Experimental investigation of the effects of horizontally oriented vertical
sinusoidal wavy fins on heat transfer performance in case of natural
convection
Aziz Hakan Altun
a,⇑, Orkun Ziylan
ba
Department of Airframe and Powerplant Maintenance, Selçuk University, 42250 Konya, Turkey
b
Mechanical Engineering Department, Institute of Science, Necmettin Erbakan University, Konya, Turkey
a r t i c l e i n f o
Article history:Received 10 January 2019
Received in revised form 1 April 2019 Accepted 5 May 2019
Available online 18 May 2019 Keywords:
Electronics cooling Finned surfaces
Heat transfer enhancement Natural convection heat transfer Radiation heat transfer Wavy fins
a b s t r a c t
In this work, natural convection heat transfer in horizontally oriented, vertical sinusoidal wavy fins, involving radiation heat transfer were investigated experimentally. Experiments were done with wavy fins having three different amplitudes, namely H/30, H/15 and H/10, with different heater power inputs. Results were compared to the results of a rectangular finned plate and also a reference horizontal base plate. Power of the heater was changed from 1.02 W to a maximum of 32.06 W and totally 69 experi-ments were done for 5 test sets. Results indicate that, heat transfer enhancement is better with wavy fins than with the rectangular fins. On the other hand, after a certain value of the wave amplitude the increase in the amplitude negatively affecting the natural convection due to the blockage of fluid motion. The results also indicate that, an important part of total heat transfer is by radiation and should be considered in natural convection studies of finned surface heat sinks.
Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction
For systems such as energy conversion, heating-cooling, and electronic devices, the best way to transfer heat in order to achieve energy and cost efficiency has been researched for relatively a long time. Especially in recent years, the transfer of heat from electron-ics and computer microprocessors and similar circuit elements has become very important for the performance of the devices. This sit-uation led researchers to investigate the natural convection heat sinks that are effective, inherently simple, reliable, and low long-term cost for cooling electronics components. In general, the effects of arrays, spacing and plate-fin configuration on natural convection of heat sinks were investigated in these studies in order to increase heat transfer coefficient.
From these studies on natural convection in the literature, Star-ner and McManus[1]experimentally investigated the average heat transfer coefficients for four different rectangular-fin arrays. The fin arrays were oriented in three different angles which are base vertical, 45 degrees, and horizontal. Harahap and McManus[2], have fin arrays positioned with the base oriented horizontally. In that study of eight different fin height and spacing, they state that the fin height is the most important geometric parameter. Another
experimental study on natural convection of fins was carried out by Jones and Smith [3]. In the experimental study, temperature gradients in the fins were observed by using the interferometer technique. As a result, they give two empirical correlations for optimizing the fin spacing. Sparrow and Prakash [4], made a numerical study to compare the heat transfer rate of a staggered array of discrete vertical plates with an array of continuous parallel vertical plates having the same surface area in terms of natural convection. On the vertical plates, they showed the effect of geo-metric dimensions in heat transfer enhancement. The steady-state natural convective cooling of horizontally-based vertical rectangular fins was investigated experimentally by Naik et al.
[5]. The fins were in close proximity to an adiabatic horizontal shroud, situated adjacent to and above the horizontal fin-tips. They stated that the maximum heat transfer can be achieved depending on the fin spacing in the results. Incropera[6]carried out extensive literature survey on heat transfer with natural convection in the cooling of electronic devices. He summarized the works on the channel types used for cooling the electronic equipment by giving 152 references. Ko and Leung [7] experimentally measured the heat dissipation from an array of stainless-steel, vertical rectangu-lar fins, under natural-convection conditions. They report the opti-mal fin spacing for the vertically-based finned system while the excess temperature is changing from 20 K to 40 K. Karagiozis et al.[8], experimentally examined the heat transfer by natural
https://doi.org/10.1016/j.ijheatmasstransfer.2019.05.009
0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
⇑ Corresponding author.
E-mail address:ahaltun@selcuk.edu.tr(A.H. Altun).
