the
proposed measurement technique.
After considerable algebraic manipulation,
“Eq. (17)” can be expressed as:
(22)
By using “Eqs. (18) and (22)”, the equation
for indirect measurement of the heat transfer
coefficient, h, can be expressed as:
(23)
The model in “Eq. (23)” provides a means for
indirectly measuring the convective heat transfer
coefficient, h, as a function of air velocity, .
It is recognized that because the fin
efficiency, , also involves the convective heat
transfer coefficient, h, an iteration scheme must
be used to solve for h for each experimental data
point, and therefore for each different air
velocity,
3. Design of experiment
“Eq. (17)” represents a theoretical model for
predicting the effective thermal resistance of heat
sink, , in terms of area of fin heat sink
base, , fin bundle void fraction, , number of
pin fins, n, efficiency of pin fin, , perimeter of
pin fin, P, height of pin fin, H, and the
convective heat transfer coefficient, h, between
the fins and flowing air. It is assumed in this
model that the convective heat transfer coefficient,
h, is the same for each fin and also for the base.
For doing the experimental investigation to
evaluate the performance of elliptical pin fin heat
sink in terms of thermal resistance, the
parameters like longitudinal pitch, SL, transverse
pitch, ST, fin bundle void fraction, α and aspect
ratio, ϒ, defined as H/D need to be varied in some
specific interval along with the approach velocity,
U∞.
A change in diameter has relatively little
influence on the effective thermal resistance for
the air velocities in the mixed convection region.
For very less velocities where natural convection
starts to dominate the heat transfer mechanism, a
25% change in diameter has 6% change in
thermal performance [12, 13]. The fin height has
a significant effect on air side performance of
heat sink [14-16] with a limitation on aspect ratio.
Too short fin can’t be modeled with adiabatic tip
which may lead to poor performance and
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
6
Paper ID TSF1009
overheating of sink surface. Too long fins will
have to compromise upon the fin efficiency since
fin efficiency is the strong function of fin height.
Therefore, the variation in aspect ratio will be
done by varying the height of the pin fin with fin
efficiency close to 90%.
The parameters like longitudinal pitch, SL,
transverse pitch, ST and fin bundle void fraction, α,
has a strong effect on the pin density. Too wide
spacing in longitudinal and transverse directions
will lead to less dense structure resulting in less
number of pins on base plate which may have
poor effect on air side performance. The selection
and variation in approach velocity is the most
critical parameter in view of the current study of
mixed convection. A careful selection of velocity
and its variation should result in providing room
for both natural convection and forced convection.
The mixed convection parameter, Gr/Re2, should
be in the range of 0.1< Gr/Re2 <10 so that neither
natural convection nor the forced convection will
dominate the flow field.
For selection and variation of the parameters
like longitudinal pitch, SL, transverse pitch, ST, fin
bundle void fraction, α, aspect ratio, ϒ, and
approach velocity, U∞, the Taguchi [3] method of
an orthogonal array is used with five levels of
parameters as represented in Table. 1.
Table. 1 Parameters selected for analysis.
Levels
Aspect
Ratio ϒ
Approach
Velocity U∞ (m/s)
Void Fraction
α
Heat Flux
q
(W/m2)
1 5.1 0.1 0.534 2000
2 6.12 0.2 0.702 2500
3 7.14 0.3 0.793 3000
4 8.16 0.4 0.848 3500
5 9.18 0.5 0.884 4000
The corresponding values of longitudinal pitch, SL,
and transverse pitch, ST, for the resulting fin
bundle void fraction, α, are represented in Table.
2.
Table. 2 Longitudinal Pitch
SL (mm) Transverse Pitch
ST (mm) Void Fraction
α
18 9 0.534
22.5 11.25 0.702
27 13.5 0.793
31.5 15.75 0.848
36 18 0.884
As per Taguchi method of orthogonal array,
for four independent parameters with five levels,
L25 orthogonal array method was used to arrange
the input data in 25 combinations.
4. Results and discussion
The data was analyzed by using statistical
analysis software JMP 3.14. This software
analyzes the data by using analysis of variance
(ANNOVA). The outcome is presented in “Figs.
5 – 9”. “Fig. 9” is presenting the summary of the
influence of the selected independent parameter
on the response, thermal resistance.
(a) Inline
(b) Staggered
Fig. 5 Influence of approach velocity, U∞, on
thermal resistance
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
7
Paper ID TSF1009
(a) Inline
(b) Staggered
Fig. 6 Influence of fin bundle void fraction, α, on
thermal resistance.
(a) Inline
(b) staggered
Fig. 7 Influence of aspect ratio, ϒ, on thermal
resistance.
(a) Inline
(b) Staggered
Fig. 8 Influence of input heat flux, q, on thermal
resistance.
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
8
Paper ID TSF1009
The Pareto chart in “Fig. 9” show the
significant contribution of approach velocity on
the air side performance of heat sink. In mixed
convection, with assisting flow, the approach
velocity has a significant role to play. Also it is
observed that thermal resistance as a response has
a weak function with input heat flux (see “Fig.
7”) and aspect ratio (see “Fig. 8”).
(a) Inline
(b) Staggered
Fig. 9 Pareto charts showing %
significance of independent variables.
The regression analysis has provided the
platform for deciding the selection and omission
of parameters for further experimentation by
studying the Pareto charts. The Pareto charts
shown that input heat flux is having a very weak
function with the air side performance of heat
sink, i.e. the thermal resistance. Hence, the
further experimentation is performed at a constant
heat input. Also, it is revealed from the Pareto
charts that, the aspect ratio, both in inline and in
staggered arrangement is having a little influence.
