Experimental Study of Heat Transfer from Horizontal Rectangular Fins with Perforations under Natural Convection

Experimental Study of Heat Transfer from Horizontal Rectangular Fins with Perforations under Natural Convection

Mr. Harshad N. Deshpande Research Scholar

Dept of Mechanical Engg PES MCOE Pune, India

Prof. S. G. Taji Assistant Professor

Dept of Mechanical Engg PES MCOE Pune, India

AbstractIn this paper experimental study of heat transfer from horizontal rectangular fins with perforations under natural convection is presented. The parameters varied for the experiment are heater inputs (Q= 25-100 W), even fin spacing (S

= 2-14 mm) by keeping fin length, fin height and width of array constant. The measurement of convective heat transfer is very critical and depends on estimation of average heat transfer coefficient. The experimentation results are presented in terms of various heat transfer parameters such as average heat transfer coefficient (ha), base heat transfer coefficient (hb). Dimensionless parameters such average Nusselt number (Nua), base Nusselt number (Nub), and Rayleigh number (Ra). The natural convection results are compared with results of plain Horizontal Rectangular Fin Array (HRFA) from previous researcher study. It is observed that there is a significant effect of variation in fin spacing on average and base heat transfer coefficients. For natural convection study the optimum fin spacing is found to be 10 mm. For perforated fins ha is enhanced by about 15% as compared to plain horizontal fins.

Keywords Perforated Horizontal Rectangular Fins, Natural Convection, Heat Transfer

1. INTRODUCTION

   Thermal management of electronic components is a current issue which is increasingly gaining importance in line with the advances in technology. The consistency of the electronics of a system is a major factor in the overall reliability of the system. The tininess of electronic systems has resulted in a remarkable increase in the amount of heat generated per unit volume. The high rates of heat generation result in high operating temperatures for electronic equipment, which compromises its safety and reliability. The failure rate of electronic equipment increases exponentially with temperature. Heat removal in an efficient way is necessary in order to maintain reliable operation of electronic devices. The main purpose of improving the thermal control of electronic systems is to increase cooling capacity. Extended surfaces or fins are in common use in the electronic industry and serve to enhance the thermal capability of natural convective cooling with air.

   Starner K.E. et.al [1] experimentally investigated rectangular fin arrays for horizontal and vertical orientation under natural convection firstly. They had used four fin arrays

   sets positioned with base vertical, at 45° and horizontal to determine average heat transfer coefficients. Harahap F et.al

   1. investigated the horizontal fin arrays to obtain relevant dimensionless parameters, the governing equations of continuity, momentum and energy were examined on the basis of similarity and a correlation was proposed. Jones C.D. et.al.

   2. experimentally determined average heat transfer coefficients for horizontal arrays over a wide range of spacing. A simplified correlation for average heat transfer coefficient for all the arrays tested was suggested. The following important findings reported as the heat transfer rate is maximum for an optimum fin spacing exists at the given fin height, length and T and the average heat transfer coefficient increases with spacing and asymptotically approaches the flat plate value for large spacing. Mannan K.D. [4] determined the effect of all related geometrical parameters of the fin array on its performance. The wide range of length: 127 mm < L < 508 mm. Height: 25.4 mm < H < 101.6 mm and spacing: 4.8 mm < S < 28.6 mm, with T varying from 39° C to 156° C. Some important inferences of authors study are: the fin spacing is most important geometrical parameter and from a given height, length and temperature difference, an optimum spacing exists for which the heat transfer rate is maximum. The fin length is another important geometrical parameter. Short fin arrays perform better than long arrays, due to prevailing single chimney flow pattern up to L/H < 5. Sane