Contents lists available atScienceDirect
International Journal of Heat and Mass Transfer
convection from isothermal triangular-sectioned fins. They suggest correlations for Nusselt number, based on empirical data. Yüncü and Anbar [9]experimentally examined natural convection heat transfer for different geometrical dimensions and rectangular fin arrays on horizontal base by considering the radiation effect. They state that the heat transferred from the fins is highly dependent on the fin spacing to fin height ratio and number of fins. Harahap and Setio[10]experimentally examined and obtained new relations for heat dissipation from five duralumin vertical rectangular fin-arrays, while the base was horizontally oriented. Kulkarni and Das[11]investigated thermal models for cooling microscale elec-tronic processor chips through forced and natural convection heat sinks by considering the radiation effect. Sertkaya et al.[12] inves-tigated the heat transfer by considering the effect of radiation heat transfer from the pin-finned surface oriented at different angles. They found that the pins increased the heat transfer significantly and the heat transfer decreased with the increase of the angle rel-ative to the vertical axis. Yu et al.[13]examined heat transfer in radial heat sink considering natural convection and radiation by experimental and numerical means. They performed experiments using three radial heat sinks with different emissivity values. They show that the radiation amount in total heat transfer is 27% for dif-ferent emissivity values. Feng et al.[14]investigated a novel cross-fin heat sink for natural convective heat transfer enhancement with a rather simple geometry by considering radiation heat trans-fer. They reported that the proposed cross-fin heat sink provides a practical alternative to the widely adopted plate-fin heat sinks. Jeon and Byon[15] investigated numerically the effect of dual-height configuration, fin spacing and channel length on the ther-mal performance of the heat sink. They point out that the therther-mal performance of dual height heat sink decreases as the secondary fin height decreases. Zaretabar et al.[16]investigated a numerical simulation of heat transfer in a heat sink installed on the transis-torized square chip of a computer. Heat sink geometry is made from different materials such as aluminum and copper with vari-ous heights. They obtained Nusselt numbers and heat transfer coefficients for different air velocities. Kwon et al.[17]analytically and experimentally optimized horizontally oriented radial plate-fin heat sinks in natural convection. A new empirical correlation is presented for the radial plate-fin heat sink. They optimized this new correlation according to fin thickness (t), fin length (L), and number of fins (n).
In this study, natural convection heat transfer, involving radia-tion heat transfer in vertical wavy (sinusoidal) fins attached on a horizontal base plate is investigated experimentally. This is a new heat sink design for improving performances of cooling equip-ment such as electronic devices in which geometric dimensions gained more importance recently. Rectangular fin forms are con-verted to wavy fin forms which have different amplitude values while fin height is fixed. Fin surface area is enlarged by increasing the amplitude value of the wavy fins and hence to obtain more flow disturbance is aimed. Heat transfer enhancement with wavy fins having different amplitude values is compared with the rect-angular fins.
2. Experimental setup
Schematic of experimental setup used in this study is shown in
Fig. 1. The setup is mainly consisted of the insulated casing box, instrumentation for measurement of base plate temperature for rectangular and wavy fins, and ambient temperature, heater, cur-rent regulator dimmers, thermocouples, digital multi-meter, and data-logger. The laboratory environment is protected from air flow and sunlight.
In the experimental setup, the electric energy which is adjusted by means of a dimmer is transferred to heater. The heating power is calculated by multiplying the measured current and voltage.
Base plate surface temperatures are measured with K-type ther-mocouples that are placed in holes drilled at 4 different points near the surface as shown inFig. 2. Ambient temperature is also mea-sured with a K type thermocouple. The temperature values taken from these thermocouples are transferred to the computer by a data-logger.
