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Thermal performance of elliptical pin fin heat sink under combined natural and forced convection
Experimental Thermal and Fluid Science 50 (2013) 61–68
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Thermal performance of elliptical pin fin heat sink under combined natural and forced convection P.A. Deshmukh a,⇑, R.M. Warkhedkar b a b
Mechanical Engineering Department, Government Engineering College, Aurangabad, MS 431 003, India Mechanical Engineering Department, Government College of Engineering, Karad, MS 415 110, India
a r t i c l e
i n f o
Article history: Received 9 November 2012 Received in revised form 23 April 2013 Accepted 11 May 2013 Available online 21 May 2013 Keywords: Heat sink Elliptical pin fins Mixed convection
a b s t r a c t In this paper, the effects of design parameters have been experimentally investigated for the air side thermal performance under mixed (combined natural and forced) convection of the fully shrouded elliptical pin fin heat sinks and the values of optimum design parameters are sought. A theoretical model is used to predict the influence of various geometrical, thermal and flow parameters on the thermal resistance of the heat sink. An experimental measurement technique is utilized to indirectly measure the overall heat transfer coefficient of the heat sink in mixed convection with assisting flow. The thermal performance characteristics are obtained for various parameters with inline and staggered layout of the pin fin heat sinks resulting in optimum heat sink void fraction (a), and pin fin aspect ratio ( ). The comparative thermal performances of circular and elliptical profiled pin fin heat sinks are presented. Based on experimental data for the range of fin, air flow and heat sink parameters, with aspect ratio, 5.1 6 6 9.18; heat sink void fraction, 0.534 6 a 6 0.884; approach velocity, 0.1 6 U1 6 0.5; longitudinal fin pitch, 18 6 SL 6 36 mm; transverse fin pitch, 9 6 ST 6 18 mm; elliptical pin fin axis ratio ¼ 0:66 and mixed convection parameter, 1 6 Grd/Red 6 100; generalized empirical correlations are developed for elliptical pin fin heat sink. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Heat sinks are extensively used to enhance heat transfer to ambient air. There are variety of heat sink types, with differing fin geometries and operating with natural or forced convection [1]. A common geometry is a pin fin array heat sink. However, the rationale for selecting a particular design of heat sink or more specifically a particular fin cross sectional profile remains somewhat uncertain. A careful review of the literature reveals that elliptical profiled pin fins outperform compared with circular and square cross section. Chapman et al. [2] experimentally investigated the air side thermal performance of pin fin heat sinks with square, circular and elliptical cross-section and found that elliptical pin fins are superior on air side performance in forced convection. Khan et al. [3] analytically developed a forced convection model for determining heat transfer from in-line and staggered pin-fin heat sinks used in electronic packaging applications and examined the effect on overall thermal/fluid performance associated with different fin geometries including rectangular plate fins as well as square, circular and elliptical pin fins. An experimental study was performed by Yang et al. [4] for pin fin heat sinks having circular,
⇑ Corresponding author. Tel.: +91 20 22934344; fax: +91 20 22934084. E-mail address: [email protected] (P.A. Deshmukh). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.05.005
elliptic and square cross-section with inline and staggered arrangements to study the effect of fin density on the heat transfer performance. The work on numerical investigations for elliptical pin fin heat sinks was reported by Seyf et al. [5]. Elliptical cross section pin fins provide more general geometrical configuration than circular pins. In the limiting cases, they represent a horizontal plate fin when the axis ratio ! 0 and a circular pin fin when ! 1. Further, mixed or combined free and forced convective heat transfer arise in many transport processes in engineering devices and in nature [6] which is frequently encountered in industrial and technical processes including electronic devices cooled by fan, nuclear reactors cooled during emergency shutdown, heat exchangers placed in a low-velocity environment, solar receivers exposed to winds, etc. At low velocities, the presence of temperature gradient in a fluid in a gravity field always gives rise to natural convection currents. Therefore, forced convection is always accompanied by natural convection both being strong function of fluid velocity. The error involved in ignoring natural convection is negligible at high velocity but may be considerable at low velocities. In the open literature, very few studies are observed dealing with this kind of mixed convection where forced convection is accompanied by natural convection in pin fin heat sink applications. Deshmukh et al. [7] has documented a comprehensive literature review on thermal performance of pin fin heat sinks covering all modes of heat transfer, including mixed convection. Kobus et al. [8,9] carried
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Nomenclature a b d W L tb ST SL H U1 Tb Tf Tfi
semi-minor axis of elliptical pin fin (m) semi-major axis of elliptical pin fin (m) mean diameter (m) width of base plate (m) length of base plate (m) thickness of base plate (m) transverse pitch (m) longitudinal pitch (m) height of pin fin (m) approach velocity (m/s) base temperature of heat sink (°C) ambient air temperature (°C) inlet air temperature (°C)
Tfo Rt,s q Red Pr Grd Nud
Greek symbols a void fraction aspect ratio axis ratio
out a comprehensive theoretical and experimental study on the thermal performance of a circular pin-fin heat sink under combined natural and forced convection with impinging flow. The present study focuses upon characterizing the thermal performance of elliptical pin fin heat sink subjected to mixed convection with assisting flow. The purpose of current work is to indirectly measure the average convective heat transfer coefficient for the fin array and the effective thermal resistance of the heat sink by using an experiential measurement technique. Also it is aimed at predicting the thermal performance characteristics of the elliptical pin fin heat sink in terms of various design parameters and to reveal their influence. The experimental investigation for the fin array will provide design insight including the existence of optimum fin density and spacing.
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:
The shape of the elliptical pin fin is selected in such a way that the masses of the elliptical and circular fin are same. Assuming the material and volume are the same for both the fins, the equivalent diameter of elliptical pin fin can be expressed as,
ð1Þ
where a and b are semi-minor and semi-major axes of elliptical pin, respectively. The aspect ratio ( ) and axis ratio ðÞ for the elliptical pin fin can be defined as,
¼ a=b
qffiffiffiffi
ð2Þ
ð3Þ
. where m ¼ hP kA 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, Qb, can be expressed as,
Q b ¼ hAb ðT b T f Þ
ð4Þ
where Ab ¼ ðWL nAÞ. Therefore, the total rate of heat transfer from the heat sink, Qs, which contains n fins, can be expressed as,
ð5Þ
Using Eqs. (5)–(7), the effective thermal resistance of the heat sink, Rt,s, can be modeled as,
Rt;s ¼
Tb Tf Qs
ð6Þ
Rt;s ¼
Tb Tf hAb ðT b T f Þ þ nkmAðT b T f Þ tanh mH
ð7Þ ð8Þ
Further Eq. (8) can be modified in the least number of parameters by considerable algebraic manipulation as,
pffiffiffiffiffiffiffiffiffiffiffi Rt;s ¼ ½hðWL nAÞ þ nð hPkA tanh mHÞ1 tanhmH mH
where n ¼ tip heat loss.
Rt;s ¼
ð9Þ
is the efficiency of each pin fin assuming negligible
1 nA þ ngPH h WL 1 WL
Rt;s ¼ ½hðWLa þ ngPHÞ1
2.2. Theoretical model
¼ H=d;
Q fin ¼ kmAðT b T f Þ tanh mH
Rt;s ¼ ½hðWL nAÞ þ nðkmA tanh mHÞ1
1. Each pin is of uniform cross section and height, H, with elliptical cross section. 2. The pin 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 and laminar. 7. Radiation heat transfer is negligible. 8. There is no slip at the base plate and the fin surface.
pffiffiffiffiffiffiffiffi 4ab
Using the temperature distribution, along with Fourier model for conduction, the rate of heat transfer from a single elliptical pin fin, Qfin, can be modeled as,
Q s ¼ Q b þ nQ fin
2. Formulation of a theoretical model
d¼
outlet air temperature (°C) thermal resistance (°C/W) heat flux (W/m2) Reynolds number Prandtl number Grashof number Nusselt number
ð10Þ ð11Þ
nA where a ¼ 1 WL is an important parameter coefficient for a fin bundle and can be called the fin bundle void fraction. The void fraction, a, of a fin bundle is that fraction of a cross sectional area of the fin bundle that is occupied by air. The fin bundle void fraction, a, in terms of longitudinal pitch, SL, and transverse pitch, ST, can be defined as a ¼ 1 SLAST .