   N.K. et.al [5] solved the governing equations neglecting the velocity component normal to the fin flats in the case of single chimney flow problem and employing vorticity stream function formulation. They concluded that beyond certain values of S/Hon lower side, the single chimney flow pattern ceases to exist due to choking effect on the entering side flow. They proved that the point of maximum heat transfer lies at the transition from single chimney flow pattern to sliding chimney and the corresponding S/H becomes the optimum spacing. Dayan.et.al. [6] studied a horizontal rectangular hot fin array under natural convection analytically, numerically and experimentally. Optimum analyses were conducted by author to determine the minimum fin height that provides the necessary cooling capability of a specified array base area. It is proved that the optimal fin spacing varies within a narrow range which depends primarily on the array length. Sane S.S. et.al [7].investigated the horizontal rectangular fin array under

   natural convection by providing notch at the centre and suggested the selection of optimum notch dimensions, and spacing by analyzing variety of fin arrangements for performance improvement. It is observed that total heat flux as well as the heat transfer coefficient increase as the notch depth increases. This analysis reveals that the recommended single chimney flow pattern is maintained for the notched fin arrays. The performance of notched fin arrays is 30 to 50% superior than corresponding unnotched arrays, in terms of average heat transfer coefficient. Suyawanshi S.D. et.al [8] experimentally investigated normal and inverted notched fin arrays (INFAs) for variation in fin spacing, and %of area removed in form of inverted notch are the parameters. It is concluded that the average heat transfer coefficient for INFAs is nearly 30 to 40

   % higher as compared to normal array. The value of ha increases with spacing giving an optimum value at about S=6mm. When single chimney flow pattern is present, in mid channel stagnant bottom portion becomes ineffective. Modified array is designed in inverted notched form and that has proved to be successful retaining single chimney together with removal of ineffective fin flat portion. Pawar A.L. et.al

   [9] experimentally investigated the perforated horizontal fin array under free convection. The authors concluded that the values of ha are 1520% higher for PFAs giving better performance, for smaller spacing, increment in ha is small due to the flow constriction effect . The spacing giving an optimum value at about S=6 mm. Single chimney flow pattern is retained in PFAAs also with a wider chimney zone. The modified array is designed in perforated form and that has proved to be successful retaining single chimney together with the removal of ineffective fin flat portion.

2. EXPERIMENTATION

   For experimentation seven arrays with even fin spacing 2 to 14 mm are tested. Horizontal Rectangular fins plate of length 205 mm, height 70 mm, spacers of height 30 mm and thickness 2 mm with perforations in triangular form at the fin centre are used in the assembly as shown in Fig 1. Fin arrays of 100mm are formed by assembling fins and separate spacer pieces by tie bolts. The minimum air gap between the fins and spacers is ensured by proper tightening of the nuts. Te fin array sides are insulated with Bakelite and base is housed in siporex insulating block (1200 mm × 240 mm × 220 mm) in order to reduce heat loss from bottom and sides. Fin array configuration and mounting is shown in Fig 2. For temperature measurement seventeen copper constantan thermocouples are mounted at proper locations. The direct metal to metal contact between thermocouples and fin surface is ensured. Thermocouples are cut from same spool of wire and the error in the temperature is adjusted. Eight thermocouples are used to measure fin surface temperature, two are used to measure base fin temperatures, four thermocouples are also provided in siporex block temperature measurement and two thermocouples are Bakelite temperature measurement.

   Fig.1. Details of Fin Flat used for Experimental Analysis

   Fig.2. Photograph of Fin Array Used for Experimental Analysis

   Fig.3. Photograph of Digital Wattmeter and Digital Temperature Indicator

   Digital Wattmeter is used to measure heater input of three cartridge heaters. The digital wattmeter is calibrated and direct value in Watt is displayed by it.

   2.1 Heat Loss Calculations

   The measurement of convective heat transfer is very vital and depends on estimation of average heat transfer coefficient. The evaluation of average heat transfer is accurate if the losses calculated are perfect. The heat transfer from array is mainly by convection in addition to various other losses. The assembly is placed in siporex block to reduce loss of heat by conduction. An attempt was made to measure these losses mainly conduction loss from bottom and sides of horizontal rectangular fin array. The end fins have bakelite strips to reduce end loss. The radiation losses from array and bakelite end plates are also measure. The estimation of conduction loss from bottom and side, radiation loss form bakelite ends and fin array. As mentioned in above points the set up has provisions for measurements of temperature at bottom siporex and side siporex with respect to fin array for conduction loss estimation. For calculation of radiation losses

   temperatures of end bakellite plate and fin surfaces are noted. The conduction and radiation losses are calculated as above method.