The base plates, made of ‘‘Al 5083” quality aluminum, used in the experiment have 90 58 8 mm dimensions. As shown in
Fig. 1, the plates are heated from the base with an electrical resis-tance. A copper plate is placed underneath the base to ensure uni-form heat distribution between the heater and the base plate. In order to increase the adiabatic system requirements, the plates are placed in a casing box insulated with glass wool and the top cover is a heat-resistant glass-fiber composite sheet. The dimen-sions of the casing box were determined as 300 200 300 mm by considering similar studies in the literature[9].
h convection heat transfer coefficient (W/m K) k thermal conductivity (W/m K)
L fin base plate length (mm)
l length (mm) n number of fins Nu Nusselt number p period length (mm) Pr Prandtl number Q heat transfer (W) Ra Rayleigh number S fin spacing (mm) T temperature (K) t fin thickness (mm)
r
Stefan-Boltzmann constant (=5.67 108W/m2 K4 )t
kinematic viscosity (m2/s) Subscripts a arc b base plate con convection rad radiation tot total 1 ambient f film 1 surface 1 2 surface 2During the experiments, two different fin types were used, rect-angular and sinusoidal wavy with three different amplitude values, and having the same fin heights with the rectangular fin. Rectangu-lar fins were utilized in order to constitute a reference for sinu-soidal wavy fins. Schematics of the rectangular and wavy fins are shown inFigs. 3 and 4and related dimensions are given inTables 1 and 2. The amplitude values inTable 2were chosen considering
the distance between fins. Considering that fins with higher ampli-tude values would block fluid flow, values higher than H/10 were not investigated. Fins were also manufactured of ‘‘Al 5083” alu-minum by using an electrical discharge machining method. Base plate, rectangular and sinusoidal wavy fin-arrays were black ano-dized and casing box was covered with black paint in order to approach blackbody radiation.
The experiments were carried out for two-period and three dif-ferent amplitudes sinusoidal wavy fins. In order to compare the thermal performance of these fins, experiments were also made for plain base plate and for rectangular fins. During the experi-ments, the fins were placed horizontally upwards. Heater power was changed with about 2 W increments. 15 different heating powers for finned plates and 10 different heating powers for the base plate without fin were set.
3. Data reduction
The experiments were repeated for base plate without fin, and with rectangular and different amplitude wavy fins. First, the results for the base plate without fin were obtained and considered as reference for the other experiments. In the experiments, the ambient temperature and plate surface temperature values were measured and heat transfer characteristics are calculated from the following equations[18].
1. Carrier stand and Casing box 9. Table
2. Styrofoam (insulation material) 10. Volt, Watt and Ammeter 3. Glass wool (insulation material) 11. Dimmer
4. Testzone 12.FinSection 5. Composite cover 13. Base plate with fins 6. Thermocouples 14.Copperplate 7. Datalogger 15.Heater 8. Computer 16.Fiberglass
Fig. 1. Schematics of the experimental setup.
Fig. 2. Locations of the thermocouples.
Convection heat transfer coefficient and Nusselt number can be calculated as; h¼ Qconv AbðTb T1Þ ð1Þ and Nu¼ QconvL Abk Tð b T1Þ ð2Þ
The independent variable of the problem is the temperature dif-ference, Tb T1, and is represented via the Rayleigh number; Ra¼ GrPr ¼gb Tð b T1ÞL3Pr
v
2 ð3ÞHere, the coefficient of thermal expansion can be found as;
b ¼T1
f ð4Þ
All thermo-physical properties of air are evaluated at the film temperature which is defined as;
Tf ¼
Tbþ T1
2 ð5Þ
Assuming that conduction heat loss is negligible through the insulated sides of the base plates, the convection part of the total heat transfer from the surfaces may be written as;
Qconv¼ Qtot Qrad ð6Þ
where Qtotis equal to the electrical power of the heaters. The
radi-ation heat transfer from the surfaces can be calculated as;
Qrad¼ Fð ÞF
e
12r
A T4b T 4 1
ð7Þ
For determining the view factor, a modular analysis, similar to as in Ref.[12], is made for the fin configurations used in the exper-iments with the following assumptions.
i. All the test and surrounding surfaces were assumed having as black body emissivity, ið:e:;
e
¼ 1Þ,ii. The fins are isothermal at temperature Tb,
iii. Surrounding surfaces are isothermal and the temperature is equal to the surrounding air temperature,
iv. Surrounding air is a non-participating medium.