Further, by doing simple algebraic manipulations, Eq. (12) can be represented by using the definition of void fraction and aspect ratio as,
Rt;s ¼ fhSL ST ½a þ 4ngð1 aÞ g1
ð12Þ
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Eq. (13) represents a theoretical model for predicting the effective thermal resistance of heat sink, Rt,s, in terms of area of fin heat sink base, WL, fin bundle void fraction, a, number of pin fins, n, efficiency of pin fin, g, aspect ratio, and the convective heat transfer coefficient, h, between the fins and flowing air. 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 and fluid properties in addition to the bundle effect. The complexity of the physical mechanisms governing this particular physical parameter is such that they can only partially be modelled. Therefore, 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 is the convective heat transfer coefficient, h. Therefore in order to determine the required convective heat transfer coefficient, h, there will be the need for indirect measurement.
4. Experimental facility 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 (see Fig. 1).
3. Design of experiment For doing the experimental investigation to evaluate the performance of the pin fin heat sink in terms of thermal resistance, the parameters like longitudinal pitch, SL, transverse pitch, ST, fin bundle void fraction, a and aspect ratio, , need to be varied in some specific interval along with the approach velocity, U1. A change in diameter has relatively little influence on the effective thermal resistance for the air velocities in the mixed convection region. For lower velocities where natural convection starts to dominate the heat transfer mechanism, a 25% change in diameter has a 6% change in thermal performance [8]. The fin height has a significant effect on air side performance of heat sink with a limitation on aspect ratio. Fins that are too short cannot be modeled with an adiabatic tip which may lead to poor performance and overheating of the sink surface. Fins that are too long will have compromised fin efficiency since fin efficiency is a strong function of fin height. Therefore, the variation in aspect ratio was done by varying the height of the pin fin with fin efficiency close to 90%. The parameters, longitudinal pitch, SL, and transverse pitch, ST, (and hence the fin bundle void fraction, a), has a strong effect on the pin density. When the spacing are too wide, the structure will be less dense resulting in a fewer number of pins on the base plate, both in inline and staggered arrangements, which may have poor effects on air side performance. The selection and variation in approach velocity was 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 Grd/Red should be in the range of 1 < Grd/Red < 100, so that neither natural convection nor the forced convection would dominate the flow field. For selection and variation of the parameters like longitudinal pitch, SL, transverse pitch, ST, fin bundle void fraction, a, aspect ratio, , and approach velocity, U1, the Taguchi [10] method of an orthogonal array was used with five levels of parameters as represented in Table. 1. Note that the void fraction, a, is a function of SL and ST.
Fig. 1. Schematics of elliptical pin fin array.
Fig. 2. Schematic representation of experimental set up with assisting flow.
Table 1 Parameters used for experimentation. Levels
Aspect ratio
Approach velocity U1 (m/s)
Longitudinal pitch SL (mm)
Transverse pitch ST (mm)
Void fraction a
1 2 3 4 5
5.1 6.12 7.14 8.16 9.18
0.1 0.2 0.3 0.4 0.5
18 22.5 27 31.5 36
9 11.25 13.5 15.75 18
0.534 0.702 0.793 0.848 0.884
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Fig. 3. Photograph of circular and elliptical pin fin heat sinks.
Fig. 2 is representing a 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. 4.1. Wind tunnel and test section The main body of the rectangular cross-section wind tunnel duct was manufactured from wooden sheet and was 2 m high with uniform internal width of 180 mm. However, the depth of the duct, and hence the duct’s cross-sectional area, could 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 was used to enable the pin fin array. An air straightener with proper meshing was chosen to straighten the air. The air with controlled velocity, properly straightened, was then passed through the test section. Air velocities were measured with a Lutron make AM-4204 hot wire anemometer. The test section consists of aluminum elliptical and circular pin fin heat sink. Pin fins were mounted on the square base plate of 164 mm 164 mm with 12 mm thickness (see Fig. 3). Each elliptical pin fin has 12 mm major axis and 8 mm minor axis whereas the circular pin fins are with 10 mm diameter. 4.2. Heating system The base of the heat sink was heated by a patch heater with 400 W electrical-resistance 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 the main heater block were insulated thermally with a 50 mm thick mineral wool blanket. A horizontal guard heater, rated at 50 W, was 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, was located in a well-fitting, opentopped, asbestos sheet box lined with wooden sheets. The patch heater was sandwiched between the base plate and supporting aluminum plate. The thickness and bottom side of heater arrangement was completely insulated by using asbestos sheet insulation to avoid the heat loss. The power supplied to the main heater was adjusted by altering the Variac setting and measured by a calibrated, in-line voltmeter and ammeter. The heat input to the guard heater was adjusted until the steady state temperature difference, across the layer of insulant, sandwiched between two heaters, was 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 [11].
Uncertainty variable
Measurement range
Error
Free stream velocity, U1 Mean diameter of pin fin, d Aspect ratio, Void fraction, a Temperature, T Average surface temperature, Tb Heat flux, Q/A Heat transfer coefficient, h Thermal resistance, Rt,s Nusselt number, Nud Grashof number, Grd Renolds number, Red
0.1–0.6 m/s NA 5.1–9.18 0.534–0.884 NA NA NA NA NA NA NA NA
5.59% 2.1% 2.17% 4.2% ±1 °C ±0.45 °C 7.8% 10–15% 10–15% 10–15% 15–20% 6%
The steady state temperature at the base of the fin array was measured by an appropriately distributed set of five J-type (IronConstantan) thermocouples, embedded within the base. Each thermocouple was screwed in position, so as to ensure a good thermal contact. The average value obtained from this thermocouple was regarded as the mean overall base temperature. The inlet and outlet air stream temperatures across the test section in the wind tunnel were measured by eight thermo-junctions: four were located immediately upstream the entrance and another four just downstream of the array. All the thermocouples were connected to the digital temperature indicator through a junction box. At half-hourly intervals, observations were recorded. When consecutive values were identical, it was assumed that steady state conditions were attained. The actual rate of heat transfer, Q, to the air by the heat sink is found by doing the energy balance on the air as it flows past the heat sink as,
_ p ðT fo T fi Þ Q ¼ mC
ð13Þ
_ based on mean flow velocity of air in wind The mass flow rate m tunnel is defined as,
_ ¼ qAf U 1 m
ð14Þ
where Af ¼ ST H After considerable algebraic manipulation, Eq. (13) is expressed as,
T fi þ T fo Q s ¼ hSL ST ½a þ 4ngð1 aÞ T b 2
ð15Þ
By using Eqs. (14) and (16), the equation for indirect measurement of the heat transfer coefficient, h, can be expressed as,
h¼
_ p ðT fo T fi Þ mC
T þT SL ST ½a þ 4ngð1 aÞ T b fi 2 fo
ð16Þ
The model in Eq. (17) provides a means for indirectly measuring the convective heat transfer coefficient, h, as a function of air velocity U1. It is recognized that because the fin efficiency, g, 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, U1. 4.3. Experimental uncertainties The uncertainties associated with the measured values were obtained from the manufacturers’ specification sheets (Table 2) while the uncertainties associated with the derived quantities were obtained by using the propagation of uncertainty analysis, and are also given in Table 2.