3. RESULTS AND DISCUSSION

   The experimental investigation carried out for horizontal rectangular fin array with perforations in triangular form under natural convection. The objective of present chapter is to investigate possible heat transfer characteristics. The results obtained from the observations for both experiments are presented here in the form of graphs. Results obtained are compared with previous investigators. The fin spacing, heater input and air flow velocity are the key parameters of an experimental investigation.

   The results obtained for different fin spacing (S = 2, 4, 6, 8, 10, 12 and 14mm), for heater input (Q = 25, 50, 75,

   100 W) under natural convection. The heater inputs are selected so as to achieve actual working range temperature of the application for which the array can be used.

   The heat is supplied to fins by cartridge heater; majority of heat transfer is by convection (Qconv). Heat losses are also considered as per section 2.1 to determine Qconv hence heat transfer coefficient more precisely. The heat loss through base and side of the siporex block by conduction is noted as Qcond and heat loss for fin array and bakelite ends by radiation is noted as Qrad. The results are presented in terms of various heat transfer parameters such as average heat transfer coefficient (ha), base heat transfer coefficient (hb). Dimensionless parameters such average Nusselt number (Nua), base Nusselt number (Nub), Rayleigh number (Ra) For determination dimensionless parameters fluid properties such as thermal conductivity, kinematic viscosity of air and

   Fig 4 shows the effect of fin spacing S variation on average convective heat transfer ha with various heater input. As the fin spacing increases, the average heat transfer coefficient (ha) increases for the fin array up to maximum value at S = 10 mm then and then (ha) decreases with the increase in fin spacing (S = 12 and 14 mm). At starting, ha values are very small for S = 2 and 4 mm 1.43 to 2.72 W/m2K at 100W. The highest value of ha is 8.98 W/m2K at 100W and 10 mm fin spacing. The increasing trend of ha is steep up to spacing that about 10 mm after which ha is gradually decreases to 8.52 W/m2K for S=14 mm and 100 W. This trend is same for all heater inputs.

   For smaller fin spacing flow between fin spacing get blocked hence less fin surface area is effective in convective heat transfer hence small value of ha. Whereas, for larger fin spacing, the fluid through the fin channel is flowing more freely without fin array interference so value of ha increases. But this rise in ha with increase in fin spacing is up to particular spacing beyond that air moves out without contacting fin surface so temperature increases hence ha decreases. Thus, there is a significant effect of variation in fin spacing on average heat transfer coefficient.

   3.2 Effect of Fin Spacing (S) on Base Heat Transfer Coefficient (hb)

   70

   60

   hb (W/m2-K)

   50

   volumetric thermal expansion coefficient are evaluated at mean film temperature Tmf.

   3.1 Effect of Fin Spacing (S) on Average Heat Transfer Coefficient (ha)

   40

   30

   20

   0 2 4 6 8 10 12 14 16

   S (mm)

   Q=25 W Q=50 W Q=75 W Q=100 W

   10

   8

   6

   4

   2

   0

   Fig.5. Effect of Fin Spacing (S) on Base Heat Transfer Coefficient (hb)

   Q= 25 W

   Q=50 W Q=75 W Q=100 W

   ha (W/m2-K)

   Base heat transfer coefficient (hb) is also the significant parameter in study of the convection heat transfer. It can be determined as dividing convection heat transfer Qconv by product of base area for heat transfer and temperature difference between average fin surfaces, ambient. The base area for heat transfer remains constant with increase in fin spacing.

   0 2 4

   6 8

   10 12 14 16

   S (mm)

   Fig.4. Effect of Fin Spacing (S) on Average Heat Transfer Coefficient (ha)

   Average heat transfer coefficient (ha) is important parameter in the convection heat transfer study. It can be determined as dividing convection heat transfer (Qconv) by product of exposed fin area and temperature difference between average fin surfaces, ambient. The exposed area deceases with increase in fin spacing.