Additionally, in the modular analysis the arc lengths of the wavy fins were used as if they are rectangular.
The fins and the base plate were made of aluminum due to high thermal conductivity, easy machinability, receptiveness to a dur-able and high-emissivity surface coating properties of aluminum.
Actually, black-anodized aluminum has typical emissivity values of 0.76–0.82[18,19,20]. However, mutual reflections between fins lead to the cavity effect making this value to be increased almost to the value of blackbody[18,19].
Part of the transferred heat from the finned base plate by radi-ation remains in between the solid surfaces of the heat sink and the other part is transferred to the surrounding environment. Radia-tion heat transfer occurs in 4 direcRadia-tions, namely; from the base plate to the fins; from the fins to the fins; from the fins to the base plate and finally from the fins and base plate to the surroundings. Then;
Q1-1 Part of the radiation heat transfer remaining in the heat
sink
Q1-2Part of the radiation heat transfer which is transferred from
the finned surface to the surroundings.
The view factors may be expressed simply as;
F11þ F12¼ 1
Here, 1 denotes the surfaces of assembly (fins and the base plate) and 2 does the surrounding surfaces. In order to calculate F11,
which is the part of emitted radiation captured by the surface itself, the fin plate is divided into modular sections as shown inFig. 5. Modules in these sections can be considered as two perpendicular plates in the form of X-Y and Z-Y surfaces and parallel plates in the form of X-Z surfaces in the figure. Since all dimensions and dis-tances between these surfaces are known, view factors are deter-mined using diagrams and equations that are proposed by Incropera and DeWitt [20]. F1-2values are calculated as 0.3738,
0.3596, 0.3653 and 0.3616 respectively for the rectangular, H/30, H/15 and H/10 amplitude wavy fins. The details of the calculations are given in Ziylan[21].
4. Uncertainty analysis
In the present study, uncertainty analysis of Nusselt Number as the final parameter was done. The effect of the errors on the Nus-selt Number during the measurements was determined by the equation of uncertainty analysis proposed by Kline and McClintock
[22]. By following the procedure for uncertainty analysis, first uncertainties for radiation and convection heat transfer were cal-culated, and then uncertainty value of Nusselt Number was calculated.
In the calculations, the error values for measurements were taken as 0.2% for ambient temperature and mean base plate tem-peratures, 2.5% for electrical current and 1.2% for voltage. Accord-ingly, uncertainty of radiation, convection and Nusselt Number were calculated as 0.38%, 1.1% and 7% respectively.
Fin base plate length L (mm)
Fin length W (mm)
Fin base plate thickness M (mm) Fin height H (mm) Fin spacing S (mm) Fin thickness t (mm) Number of fins n Period length p (mm) Amplitude a (mm) Arc length la (mm) 90 58 5 30 10 1.5 8 H/2 H/30 31.15 90 58 5 30 10 1.5 8 H/2 H/15 33.84 90 58 5 30 10 1.5 8 H/2 H/10 36.93
5. Results and discussions
The results obtained for horizontal base plate are compared to the correlation given by Mc Adams[23] for different commonly used characteristic lengths inFig. 6. As shown in the Figure, a good agreement is obtained. In this study, the characteristic length, L*, is taken as the length of the base plate, L, which is the most common case in the literature for finned surfaces.
InFig. 7, variations of Nusselt numbers with Rayleigh numbers are given for all the finned and unfinned plates. For the purpose of comparison, a curve obtained from the correlation proposed by Hararap and Setio[10]for rectangular fins, with similar geometric parameters, is also inserted in this Figure. It is seen that, the exper-imental results obtained for rectangular fins are in fairly good agreement with the results of the correlation.
The first result to be drawn from this figure is that, Nusselt numbers are too much higher in finned plates than for the unfinned plate. It is also clearly shown that, wavy fins increased heat transfer more than the rectangular fins. Meanwhile, Nusselt number curves show only a little increase with Rayleigh number for unfinned plate, while this increase is quite high in finned plates. The highest Nusselt number values are seen for H/30 amplitude
wavy fin, especially at values of Rayleigh numbers higher than about 1E106. Therefore, heat transfer is decreasing with increasing
the wave amplitudes of the fins. In fact, for high values of Rayleigh
Fig. 5. Modular geometries for view factor analysis.