But from the point of view of natural convection
assisting the forced convection, the fin height and
its variation can’t be ignored.
5. Conclusion
The main objective of numerical simulation
was to provide a physical insight of the mixed
convection mechanism and to study the influence
of number of independent parameters on the air
side performance of elliptical pin fin heat sink
both in inline and staggered arrangement.
The regression analysis has provided the
platform for deciding the selection and omission
of parameters for further experimentation by
studying the Pareto charts.
The Pareto charts shown that input heat flux is
having a very weak function with the airside
performance of heat sink, i.e. the thermal
resistance. Hence, the further experimentation can
be performed at a constant heat input.
Also, it is reveled from the Pareto charts that,
the aspect ratio, both in inline and in staggered
arrangement is having a little influence. But from
the point of view of natural convection assisting
the forced convection, the fin height and its
variation can’t be ignored.
6. References
6.1 Article in Journals
[1] Deshmukh, P. A., Warkhedkar, R. M (2011).
Thermal Performance of Pin Fin Heat Sinks-A
Review of Literature, International Review of
Mechanical Engineering, Volume 5. N. 4 May
2011, pp.-726-732
[2] Tahat, M., Kodah, Z.H., Jarrah, B. A., Probert,
S. D., Heat transfers from pin-fin arrays
experiencing forced convection, Applied Energy,
67 ,2000, pp. 419-442.
[3] Lyall, M. E., Thrift, A. A., Thole, K. A.,
Kohli, A., Heat Transfer From Low Aspect Ratio
Pin Fins, ASME Journal of Heat Transfer, 2011,
Vol. 133 011001-1-10.
[4] Khan, W. A., Culham, J. R., Yovanovic,M.
M., Modeling of Cylindrical Pin-Fin Heat Sinks
for Electronic Packaging, IEEE Transactions on
Components and Packaging Technologies, Vol.
31, No. 3, September 2008.
[5] Tzer-Ming Jeng, Sheng-Chung Tzeng.
Pressure drop and heat transfer of square pin-fin
arrays in in-line and staggered arrangements,
International Journal of Heat and Mass Transfer,
50, 2007, pp. 2364–2375.
[6] Khan, W. A., Culham, J. R., Yovanovic,M. M.
The Role of Fin Geometry in Heat Sink
Performance, ASME Journal of Heat Transfer,
2006, Vol. 128 , pp 324-330.
[7] Ghosh, M. S., Yao, L.S. Mixed convection
along a semi-infinite vertical flat plate with
uniform surface heat flux, ASME Journal of Heat
Transfer, Vol. 131, 2009, pp. 022502-1 to
022502-8.
[8] Selvarasu, N. K. C., Tafti, D. K., Blackwell, N.
E. Effect of Pin Density on Heat-Mass Transfer
The 3rd TSME International Conference on Mechanical Engineering
October 2012, Chiang Rai
9
Paper ID TSF1009
and Fluid Flow at Low Reynolds Numbers in
Minichannels, ASME Journal of Heat Transfer,
2010, Vol. 126 061702-1-8.
[9] Teertstra, P., J.R., Culham, Yovanovich,
M.M. Comprehensive review of natural and
mixed convection heat transfer models for circuit
board arrays, Journal of Electronic
Manufacturing, 1997,Vol.7, No.2, pp 79-92.
[10] Hamouche , Bessaїh, R. Mixed Convection
Air Cooling of Electronic Components Mounted
In a Horizontal Channel, International Journal of
Theoretical and Applied Mechanics, V. 3 N.1,
2008, pp.53–64.
[11] Bhopte, S., Musa, S. A., Dereje, A., Gamal
Refai-Ahmed. Mixed Convection of Impinging
Air Cooling Over Heat Sink in Telecom System
Application, ASME Journal of Heat Transfer,
2004, Vol. 126 , pp 519 -523.
[12] Kobus, C.J., Oshio, T. Predicting the thermal
performance characteristics of staggered vertical
pin fin array heat sinks under combined mode
radiation and mixed convection with impinging
flow, International Journal of Heat and Mass
Transfer, V.48,2005, pp. 2684–2696.
[13] Kobus, C.J., Oshio, T. Development of a
theoretical model for predicting the thermal
performance characteristics of vertical pin fin
array heat sinks under combined forced and
natural convection with impinging flow,
International Journal of Heat and Mass Transfer,
2005, Vol.48, pp 1053-1063.
[14] Kai-Shing Yang, Wei-Hsin Chu, Ing-Yong
Chen, Chi-Chuan Wang, A comparative study of
the airside performance of heat sinks having pin
fin configurations, International Journal of Heat
and Mass Transfer, 2007, Vol.50, pp 4661–4667
[15] Sahray, D., Ziskind, G., Letan, R. Scale-Up
and Generalization of Horizontal-Base Pin-Fin
Heat Sinks in Natural Convection and Radiation,
ASME Journal of Heat Transfer, 2010, Vol. 132
pp. 112502-1-10.
[16] Dharma Rao, V., Naidu, S. V., Govinda Rao,
B., Sharma, K. V. Heat Transfer from a
Horizontal Fin Array by Natural Convection and
Radiation- A Conjugate Analysis, International
Journal of Heat and Mass Transfer, 49, 2006, pp.
3379-3391.
6.2 Books
[1] Cengel, Y. A.(2010). Heat and Mass Transfer-
A Practical Approach, Tata McGraw-Hill, New
Delhi, Tenth Reprint.
[2] Incropera FP, DeWitt DP.(1985).
Fundamentals of Heat and Mass Transfer, 2nd
edition, New York, John Wiley.
[3] Ginichi Taguchi,(1987). System of
Experimental Design, Quality Resources, Volume
2, pp. 1173.