   Fig 5 shows the effect of variation in fin spacing S on base convective heat transfer (hb) with various heater input. As the fin spacing increases, the base heat transfer coefficient hb increases for the fin array up to maximum value at S = 10 mm then and then hb decreases sharply with the increase in fin spacing (S = 12 and 14 mm). The hb values for S = 2 and 4 mm varies from 29.05 to 36.74 W/m2K for 100W. The highest value of hb is 66.92 W/m2K at 100W and 10 mm fin spacing. The increasing trend is steep up to spacing that about 10 mm after which there is sharply decreases to 49.85 W/m2K for S=14 mm and 100 W. This trend is same for all heater inputs.

   For all fin spacing the base heat transfer area remains constant hence variation in hb is depends only on fin surface temperature. For smaller fin spacing due to choking of flow, convective heat transfer is less hence small value of hb. Whereas, for larger fin spacing, the fluid flow through the fin channel is flowing more freely without fin array interference therefore fin temperature start reducing therefore value of hb increases. But this rise in hb with increase in fin spacing is up to particular spacing beyond that air moves out without contacting fin surface so temperature increases hence sharp decrease in hb. Thus, there is a significant effect of variation in fin spacing on base heat transfer coefficient.

   3.3 Effect of (S/H) on Average Nusselt Number (Nua)

   13

   11

   9

   Nua

   7 Q=25 W

   5 Q=50 W

   3Q=75 W

   1 Q=100 W

   0 0.1 0.2 0.3 0.4

   S/H

   Fig.6. Effect of (S/H) on Average Nusselt Number (Nua)

   90

   80

   70

   60

   50

   40

   30

   0

   0.1

   0.2

   S/H

   0.3

   Q=25 W

   Q=50 W Q=75 W Q=100 W 0.4

   Nub

   Fig.7. Effect of (S/H) on Base Nusselt Number (Nub)

   Fig 7 shows the effect of variation of S/H on average Nusselt number (Nub) with various heater input. It is observed that as the S/H increases, the base Nusselt number (Nub) increases for the fin array up to maximum value at S/H

   = 0.25 and then (Nub) decreases with the increase in fin spacing (S/H = 0.3 and 0.35). At start, values of Nub are very small for change S/H = 0.05 and 0.1 (37.35 to 48.49) for 100W. The highest value of Nub is 92 at 100W and S/H =

   0.25. The increasing trend is steep up to spacing that about 10 mm after which Nub drastically decreased to 67 for S/H=0.35 and 100 W. This trend is same for all heater inputs.

   3.5 Effect of (T) on Average Heat Transfer Coefficient (ha)

   Fig 6 shows variation of dimensionless parameter average Nusselt number (Nua) with(S/H).Undetermined from average heat transfer coefficient (ha), fin height (H) and thermal conductivity (k) of air which depend on temperature. Trends obtained for Nua are same as that of ha because the fin height is constant and thermal conductivity not vary drastically.

   The effect of variation of S/H on average Nusselt number (Nua) for various heater inputs is shown in Fig 6. As the S/H increases, the average Nusselt number (Nua)

   10

   8 25 W

   ha (W/m2-K)

   6

   4

   2

   0

   50 W

   75 W 100 W

   S=2 mm S= 4 mm

   S= 6 mm

   S= 8 mm

   S = 10 mm S=12 mm S = 14 mm

   increases for the fin array up to maximum value at S/H = 0.25 and then (Nua) decreases with the increase in fin spacing S/H

   = 0.3 and 0.35. At beginning, Nua values are very small for S/H = 0.05 and 0.1 (1.83 to 3.59 for 100W). The highest value of Nua is 12.35 at 100W and S/H = 0.25. The increasing trend is steep up to spacing that about 10 mm after which there is gradual decreases to 11.45 for S/H=0.35 and 100 W. This trend is same for all heater inputs.