Fig. 6. Comparison of experimental results for base plate with McAdams correlation[23].
Fig. 7. Variation of Nusselt number with Rayleigh number for rectangular and wavy fins.
numbers, Nusselt values for H/10 amplitude wavy fin are lower than the values of the rectangular fins. This may be explained by the fact that, the increased amplitude decreases the space between the adjacent fins and results the blocking of the fluid motion. At the same time, after a certain value, the increase in lengths of the fins does not have enough impact on the effectiveness of the fins.
Figs. 8and9show variations of the percentages of radiation and convection in total heat transfer by Rayleigh numbers, respec-tively. When these two figures are analyzed together, it is shown that, the percentage of radiation is much higher in unfinned plate than in the finned plates. This is due to the fact that, part of radia-tion in finned plates remains in itself because of mutual reflecradia-tions and only some goes to the surroundings. Since, these mutual reflections are increasing in wavy fins, the part of radiation is also high in rectangular finned plate than wavy finned plates. Another finding is that, the percentage radiation in total heat transfer is also increasing with the increase of amplitude in wavy finned plates. The reason for that is probably the blockage of fluid motion and decrease in natural convection in wavy finned plates having high amplitude, as explained before. The percentage of radiation in wavy finned plates is changing from 25% to 50%, while this ratio is between 30% and 60% in rectangular finned plate. The percent-age of radiation in finned plates is decreasing with Rayleigh until a certain value and then almost does not change with Rayleigh number. On the other hand, the percentage of radiation and there-fore of natural convection, remains almost constant with Rayleigh number in unfinned plate. These results imply that, in natural con-vection the effect of radiation should be taken into consideration in the finned surface design in heat sink applications.
gular fins.
Heat transfer enhancement is decreasing with increasing wave amplitude of the fins. Increased amplitude decreases the space between the adjacent fins and results the blocking of fluid motion.
Nusselt number values increase slightly with Rayleigh number for unfinned plate, while this increase is quite high in finned plates.
The percentage of radiation in total heat transfer in wavy finned plates is changing from 25% to 50%, and is also increasing with the increase of amplitude. The percentage of radiation is decreasing with Rayleigh number until a certain value, and then almost does not change with Rayleigh number.
In natural convection the effect of radiation should be taken into consideration in the finned surface design of heat sink applications.
Declaration of Competing Interest None.
References
[1] K.E. Starner, H.N. McManus, An experimental investigation of free-convection heat transfer from rectangular-fin arrays, J. Heat Transf. 85 (3) (1963) 273–277,
https://doi.org/10.1115/1.3686097.
[2] F. Harahap, H.N. McManus, Natural convection heat transfer from horizontal rectangular fin arrays, J. Heat Transf. 89 (1) (1967) 32–38,https://doi.org/ 10.1115/1.3614318.
[3] C.D. Jones, L.F. Smith, Optimum arrangement of rectangular fins on horizontal surfaces for free-convection heat transfer, J. Heat Transf. 92 (1) (1970) 6–10,
https://doi.org/10.1115/1.3449648.
[4] E.M. Sparrow, C. Prakash, Enhancement of natural convectıon heat transfer by a staggered array of discrete vertıcal plates, J. Heat Transf. 102 (2) (1980) 215– 220,https://doi.org/10.1115/1.3244263.
[5] S. Naik, S.D. Probert, C.I. Wood, Natural-convection characteristics of a horizontally-based vertical rectangular fin-array in the presence of a shroud, Appl. Energy 28 (4) (1987) 295–319,https://doi.org/10.1016/0306-2619(87) 90033-X.
[6] F.P. Incropera, Convection heat transfer in electronic equipment cooling, J. Heat Transf. 110 (1998) 1097–1111,https://doi.org/10.1115/1.3250613.