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5. Results and discussion
Red ¼
5.1. Applicable domain of thermal characteristics The thermal characteristics obtained in this study are applicable for this particular heat sink geometry with assisting flow in combined natural and forced convection with the following range of fin, air flow and heat sink parameters: 5.1 6 6 9.18, 0.534 6 a 6 0.884, 0.1 6 U1 6 0.5, 18 6 SL 6 36 mm, 9 6 ST 6 18 mm and ¼ 0:66. 5.2. Development of convective heat transfer correlation function
ð18Þ
q2 gbðT b T f Þd3 l2
ð19Þ
100
1 ≤ Grd / Red ≤ 100 Pr = 0.7
Nud
10
Nud = 1.008 (α )1.34 ( )0.5 Red / Grd0.5 R² = 0.9844
0 0
5.2.1. Elliptical pin fin heat sink with inline arrangement 0:5
ðcÞ
5
10
(α )1.34 ( )0.5 Red / Grd
15
0.5
Fig. 4. Generalized heat transfer correlation for elliptical pin fin heat sink with inline configurations.
!
Red
Grd where 0:534 6 a 6 0:884, 5:1 6 c 6 9:18 and 1 6 Re 6 100 . d
5.2.2. Elliptical pin fin heat sink with staggered arrangement
Nud ¼ 1:26ðaÞ
1:25
ðcÞ
0:46
Red
!
Grd where 0:534 6 a 6 0:884, 5:1 6 c 6 9:18 and 1 6 Re 6 100 . d
5.3. Design insight obtained With the theoretical model, in conjunction with the experimentation, a parametric analysis was carried out to study the influence of various design parameters on the thermal performance of the circular and elliptical pin fin heat sinks. 5.3.1. Influence of void fraction The test results of heat sink thermal resistance vs. Fin bundle void fraction for the elliptical and circular pin fin heat sink test samples having inline and staggered arrangement are plotted in Figs. 6 and 7 respectively. For the sake of comparison, the test results are plotted for all the selected range of fin aspect ratios and at constant approach velocity, U1 = 0.3 m/s. The nature of thermal resistance variation for all configurations is observed to be qualitatively similar due to curved surface nature of both circular and elliptical pin fin heat sink. Quantitatively, the least thermal resistance is offered by elliptical pin fin heat sink as compared to circular pin fin heat sink, both in inline and staggered arrangement. This can be attributed to higher streamlined flow patterns in assisting flow mixed convection in case of elliptical profile. In all cases, the minimum heat sink thermal resistance is observed at a = 0.7. The effect of fin aspect ratio is observed to be diminishing close
Nud
1 ≤ Grd / Red ≤ 100 Pr = 0.7
10
Nud = 1.26 (α )1.25 ( )0.46 Red / Grd0.5 R² = 0.9748
0
5
10 1.25
( α)
15 0.46
( )
ð22Þ
Gr 0:5 d
100
1
ð21Þ
Gr 0:5 d
ð17Þ
hd Nud ¼ kf
1
The functional relationship between the dimensionless terms was determined by regression analysis. For the range of experimental variables tested, steady state heat transfer correlations were obtained by least square fit for both the inline and staggered arrangements of pin fins. (see Figs. 4 and 5).
Nud ¼ 1:008ðaÞ
The dimensionless convective heat transfer coefficient Nud is the classic Nusselt number. The parameters Grd and Red are the classical Grashof and Renolds numbers, respectively. Thus,
Grd ¼
ð20Þ
1:34
It was assumed that the steady state combined convective behavior of the fully shrouded elliptical pin fin heat sinks could be described in terms of fin bundle void fraction, a, pin fin aspect ratio, , Reynolds number, Red and Grashof number, Grd, by
Nud ¼ f ða; c; Red ; Grd Þ
qU 1 d l
Red / Grd
20
25
0.5
Fig. 5. Generalized heat transfer correlation for elliptical pin fin heat sink with staggered configurations.
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(a)
1.2
= 5.1 = 6.12
1
= 7.14
Elliptical Inline arrangement U∞ = 0.3 m/s
(b)
= 6.12 0.8
= 9.18
Rt,s, 0C/W
Rt,s, 0C/W
= 5.1
0.9
= 8.16 0.8
1
0.6
= 7.14
0.7
= 8.16
0.6
= 9.18
Elliptical Staggered arrangement U∞ = 0.3 m/s
0.5 0.4
0.4 0.3 0.2
0.2
0.1 0
0.534
0.702
0.793
0.848
0
0.884
0.534
0.702
Void Fraction, α
0.793
0.848
0.884
Void Fraction, α
Fig. 6. Thermal performance of elliptical pin fin heat sink: (a) inline; and (b) staggered.
1.4
γ = 5.1 1.2
= 6.12 = 7.14
Rt,s, 0C/W
1
Circular Inline arrangement U∞ = 0.3 m/s
(b)
γ = 5.10 = 6.12 = 8.16
0.8
= 9.18
0.6
Circular Staggered arrangement U∞ = 0.3 m/s
= 7.14
= 8.16
0.8
1.2
1
Rt,s, 0C/W
(a)
= 9.18 0.6
0.4 0.4 0.2
0.2
0
0 0.534
0.702
0.793
0.848
0.884
0.534
0.702
Void Fraction, α
0.793
0.848
0.884
Void Fraction, α
Fig. 7. Thermal performance of circular pin fin heat sink: (a) inline; and (b) staggered.
13
Experimental Theoretical Experimental Theoretical
Staggered 12 11
Red = 150 γ = 8.16
10
Nud
to c = 8 for staggered circular and in both arrangements of elliptical pin fin heat sinks. It was found that a change in void fraction, a, has a major influence on the air side performance of heat sinks. At all aspect ratios in the range mentioned, the heat sinks offer minimum thermal resistance at void fraction close to 0.7. The theoretical model and experimental data confirms the optimum fin spacing in terms of void fraction. These results have considerable practical significance as it relates to the design of efficient finned heat sink. The physics behind these observed results is related with the fin density. As the fin spacing increases in longitudinal and transverse directions, the fin bundle void fraction, a, also increases. As the void fraction increases, for a fixed base area, the number of fins and, thus, the heat transfer area decreases. As the void fraction increases from 0.534 to 0.702, the convective heat transfer coefficient apparently increases faster than the fin surface area decrease, thus causing the thermal performance increase. When the void fraction increases much beyond a = 0.702, however, the convective heat transfer coefficient apparently no longer increases as fast as the fin surface area decreases, thus causing the thermal performance to drop off. When one compares between inline and staggered arrangement, the better air side performance is observed for staggered arrangement due to better intermixing of fluid and more fin surface area coming in contact with the cooling fluid, hence increasing the convective heat transfer coefficient.
9 8
Inline
7 6 5
0.534
0.702
0.793
0.848
0.884
Void Fraction, α Fig. 8. Influence of void fraction on thermal performance of elliptical pin fin heat sink, comparison with theoretical prediction.
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(a)
Circular, Inline
0.9
1
Circular, Inline
0.9
Circular, Staggered
Circular, Staggered
0.8
0.8
Elliptical, Inline
0.7
Elliptical, Inline
0.7
Elliptical, Staggered o Rt,s, C/W
Rt,s, oC/W
(b)
1
0.6 0.5 0.4
Elliptical, Staggered
0.6 0.5 0.4
0.3
0.3
U∞ = 0.2 m/s
0.2
0.2
α = 0.702
U∞ = 0.2 m/s
0.1
0.1
γ = 8.16
0
0 0.534
0.702
0.793
0.848
0.884
5.1
6.12
Void Fraction, α
7.14
8.16
9.18
Aspect Ratio, γ
Fig. 9. Comparative thermal performance of pin fin heat sinks: (a) influence of fin density; and (b) influence of fin aspect ratio.
15
1.2
Experimental Theoretical
13
Circular, Inline
Staggered
Circular, Staggered
Experimental
1
Theoretical
Elliptical, Inline
11
Nud
Red = 150 9
Elliptical, Staggered 0.8
α = 0.7
Rt,s, oC/W
α = 0.702 7
Inline
5
γ = 8.16
0.6
0.4 3
5.1
6.12
7.14
8.16
9.18
Aspect Ratio, γ Fig. 10. Influence of aspect ratio on thermal performance of elliptical pin fin heat sink, comparison with theoretical prediction.