   3.4 Effect of (S/H) on Base Nusselt Number (Nub)

   Variation of dimensionless parameter base Nusselt number (Nub) with (S/H) is as shown in Fig 7. The base heat transfer coefficient (hb), fin height (H) and thermal conductivity (k) of air are the parameter from which Nub is determined. Nature of graph for Nub is same as that of hb because the fin height is constant and thermal conductivity not varies drastically.

   10 30 50 70 90 110

   T (K)

   Fig.8. Variation of ha with T

   Fig 8 explains effect of variation of temperature difference (T) on the average heat transfer coefficient (ha).The (T) is the difference between average fin surface temperature (Ts) and surrounding fluid temperature (T). For a particular fin spacing pancreases with increase in T and heater input. For lower fin spacing S= 2 and 4 mm increase in ha is small with increase in T and heater input.

   For 100 W and S=2 to 10 mm T decreases from

   112.5 K to 62.85 K and ha increases from 1.43 W/m2K to 8.98 W/m2K. For 100 W and S= 12 and 14 mm T increases gradually from 68.85 K to 79.15 K and hence ha decrease from

   8.8 W/m2K to 8.5 W/m2K. The similar effect is for all fin spacing and remaining wattages.

   The value of ha for same heater input increases because T and fin exposed area are decreases with increase in fin spacing. This effect is only up to S= 10 mm and then

   onwards even though fin spacing increases S= 12 and 14 mm the value of ha decreases because of increase in T.

   S= 2 mm

   S = 4 mm S = 6 mm S = 8 mm S = 10 mm S = 12 mm S = 14 mm

   50

   40

   25 W

   60

   50 W

   hb (W/m2-K)

   3.6 Effect of (T) on Base Heat Transfer Coefficient (hb)

   70

   100 W

   75 W

   (ha) from present data and plain horizontal rectangular fins under natural convection is used. The trend obtained for present study is same as that of plain fins. For comparative point of view only 100 W readings are used. Trends obtained for remaining wattages are also same shown in Figure 10. The graph also shows that maximum value of ha for perforated fins is at S = 10mm and for plain fins at S = 12mm. It is observed that for perforated fins ha is enhanced by about 15%. This shows that perforations crated at the centre of fins helps to improve heat transfer. From the comparison, it is cleared that the results for present study are satisfactory.

   3.8 Correlation for Natural Convection

   The experimental data obtained for natural convection is used for correlating the results in dimensionless form.

   10 30 50

   70

   T (K)

   90 110 130

   30

   20

   Fig.9. Variation of hb with T

   Figure 9 shows effect of variation of temperature difference (T) on the base heat transfer coefficient (hb).The (T) is the difference between average fin surface temperature (Ts) and surrounding fluid temperature (T). For a specific fin spacing hb increases with increase in T and heater input.

   For 100 W and S=2 to 10 mm T decreases from

   112.5 K to 62.85 K and ha increases steeply from 29.05 W/m2K to 66.95 W/m2K. For 100 W and S= 12 and 14 mm

   T increases gradually from 68.85 K to 79.15 K and hence hb decrease sharply from 59.26 W/m2K to 49.85 W/m2K. The similar effect is for all fin spacing and remaining wattages.

   The value of hb increases with in fin spacing as T decreases as base fin area is constant. This effect is only up to S= 10 mm and then onwards even though fin spacing increases S= 12 and 14 mm the value of hb decreases drastically because of increase in T.

   10

   8

   6

   4

   2

   ha (W/m2-K)

   3.7 Comparison of Heat Transfer from Plain and Perforated Fins

   In natural convection heat transfer is due to the buoyancy force. It is governed by the dimensionless Grashof number, which represents the ratio of the buoyancy force to the viscous force acting on the fluid. Nua is dimensionless convective heat transfer coefficient. Natural convection heat transfer from a fin surface depends also on the fin geometry of the surface as well as fin spacing. It also depends on the variation of temperature on the surface and the thermo physical properties of the fluid involved. From Nu vs S/H plot, as the S/H increases, the average Nusselt number (Nua) increases for the fin array up to maximum value at S/H = 0.25 and then (Nua) decreases with the increase in fin spacing S/H

   = 0.3 and 0.35. That means the S/H is also important parameter governing heat transfer from horizontal fins under natural convection.