[7] Y.M. Ko, C.W. Leung, S.D. Probert, Steady-state free-convective cooling of heat exchangers with vertical rectangular fins: effect of fin material, Appl. Energy 34 (3) (1989) 181–191,https://doi.org/10.1016/0306-2619(89)90045-7. [8] A. Karagiozis, G.D. Raithby, K.T. Hollands, Natural convection heat transfer
from arrays of isothermal triangular fins in air, J. Heat Transf. 116 (1) (1994) 105–110,https://doi.org/10.1115/1.2910842.
[9] H. Yüncü, G. Anbar, An experimental investigation on performance of rectangular fins on a horizontal base in free convection heat transfer, Heat Mass Transf. 33 (1998) 507–514,https://doi.org/10.1007/s002310050222. [10] F. Harahap, D. Setio, Correlation for heat dissipation and natural convection
heat-transfer from horizontally based, vertically-finned arrays, Appl. Energy 69 (1) (2001) 29–38,https://doi.org/10.1016/S0306-2619(00)00073-8. [11] D.P. Kulkarni, D.K. Das, Analytical and numerical studies on microscale heat
sinks for electronic applications, Appl. Therm. Eng. 25 (2005) 2432–2449,
https://doi.org/10.1016/j.applthermaleng.2004.12.010.
[12] A.A. Sertkaya, Sß. Bilir, S. Kargıcı, Experimental investigation of the effects of orientation angle on heat transfer performance of pin-finned surfaces in natural convection, Energy 36 (2011) 1513–1517,https://doi.org/10.1016/j. energy.2011.01.014.
[13] S.H. Yu, D. Jang, K.S. Lee, Effect of radiation in a radial heat sink under natural convection, Int. J. Heat Mass Transf. 55 (2012) 505–509, https://doi.org/ 10.1016/j.ijheatmasstransfer.2011.09.026.
[14] S. Feng, M. Shi, H. Yan, S. Sun, F. Li, T.J. Lu, Natural convection in a cross-fin heat sink, Appl. Therm. Eng. 132 (2018) 30–37, https://doi.org/10.1016/j. applthermaleng.2017.12.049.
Fig. 8. Percentage of radiation heat transfer in total heat transfer.
[15] D. Jeon, C. Byon, Thermal performance of plate fin heat sinks with dual-height fins subject to natural convection, Int. J. Heat Mass Transf. 113 (2017) 1086– 1092,https://doi.org/10.1016/j.ijheatmasstransfer.2017.06.031.
[16] M. Zaretabar, H. Asadian, D.D. Ganji, Numerical simulation of heat sink cooling in the mainboard chip of a computer with temperature dependent thermal conductivity, Appl. Therm. Eng. 130 (2018) 1450–1459, https://doi.org/ 10.1016/j.applthermaleng.2017.10.127.
[17] H. Kwon, Y. Joo, S.J. Kim, Analytic approach to thermal optimization of horizontally oriented radial plate-fin heat sinks in natural convection, Energy Convers. Manage. 156 (2018) 555–567, https://doi.org/10.1016/j. enconman.2017.11.076.
[18] E.M. Sparrow, S.B. Vemuri, Natural convection/radiation heat transfer from highly populated pin fin arrays, J. Heat Transf. 107 (1) (1985) 190–197,https:// doi.org/10.1115/1.3247377.
[19] E.M. Sparrow, S.B. Vemuri, Orientation effects on natural convection / radiation heat transfer from highly populated pin - fin arrays, Int. J. Heat Mass Transf. 29 (3) (1986) 359–368,https://doi.org/10.1016/0017-9310(86) 90206-1.
[20] F.P. Incopera, P.D. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, sixth ed., John Wiley & Sons, 2007, pp. 811–848.
[21] O. Ziylan, Investigatıon of The Effects of corrugated fins on flat plates in free convection heat transfer, M.Sc, Necmettin Erbakan University, 2018. [22]S.J. Kline, F.A. McClintock, Describing uncertainties in single sample
experiments, Mech. Eng. 75 (1953) 385–392.
[23]W.H. McAdams, Heat Transmissions, third ed., McGraw Hill, New York, 1954, pp. 237–251.