0.2
For the optimum fin aspect ratio, the circular staggered configuration is 35% more effective than circular inline, the elliptical staggered is 63% more effective than elliptical inline, the elliptical inline is 24% more effective than circular inline and elliptical staggered is 50% more effective then circular staggered. The results imply that there is a considerable difference of flow patterns among these pin configurations. The Coanda effect may prevail when the air flow penetrates across the pin fin gap. The tendency of fluids to follow a curved surface is known as the Coanda effect. For airflow across the two adjacent fins, the gap flow may direct to right or left which is known as a deflection flow. The existence of deflection flow may change the general vortex structure behind pins, causing a better mixing and heat transfer performance. The deflection flow depends on the transverse and longitudinal spacing. By careful examination, it is clear that for loosely packed heat sinks, irrespective of pin profile, the vortices may form in absence of deflection flow. Notice that the presence of deflection flow pattern prevents the formation of vortices, thereby causing a significant increase of heat transfer coefficient. For the staggered arrangement, the heat transfer coefficients are all increased when the fin density is increased irrespective of the fin profile. Apparently the presence of staggered arrangement had greatly altered the flow pattern (see
0
0.1
0.2
0.3
0.4
0.5
U∞, m/s Fig. 11. Comparative thermal performance of pin fin heat sinks, influence of approach velocity.
Fig. 8). This can be evidently observed by typical flow visualization (e.g. Sparrow and Molki [12]) (see Figs. 9 and 11). 5.3.2. Influence of fin aspect ratio The experimental data were again used to carry out the parametric study to investigate the influence of fin height in terms of fin aspect ratio, , on the thermal performance of finned heat sink. The heat sinks with five different aspect ratios were tested and compared. Fig. 6b confirm that as the fin height increases, the thermal performance of heat sink increases both in inline and staggered arrangements in the range of aspect ratio, = 5.1–8.16. Thereafter, diminishing results are observed for the aspect ratio, ¼ 8:16—9:18 for elliptical profiled heat sink. No such diminishing effect is observed in case of circular profiled pin fin heat sink. This observation can be attributed to the temperature gradients
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35
Experimental Theoretical
30
Staggered
Experimental 25
Theoretical α = 0.7
Nud
20
γ = 8.16 15
Inline
10
5
0
50
100
150
200
250
Red Fig. 12. Influence of approach velocity on thermal performance of elliptical pin fin heat sink, comparison with theoretical prediction.
near to the tip of the pin fins. As the fin height increases beyond ¼ 8:16, the fin material resistance causes the pin temperature to drop off near to the tip causing the thermal performance to drop off. In case of elliptical profiled pin fin heat sink, the experimental data confirm the optimum fin height in terms of aspect ratio close to 8.2 for staggered arrangement. At the optimum value of aspect ratio and fin bundle void fraction, the thermal performance of staggered pin fin heat sink is 33% more than the inline pin fin heat sink for elliptical profile (see Fig. 10). 5.3.3. Influence of approach velocity At lower approach velocity U1 6 0.1 m/s, where the natural convection is dominating forced convection, a large variation is observed in thermal resistance for the various aspect ratios. In this range, the increase in fin height increases the heat transfer coefficient, thereby decreasing the thermal resistance. But for higher approach velocities U1 > 0.2 m/s, the influence of aspect ratio goes on diminishing both in inline and staggered arrangement. Fig. 7 compares the air side thermal performance of circular and elliptical pin fin heat sinks at optimum aspect ratio ¼ 8:16, and void fraction a = 0.702. In the approach velocity range studied, the staggered arrangement gives better air side performance by 25–51% than inline arrangement (see Fig. 12). 6. Summary and conclusions Comprehensive experimental investigations were carried out for the air side thermal performance of fully-shrouded, elliptical and circular pin fin heat sinks in mixed convection. The simple theoretical model, despite the complexity of the physical mechanism involved in this study, is used as a significant design tool to determine the influence of various design parameters on the effective thermal resistance of the heat sink. The parameters examined are pin aspect ratio, spacing along longitudinal and transverse directions, configuration, air flow and its orientation. The thermal performance characteristics are presented in terms of heat sink thermal resistance which is generally used as a design tool. The results are plotted to show the influence of various design parameters on heat sink performance. The results imply that as the fin spacing increases in longitudinal and transverse directions, the fin bundle void fraction, a, also
increases. As the void fraction increases, for a fixed base area, the number of fins and, thus, the heat transfer area decreases. As the void fraction increases, the convective heat transfer coefficient apparently increases faster than the fin surface area decrease, thus causing the thermal performance increase. When the void fraction increases much beyond a = 0.702, however, the convective heat transfer coefficient apparently no longer increases as fast as the fin surface area decreases, thus causing the thermal performance to drop off. When one compares between inline and staggered arrangement, the better air side performance is observed for staggered arrangement due to better intermixing of fluid and more fin surface area coming in contact with the cooling fluid, hence increasing the convective heat transfer coefficient. The results imply that there is a considerable difference of flow patterns among these pin configurations. The Coanda effect is prevailing when the air flow penetrates across the pin fin gap. The existence of deflection flow decides the general vortex structure behind pins, causing a better mixing and heat transfer performance. The deflection flow depends on the transverse and longitudinal spacing. By careful examination, it is clear that for loosely packed heat sinks, irrespective of pin profile, the vortices may form in absence of deflection flow. Notice that the presence of deflection flow pattern prevents the formation of vortices, thereby causing a significant increase of heat transfer coefficient. For the staggered arrangement, the heat transfer coefficients are all increased when the fin density is increased irrespective of the fin configuration. Apparently the presence of staggered arrangement had greatly altered the flow pattern. The study resulted in the successful development of generalized empirical correlations for elliptical profiled pin fin heat sinks having capability of predicting the influence of various physical, thermal and flow parameters on the air side performance. The experimental data have provided the good design insight for studying the influence of various heat sink, flow and arrangement parameters. The convective heat transfer coefficient can be determined from the generalized empirical correlations developed for elliptical pin fin heat sink. References [1] W.A. Scott, Cooling of Electronic Equipment, John Wiley and Sons, New York, USA, 1974. [2] C.L.Chapman, S. Lee, B.L. Schmidt, Thermal performance of an elliptical pin fin heat sink, in: 10th IEEE Semi-Therm, 1994, pp. 25–31. [3] W.A. Khan, R. Culham, M.M. Yovanovic, The role of fin geometry in heat sink performance, J. Heat Transfer 128 (2006) 324–330. [4] 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, Int. J. Heat Mass Transfer 50 (2007) 4661–4667. [5] H.R. Seyf, M. Layeghi, Numerical analysis of convective heat transfer from an elliptic pin fin heat sink with and without metal foam insert, J. Heat Transfer 132 (2010) 071401-1–071401-9. [6] I. Pop, D.B. Ingham, Convective Heat Transfer- Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, 2001. [7] P.A. Deshmukh, R.M. Warkhedkar, Thermal performance of pin fin heat sinks – a review of literature, Int. Rev. Mech. Eng. 5 (4) (2011) 726–732. [8] C.J. Kobus, T. Oshio, Development of a theoretical model for predicting the thermal performance characteristics of a vertical pin-fin array heat sink under combined forced and natural convection with impinging flow, Int. J. Heat Mass Transfer 48 (2005) 1053–1063. [9] C.J. Kobus, T. Oshio, Predicting the thermal performance characteristics of staggered vertical pin fin array heat sinks under combined mode radiation and mixed convection with impinging flow, Int. J. Heat Mass Transfer 48 (2005) 2684–2696. [10] G. Taguchi, System of experimental design, Qual. Resources 2 (1987) 1173. [11] M. Tahat, Z.H. Kodah, B.A. Jarrah, S.D. Probert, Heat transfers from pin-fin arrays experiencing forced convection, Appl. Energy 67 (2000) 419–442. [12] E.M. Sparrow, M. Molki, Effect of a missing cylinder on heat transfer and fluid flow in an array of cylinders in cross-flow, Int. J. Heat Mass Transfer 25 (1982) 449–456.