   Therefore at last an attempt is made to correlate the experimental results obtained in the present natural convection study. Such a correlation is quite helpful from the point of view of the designers. The average Nusselt number Nua is correlated with the other relevant governing parameters of the natural convection i.e. RaH and S/H.

   Following correlation is obtained by a least square fit applied to a set of data based on the experimental results.

   = . × . × (/). ()

   The correlation is valid for heater input Q = 25 to 100

   Q=100 W

   Perforated

   Q=100 W

   Plain

   W; S/H = 0.05 to 0.35, Pr = 0.7 and air as working fluid. The average error and RMS (Root mean Square) deviation is calculated as 3.11%, 3.88 respectively. The results obtained by the correlation are in good agreement with actual experimental results.

   0

   0 2 4 6

   8

   S (mm)

   10 12 14 16

   Fig.10. Comparison of present ha with Plain HRFA

   Figure 10 shows comparison between heat transfer from perforated and plain horizontal rectangular fins. For plain horizontal rectangular fins previous rsearcher Tajis [10] data is used. For this comparison, average heat transfer coefficient

4. CONCLUSIONS

Based on above experiential study following conclusions can be drawn

1. As the fin spacing increases, the average heat transfer coefficient (ha) and base heat transfer coefficient (hb) increases for the fin array up to maximum value at S = 10 mm and then ha, hb decreases with the increase in fin spacing (S = 12 and 14 mm). The highest values of ha, hb are 8.98 W/m2K, 66.92 W/m2K respectively at 100W and

   10 mm fin spacing. There is a significant effect of variation in fin spacing on average and base heat transfer coefficients.

2. The optimum fin spacing is found to be 10 mm under the natural convection study.

3. Trends obtained for Nua and Nub Vs S/H are same as that of ha and hb Vs S respectively as expected. The highest value of Nua and Nub are 12.35, 92 respectively at 100W and S/H = 0.25.

4. It is observed that for perforated fins ha is enhanced by about 15% as compared to plain horizontal fins. This shows that perforations crated at the centre of fins helps to improve heat transfer. From this comparison, it is cleared that the results for present study are satisfactory.

5. From comparison between present work under natural convection and previous investigator data available from literature it is observed that the results obtained from present data are satisfactory and clearly shows enhancement as compared with data from plain fins.

6. The average Nusselt number Nua is correlated with the other relevant governing parameters of the natural convection i.e. GrH and S/H. The results obtained by the correlation are in good agreement with actual experimental results.

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[3]. Jones C.D. and Smith L.F., Optimum arrangement of rectangular fins on horizontal surfaces, J of Heat Transfer, ASME, 92, pp.6-10, (1970).

[4]. Mannan K.D., An experimental investigation of rectangular fins on horizontal surfaces, Ph.D Thesis, Ohio State University, (1970).

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[6]. Dayan A., Kushnir R., Mittelman G. and Ullmann A., Laminar free convection underneath a downward facing hot fin array, Int J of Heat and Mass Transfer, 47, pp.28492860, (2004).

[7]. Sane S.S., Paishwad G.V. and Sane N.K Natural convention heat transfer enhancement in horizontal rectangular fin array with inverted notch, 18th National & 7th ISHMT-ASME Heat and mass Transfer Conference at IIT, Guwahati, 312- 317, Jan 04-06, 2006

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[10].Taji. S.G., Parishwad G.V., and Sane N.K Enhanced performance of horizontal rectangular fin array heat sink using assisting mode of mixed convection International Journal of Heat and Mass Transfer 72C (2014), pp. 250-259

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[12].Holman J.P. and Souvik B., Heat Transfer, Tata McGraw Hill Education Private Limited, 10th edition. New Delhi, pp. 348-350, (2011)

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4th Edition, (2011)