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Thermal performance of elliptical pin fin heat sink under combined natural and forced convection P.A. Deshmukh a,⇑, R.M. Warkhedkar b a b
Mechanical Engineering Department, Government Engineering College, Aurangabad, MS 431 003, India Mechanical Engineering Department, Government College of Engineering, Karad, MS 415 110, India
a r t i c l e
i n f o
Article history: Received 9 November 2012 Received in revised form 23 April 2013 Accepted 11 May 2013 Available online 21 May 2013 Keywords: Heat sink Elliptical pin fins Mixed convection
a b s t r a c t In this paper, the effects of design parameters have been experimentally investigated for the air side thermal performance under mixed (combined natural and forced) convection of the fully shrouded elliptical pin fin heat sinks and the values of optimum design parameters are sought. A theoretical model is used to predict the influence of various geometrical, thermal and flow parameters on the thermal resistance of the heat sink. An experimental measurement technique is utilized to indirectly measure the overall heat transfer coefficient of the heat sink in mixed convection with assisting flow. The thermal performance characteristics are obtained for various parameters with inline and staggered layout of the pin fin heat sinks resulting in optimum heat sink void fraction (a), and pin fin aspect ratio ( ). The comparative thermal performances of circular and elliptical profiled pin fin heat sinks are presented. Based on experimental data for the range of fin, air flow and heat sink parameters, with aspect ratio, 5.1 6 6 9.18; heat sink void fraction, 0.534 6 a 6 0.884; approach velocity, 0.1 6 U1 6 0.5; longitudinal fin pitch, 18 6 SL 6 36 mm; transverse fin pitch, 9 6 ST 6 18 mm; elliptical pin fin axis ratio ¼ 0:66 and mixed convection parameter, 1 6 Grd/Red 6 100; generalized empirical correlations are developed for elliptical pin fin heat sink. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Heat sinks are extensively used to enhance heat transfer to ambient air. There are variety of heat sink types, with differing fin geometries and operating with natural or forced convection [1]. A common geometry is a pin fin array heat sink. However, the rationale for selecting a particular design of heat sink or more specifically a particular fin cross sectional profile remains somewhat uncertain. A careful review of the literature reveals that elliptical profiled pin fins outperform compared with circular and square cross section. Chapman et al. [2] experimentally investigated the air side thermal performance of pin fin heat sinks with square, circular and elliptical cross-section and found that elliptical pin fins are superior on air side performance in forced convection. Khan et al. [3] analytically developed a forced convection model for determining heat transfer from in-line and staggered pin-fin heat sinks used in electronic packaging applications and examined the effect on overall thermal/fluid performance associated with different fin geometries including rectangular plate fins as well as square, circular and elliptical pin fins. An experimental study was performed by Yang et al. [4] for pin fin heat sinks having circular,
⇑ Corresponding author. Tel.: +91 20 22934344; fax: +91 20 22934084. E-mail address: [email protected] (P.A. Deshmukh). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.05.005
elliptic and square cross-section with inline and staggered arrangements to study the effect of fin density on the heat transfer performance. The work on numerical investigations for elliptical pin fin heat sinks was reported by Seyf et al. [5]. Elliptical cross section pin fins provide more general geometrical configuration than circular pins. In the limiting cases, they represent a horizontal plate fin when the axis ratio ! 0 and a circular pin fin when ! 1. Further, mixed or combined free and forced convective heat transfer arise in many transport processes in engineering devices and in nature [6] which is frequently encountered in industrial and technical processes including electronic devices cooled by fan, nuclear reactors cooled during emergency shutdown, heat exchangers placed in a low-velocity environment, solar receivers exposed to winds, etc. At low velocities, the presence of temperature gradient in a fluid in a gravity field always gives rise to natural convection currents. Therefore, forced convection is always accompanied by natural convection both being strong function of fluid velocity. The error involved in ignoring natural convection is negligible at high velocity but may be considerable at low velocities. In the open literature, very few studies are observed dealing with this kind of mixed convection where forced convection is accompanied by natural convection in pin fin heat sink applications. Deshmukh et al. [7] has documented a comprehensive literature review on thermal performance of pin fin heat sinks covering all modes of heat transfer, including mixed convection. Kobus et al. [8,9] carried
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Nomenclature a b d W L tb ST SL H U1 Tb Tf Tfi
semi-minor axis of elliptical pin fin (m) semi-major axis of elliptical pin fin (m) mean diameter (m) width of base plate (m) length of base plate (m) thickness of base plate (m) transverse pitch (m) longitudinal pitch (m) height of pin fin (m) approach velocity (m/s) base temperature of heat sink (°C) ambient air temperature (°C) inlet air temperature (°C)
Tfo Rt,s q Red Pr Grd Nud
Greek symbols a void fraction aspect ratio axis ratio
out a comprehensive theoretical and experimental study on the thermal performance of a circular pin-fin heat sink under combined natural and forced convection with impinging flow. The present study focuses upon characterizing the thermal performance of elliptical pin fin heat sink subjected to mixed convection with assisting flow. The purpose of current work is to indirectly measure the average convective heat transfer coefficient for the fin array and the effective thermal resistance of the heat sink by using an experiential measurement technique. Also it is aimed at predicting the thermal performance characteristics of the elliptical pin fin heat sink in terms of various design parameters and to reveal their influence. The experimental investigation for the fin array will provide design insight including the existence of optimum fin density and spacing.
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:
The shape of the elliptical pin fin is selected in such a way that the masses of the elliptical and circular fin are same. Assuming the material and volume are the same for both the fins, the equivalent diameter of elliptical pin fin can be expressed as,
ð1Þ
where a and b are semi-minor and semi-major axes of elliptical pin, respectively. The aspect ratio ( ) and axis ratio ðÞ for the elliptical pin fin can be defined as,
¼ a=b
qffiffiffiffi
ð2Þ
ð3Þ
. where m ¼ hP kA 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, Qb, can be expressed as,
Q b ¼ hAb ðT b T f Þ
ð4Þ
where Ab ¼ ðWL nAÞ. Therefore, the total rate of heat transfer from the heat sink, Qs, which contains n fins, can be expressed as,
ð5Þ
Using Eqs. (5)–(7), the effective thermal resistance of the heat sink, Rt,s, can be modeled as,
Rt;s ¼
Tb Tf Qs
ð6Þ
Rt;s ¼
Tb Tf hAb ðT b T f Þ þ nkmAðT b T f Þ tanh mH
ð7Þ ð8Þ
Further Eq. (8) can be modified in the least number of parameters by considerable algebraic manipulation as,
pffiffiffiffiffiffiffiffiffiffiffi Rt;s ¼ ½hðWL nAÞ þ nð hPkA tanh mHÞ1 tanhmH mH
where n ¼ tip heat loss.
Rt;s ¼
ð9Þ
is the efficiency of each pin fin assuming negligible
1 nA þ ngPH h WL 1 WL
Rt;s ¼ ½hðWLa þ ngPHÞ1
2.2. Theoretical model
¼ H=d;
Q fin ¼ kmAðT b T f Þ tanh mH
Rt;s ¼ ½hðWL nAÞ þ nðkmA tanh mHÞ1
1. Each pin is of uniform cross section and height, H, with elliptical cross section. 2. The pin 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 and laminar. 7. Radiation heat transfer is negligible. 8. There is no slip at the base plate and the fin surface.
pffiffiffiffiffiffiffiffi 4ab
Using the temperature distribution, along with Fourier model for conduction, the rate of heat transfer from a single elliptical pin fin, Qfin, can be modeled as,
Q s ¼ Q b þ nQ fin
2. Formulation of a theoretical model
d¼
outlet air temperature (°C) thermal resistance (°C/W) heat flux (W/m2) Reynolds number Prandtl number Grashof number Nusselt number
ð10Þ ð11Þ
nA where a ¼ 1 WL is an important parameter coefficient for a fin bundle and can be called the fin bundle void fraction. The void fraction, a, of a fin bundle is that fraction of a cross sectional area of the fin bundle that is occupied by air. The fin bundle void fraction, a, in terms of longitudinal pitch, SL, and transverse pitch, ST, can be defined as a ¼ 1 SLAST .
Further, by doing simple algebraic manipulations, Eq. (12) can be represented by using the definition of void fraction and aspect ratio as,
Rt;s ¼ fhSL ST ½a þ 4ngð1 aÞ g1
ð12Þ
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Eq. (13) represents a theoretical model for predicting the effective thermal resistance of heat sink, Rt,s, in terms of area of fin heat sink base, WL, fin bundle void fraction, a, number of pin fins, n, efficiency of pin fin, g, aspect ratio, and the convective heat transfer coefficient, h, between the fins and flowing air. 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 and fluid properties in addition to the bundle effect. The complexity of the physical mechanisms governing this particular physical parameter is such that they can only partially be modelled. Therefore, 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 is the convective heat transfer coefficient, h. Therefore in order to determine the required convective heat transfer coefficient, h, there will be the need for indirect measurement.
4. Experimental facility 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 (see Fig. 1).
3. Design of experiment For doing the experimental investigation to evaluate the performance of the pin fin heat sink in terms of thermal resistance, the parameters like longitudinal pitch, SL, transverse pitch, ST, fin bundle void fraction, a and aspect ratio, , need to be varied in some specific interval along with the approach velocity, U1. A change in diameter has relatively little influence on the effective thermal resistance for the air velocities in the mixed convection region. For lower velocities where natural convection starts to dominate the heat transfer mechanism, a 25% change in diameter has a 6% change in thermal performance [8]. The fin height has a significant effect on air side performance of heat sink with a limitation on aspect ratio. Fins that are too short cannot be modeled with an adiabatic tip which may lead to poor performance and overheating of the sink surface. Fins that are too long will have compromised fin efficiency since fin efficiency is a strong function of fin height. Therefore, the variation in aspect ratio was done by varying the height of the pin fin with fin efficiency close to 90%. The parameters, longitudinal pitch, SL, and transverse pitch, ST, (and hence the fin bundle void fraction, a), has a strong effect on the pin density. When the spacing are too wide, the structure will be less dense resulting in a fewer number of pins on the base plate, both in inline and staggered arrangements, which may have poor effects on air side performance. The selection and variation in approach velocity was 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 Grd/Red should be in the range of 1 < Grd/Red < 100, so that neither natural convection nor the forced convection would dominate the flow field. For selection and variation of the parameters like longitudinal pitch, SL, transverse pitch, ST, fin bundle void fraction, a, aspect ratio, , and approach velocity, U1, the Taguchi [10] method of an orthogonal array was used with five levels of parameters as represented in Table. 1. Note that the void fraction, a, is a function of SL and ST.
Fig. 1. Schematics of elliptical pin fin array.
Fig. 2. Schematic representation of experimental set up with assisting flow.
Table 1 Parameters used for experimentation. Levels
Aspect ratio
Approach velocity U1 (m/s)
Longitudinal pitch SL (mm)
Transverse pitch ST (mm)
Void fraction a
1 2 3 4 5
5.1 6.12 7.14 8.16 9.18
0.1 0.2 0.3 0.4 0.5
18 22.5 27 31.5 36
9 11.25 13.5 15.75 18
0.534 0.702 0.793 0.848 0.884
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P.A. Deshmukh, R.M. Warkhedkar / Experimental Thermal and Fluid Science 50 (2013) 61–68 Table 2 Uncertainty of variables.
Fig. 3. Photograph of circular and elliptical pin fin heat sinks.
Fig. 2 is representing a 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. 4.1. Wind tunnel and test section The main body of the rectangular cross-section wind tunnel duct was manufactured from wooden sheet and was 2 m high with uniform internal width of 180 mm. However, the depth of the duct, and hence the duct’s cross-sectional area, could 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 was used to enable the pin fin array. An air straightener with proper meshing was chosen to straighten the air. The air with controlled velocity, properly straightened, was then passed through the test section. Air velocities were measured with a Lutron make AM-4204 hot wire anemometer. The test section consists of aluminum elliptical and circular pin fin heat sink. Pin fins were mounted on the square base plate of 164 mm 164 mm with 12 mm thickness (see Fig. 3). Each elliptical pin fin has 12 mm major axis and 8 mm minor axis whereas the circular pin fins are with 10 mm diameter. 4.2. Heating system The base of the heat sink was heated by a patch heater with 400 W electrical-resistance 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 the main heater block were insulated thermally with a 50 mm thick mineral wool blanket. A horizontal guard heater, rated at 50 W, was 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, was located in a well-fitting, opentopped, asbestos sheet box lined with wooden sheets. The patch heater was sandwiched between the base plate and supporting aluminum plate. The thickness and bottom side of heater arrangement was completely insulated by using asbestos sheet insulation to avoid the heat loss. The power supplied to the main heater was adjusted by altering the Variac setting and measured by a calibrated, in-line voltmeter and ammeter. The heat input to the guard heater was adjusted until the steady state temperature difference, across the layer of insulant, sandwiched between two heaters, was 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 [11].
Uncertainty variable
Measurement range
Error
Free stream velocity, U1 Mean diameter of pin fin, d Aspect ratio, Void fraction, a Temperature, T Average surface temperature, Tb Heat flux, Q/A Heat transfer coefficient, h Thermal resistance, Rt,s Nusselt number, Nud Grashof number, Grd Renolds number, Red
0.1–0.6 m/s NA 5.1–9.18 0.534–0.884 NA NA NA NA NA NA NA NA
5.59% 2.1% 2.17% 4.2% ±1 °C ±0.45 °C 7.8% 10–15% 10–15% 10–15% 15–20% 6%
The steady state temperature at the base of the fin array was measured by an appropriately distributed set of five J-type (IronConstantan) thermocouples, embedded within the base. Each thermocouple was screwed in position, so as to ensure a good thermal contact. The average value obtained from this thermocouple was regarded as the mean overall base temperature. The inlet and outlet air stream temperatures across the test section in the wind tunnel were measured by eight thermo-junctions: four were located immediately upstream the entrance and another four just downstream of the array. All the thermocouples were connected to the digital temperature indicator through a junction box. At half-hourly intervals, observations were recorded. When consecutive values were identical, it was assumed that steady state conditions were attained. The actual rate of heat transfer, Q, to the air by the heat sink is found by doing the energy balance on the air as it flows past the heat sink as,
_ p ðT fo T fi Þ Q ¼ mC
ð13Þ
_ based on mean flow velocity of air in wind The mass flow rate m tunnel is defined as,
_ ¼ qAf U 1 m
ð14Þ
where Af ¼ ST H After considerable algebraic manipulation, Eq. (13) is expressed as,
T fi þ T fo Q s ¼ hSL ST ½a þ 4ngð1 aÞ T b 2
ð15Þ
By using Eqs. (14) and (16), the equation for indirect measurement of the heat transfer coefficient, h, can be expressed as,
h¼
_ p ðT fo T fi Þ mC
T þT SL ST ½a þ 4ngð1 aÞ T b fi 2 fo
ð16Þ
The model in Eq. (17) provides a means for indirectly measuring the convective heat transfer coefficient, h, as a function of air velocity U1. It is recognized that because the fin efficiency, g, 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, U1. 4.3. Experimental uncertainties The uncertainties associated with the measured values were obtained from the manufacturers’ specification sheets (Table 2) while the uncertainties associated with the derived quantities were obtained by using the propagation of uncertainty analysis, and are also given in Table 2.
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5. Results and discussion
Red ¼
5.1. Applicable domain of thermal characteristics The thermal characteristics obtained in this study are applicable for this particular heat sink geometry with assisting flow in combined natural and forced convection with the following range of fin, air flow and heat sink parameters: 5.1 6 6 9.18, 0.534 6 a 6 0.884, 0.1 6 U1 6 0.5, 18 6 SL 6 36 mm, 9 6 ST 6 18 mm and ¼ 0:66. 5.2. Development of convective heat transfer correlation function
ð18Þ
q2 gbðT b T f Þd3 l2
ð19Þ
100
1 ≤ Grd / Red ≤ 100 Pr = 0.7
Nud
10
Nud = 1.008 (α )1.34 ( )0.5 Red / Grd0.5 R² = 0.9844
0 0
5.2.1. Elliptical pin fin heat sink with inline arrangement 0:5
ðcÞ
5
10
(α )1.34 ( )0.5 Red / Grd
15
0.5
Fig. 4. Generalized heat transfer correlation for elliptical pin fin heat sink with inline configurations.
!
Red
Grd where 0:534 6 a 6 0:884, 5:1 6 c 6 9:18 and 1 6 Re 6 100 . d
5.2.2. Elliptical pin fin heat sink with staggered arrangement
Nud ¼ 1:26ðaÞ
1:25
ðcÞ
0:46
Red
!
Grd where 0:534 6 a 6 0:884, 5:1 6 c 6 9:18 and 1 6 Re 6 100 . d
5.3. Design insight obtained With the theoretical model, in conjunction with the experimentation, a parametric analysis was carried out to study the influence of various design parameters on the thermal performance of the circular and elliptical pin fin heat sinks. 5.3.1. Influence of void fraction The test results of heat sink thermal resistance vs. Fin bundle void fraction for the elliptical and circular pin fin heat sink test samples having inline and staggered arrangement are plotted in Figs. 6 and 7 respectively. For the sake of comparison, the test results are plotted for all the selected range of fin aspect ratios and at constant approach velocity, U1 = 0.3 m/s. The nature of thermal resistance variation for all configurations is observed to be qualitatively similar due to curved surface nature of both circular and elliptical pin fin heat sink. Quantitatively, the least thermal resistance is offered by elliptical pin fin heat sink as compared to circular pin fin heat sink, both in inline and staggered arrangement. This can be attributed to higher streamlined flow patterns in assisting flow mixed convection in case of elliptical profile. In all cases, the minimum heat sink thermal resistance is observed at a = 0.7. The effect of fin aspect ratio is observed to be diminishing close
Nud
1 ≤ Grd / Red ≤ 100 Pr = 0.7
10
Nud = 1.26 (α )1.25 ( )0.46 Red / Grd0.5 R² = 0.9748
0
5
10 1.25
( α)
15 0.46
( )
ð22Þ
Gr 0:5 d
100
1
ð21Þ
Gr 0:5 d
ð17Þ
hd Nud ¼ kf
1
The functional relationship between the dimensionless terms was determined by regression analysis. For the range of experimental variables tested, steady state heat transfer correlations were obtained by least square fit for both the inline and staggered arrangements of pin fins. (see Figs. 4 and 5).
Nud ¼ 1:008ðaÞ
The dimensionless convective heat transfer coefficient Nud is the classic Nusselt number. The parameters Grd and Red are the classical Grashof and Renolds numbers, respectively. Thus,
Grd ¼
ð20Þ
1:34
It was assumed that the steady state combined convective behavior of the fully shrouded elliptical pin fin heat sinks could be described in terms of fin bundle void fraction, a, pin fin aspect ratio, , Reynolds number, Red and Grashof number, Grd, by
Nud ¼ f ða; c; Red ; Grd Þ
qU 1 d l
Red / Grd
20
25
0.5
Fig. 5. Generalized heat transfer correlation for elliptical pin fin heat sink with staggered configurations.
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(a)
1.2
= 5.1 = 6.12
1
= 7.14
Elliptical Inline arrangement U∞ = 0.3 m/s
(b)
= 6.12 0.8
= 9.18
Rt,s, 0C/W
Rt,s, 0C/W
= 5.1
0.9
= 8.16 0.8
1
0.6
= 7.14
0.7
= 8.16
0.6
= 9.18
Elliptical Staggered arrangement U∞ = 0.3 m/s
0.5 0.4
0.4 0.3 0.2
0.2
0.1 0
0.534
0.702
0.793
0.848
0
0.884
0.534
0.702
Void Fraction, α
0.793
0.848
0.884
Void Fraction, α
Fig. 6. Thermal performance of elliptical pin fin heat sink: (a) inline; and (b) staggered.
1.4
γ = 5.1 1.2
= 6.12 = 7.14
Rt,s, 0C/W
1
Circular Inline arrangement U∞ = 0.3 m/s
(b)
γ = 5.10 = 6.12 = 8.16
0.8
= 9.18
0.6
Circular Staggered arrangement U∞ = 0.3 m/s
= 7.14
= 8.16
0.8
1.2
1
Rt,s, 0C/W
(a)
= 9.18 0.6
0.4 0.4 0.2
0.2
0
0 0.534
0.702
0.793
0.848
0.884
0.534
0.702
Void Fraction, α
0.793
0.848
0.884
Void Fraction, α
Fig. 7. Thermal performance of circular pin fin heat sink: (a) inline; and (b) staggered.
13
Experimental Theoretical Experimental Theoretical
Staggered 12 11
Red = 150 γ = 8.16
10
Nud
to c = 8 for staggered circular and in both arrangements of elliptical pin fin heat sinks. It was found that a change in void fraction, a, has a major influence on the air side performance of heat sinks. At all aspect ratios in the range mentioned, the heat sinks offer minimum thermal resistance at void fraction close to 0.7. The theoretical model and experimental data confirms the optimum fin spacing in terms of void fraction. These results have considerable practical significance as it relates to the design of efficient finned heat sink. The physics behind these observed results is related with the fin density. As the fin spacing increases in longitudinal and transverse directions, the fin bundle void fraction, a, also increases. As the void fraction increases, for a fixed base area, the number of fins and, thus, the heat transfer area decreases. As the void fraction increases from 0.534 to 0.702, the convective heat transfer coefficient apparently increases faster than the fin surface area decrease, thus causing the thermal performance increase. When the void fraction increases much beyond a = 0.702, however, the convective heat transfer coefficient apparently no longer increases as fast as the fin surface area decreases, thus causing the thermal performance to drop off. When one compares between inline and staggered arrangement, the better air side performance is observed for staggered arrangement due to better intermixing of fluid and more fin surface area coming in contact with the cooling fluid, hence increasing the convective heat transfer coefficient.
9 8
Inline
7 6 5
0.534
0.702
0.793
0.848
0.884
Void Fraction, α Fig. 8. Influence of void fraction on thermal performance of elliptical pin fin heat sink, comparison with theoretical prediction.
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(a)
Circular, Inline
0.9
1
Circular, Inline
0.9
Circular, Staggered
Circular, Staggered
0.8
0.8
Elliptical, Inline
0.7
Elliptical, Inline
0.7
Elliptical, Staggered o Rt,s, C/W
Rt,s, oC/W
(b)
1
0.6 0.5 0.4
Elliptical, Staggered
0.6 0.5 0.4
0.3
0.3
U∞ = 0.2 m/s
0.2
0.2
α = 0.702
U∞ = 0.2 m/s
0.1
0.1
γ = 8.16
0
0 0.534
0.702
0.793
0.848
0.884
5.1
6.12
Void Fraction, α
7.14
8.16
9.18
Aspect Ratio, γ
Fig. 9. Comparative thermal performance of pin fin heat sinks: (a) influence of fin density; and (b) influence of fin aspect ratio.
15
1.2
Experimental Theoretical
13
Circular, Inline
Staggered
Circular, Staggered
Experimental
1
Theoretical
Elliptical, Inline
11
Nud
Red = 150 9
Elliptical, Staggered 0.8
α = 0.7
Rt,s, oC/W
α = 0.702 7
Inline
5
γ = 8.16
0.6
0.4 3
5.1
6.12
7.14
8.16
9.18
Aspect Ratio, γ Fig. 10. Influence of aspect ratio on thermal performance of elliptical pin fin heat sink, comparison with theoretical prediction.
0.2
For the optimum fin aspect ratio, the circular staggered configuration is 35% more effective than circular inline, the elliptical staggered is 63% more effective than elliptical inline, the elliptical inline is 24% more effective than circular inline and elliptical staggered is 50% more effective then circular staggered. The results imply that there is a considerable difference of flow patterns among these pin configurations. The Coanda effect may prevail when the air flow penetrates across the pin fin gap. The tendency of fluids to follow a curved surface is known as the Coanda effect. For airflow across the two adjacent fins, the gap flow may direct to right or left which is known as a deflection flow. The existence of deflection flow may change the general vortex structure behind pins, causing a better mixing and heat transfer performance. The deflection flow depends on the transverse and longitudinal spacing. By careful examination, it is clear that for loosely packed heat sinks, irrespective of pin profile, the vortices may form in absence of deflection flow. Notice that the presence of deflection flow pattern prevents the formation of vortices, thereby causing a significant increase of heat transfer coefficient. For the staggered arrangement, the heat transfer coefficients are all increased when the fin density is increased irrespective of the fin profile. Apparently the presence of staggered arrangement had greatly altered the flow pattern (see
0
0.1
0.2
0.3
0.4
0.5
U∞, m/s Fig. 11. Comparative thermal performance of pin fin heat sinks, influence of approach velocity.
Fig. 8). This can be evidently observed by typical flow visualization (e.g. Sparrow and Molki [12]) (see Figs. 9 and 11). 5.3.2. Influence of fin aspect ratio The experimental data were again used to carry out the parametric study to investigate the influence of fin height in terms of fin aspect ratio, , on the thermal performance of finned heat sink. The heat sinks with five different aspect ratios were tested and compared. Fig. 6b confirm that as the fin height increases, the thermal performance of heat sink increases both in inline and staggered arrangements in the range of aspect ratio, = 5.1–8.16. Thereafter, diminishing results are observed for the aspect ratio, ¼ 8:16—9:18 for elliptical profiled heat sink. No such diminishing effect is observed in case of circular profiled pin fin heat sink. This observation can be attributed to the temperature gradients
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P.A. Deshmukh, R.M. Warkhedkar / Experimental Thermal and Fluid Science 50 (2013) 61–68
35
Experimental Theoretical
30
Staggered
Experimental 25
Theoretical α = 0.7
Nud
20
γ = 8.16 15
Inline
10
5
0
50
100
150
200
250
Red Fig. 12. Influence of approach velocity on thermal performance of elliptical pin fin heat sink, comparison with theoretical prediction.
near to the tip of the pin fins. As the fin height increases beyond ¼ 8:16, the fin material resistance causes the pin temperature to drop off near to the tip causing the thermal performance to drop off. In case of elliptical profiled pin fin heat sink, the experimental data confirm the optimum fin height in terms of aspect ratio close to 8.2 for staggered arrangement. At the optimum value of aspect ratio and fin bundle void fraction, the thermal performance of staggered pin fin heat sink is 33% more than the inline pin fin heat sink for elliptical profile (see Fig. 10). 5.3.3. Influence of approach velocity At lower approach velocity U1 6 0.1 m/s, where the natural convection is dominating forced convection, a large variation is observed in thermal resistance for the various aspect ratios. In this range, the increase in fin height increases the heat transfer coefficient, thereby decreasing the thermal resistance. But for higher approach velocities U1 > 0.2 m/s, the influence of aspect ratio goes on diminishing both in inline and staggered arrangement. Fig. 7 compares the air side thermal performance of circular and elliptical pin fin heat sinks at optimum aspect ratio ¼ 8:16, and void fraction a = 0.702. In the approach velocity range studied, the staggered arrangement gives better air side performance by 25–51% than inline arrangement (see Fig. 12). 6. Summary and conclusions Comprehensive experimental investigations were carried out for the air side thermal performance of fully-shrouded, elliptical and circular pin fin heat sinks in mixed convection. The simple theoretical model, despite the complexity of the physical mechanism involved in this study, is used as a significant design tool to determine the influence of various design parameters on the effective thermal resistance of the heat sink. The parameters examined are pin aspect ratio, spacing along longitudinal and transverse directions, configuration, air flow and its orientation. The thermal performance characteristics are presented in terms of heat sink thermal resistance which is generally used as a design tool. The results are plotted to show the influence of various design parameters on heat sink performance. The results imply that as the fin spacing increases in longitudinal and transverse directions, the fin bundle void fraction, a, also
increases. As the void fraction increases, for a fixed base area, the number of fins and, thus, the heat transfer area decreases. As the void fraction increases, the convective heat transfer coefficient apparently increases faster than the fin surface area decrease, thus causing the thermal performance increase. When the void fraction increases much beyond a = 0.702, however, the convective heat transfer coefficient apparently no longer increases as fast as the fin surface area decreases, thus causing the thermal performance to drop off. When one compares between inline and staggered arrangement, the better air side performance is observed for staggered arrangement due to better intermixing of fluid and more fin surface area coming in contact with the cooling fluid, hence increasing the convective heat transfer coefficient. The results imply that there is a considerable difference of flow patterns among these pin configurations. The Coanda effect is prevailing when the air flow penetrates across the pin fin gap. The existence of deflection flow decides the general vortex structure behind pins, causing a better mixing and heat transfer performance. The deflection flow depends on the transverse and longitudinal spacing. By careful examination, it is clear that for loosely packed heat sinks, irrespective of pin profile, the vortices may form in absence of deflection flow. Notice that the presence of deflection flow pattern prevents the formation of vortices, thereby causing a significant increase of heat transfer coefficient. For the staggered arrangement, the heat transfer coefficients are all increased when the fin density is increased irrespective of the fin configuration. Apparently the presence of staggered arrangement had greatly altered the flow pattern. The study resulted in the successful development of generalized empirical correlations for elliptical profiled pin fin heat sinks having capability of predicting the influence of various physical, thermal and flow parameters on the air side performance. The experimental data have provided the good design insight for studying the influence of various heat sink, flow and arrangement parameters. The convective heat transfer coefficient can be determined from the generalized empirical correlations developed for elliptical pin fin heat sink. References [1] W.A. Scott, Cooling of Electronic Equipment, John Wiley and Sons, New York, USA, 1974. [2] C.L.Chapman, S. Lee, B.L. Schmidt, Thermal performance of an elliptical pin fin heat sink, in: 10th IEEE Semi-Therm, 1994, pp. 25–31. [3] W.A. Khan, R. Culham, M.M. Yovanovic, The role of fin geometry in heat sink performance, J. Heat Transfer 128 (2006) 324–330. [4] 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, Int. J. Heat Mass Transfer 50 (2007) 4661–4667. [5] H.R. Seyf, M. Layeghi, Numerical analysis of convective heat transfer from an elliptic pin fin heat sink with and without metal foam insert, J. Heat Transfer 132 (2010) 071401-1–071401-9. [6] I. Pop, D.B. Ingham, Convective Heat Transfer- Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, 2001. [7] P.A. Deshmukh, R.M. Warkhedkar, Thermal performance of pin fin heat sinks – a review of literature, Int. Rev. Mech. Eng. 5 (4) (2011) 726–732. [8] C.J. Kobus, T. Oshio, Development of a theoretical model for predicting the thermal performance characteristics of a vertical pin-fin array heat sink under combined forced and natural convection with impinging flow, Int. J. Heat Mass Transfer 48 (2005) 1053–1063. [9] C.J. Kobus, T. Oshio, Predicting the thermal performance characteristics of staggered vertical pin fin array heat sinks under combined mode radiation and mixed convection with impinging flow, Int. J. Heat Mass Transfer 48 (2005) 2684–2696. [10] G. Taguchi, System of experimental design, Qual. Resources 2 (1987) 1173. [11] M. Tahat, Z.H. Kodah, B.A. Jarrah, S.D. Probert, Heat transfers from pin-fin arrays experiencing forced convection, Appl. Energy 67 (2000) 419–442. [12] E.M. Sparrow, M. Molki, Effect of a missing cylinder on heat transfer and fluid flow in an array of cylinders in cross-flow, Int. J. Heat Mass Transfer 25 (1982) 449–456.