Kuldeep Rawat*, Ayushman Srivastav* *Assistant Professor, Shivalik College of Engineering, Dehradun.

Transcription

1 International Journal o Scientiic & Engineering search, Volume 7, Issue 12, December ISSN NUMERICAL INVESTIGATION OF HEAT TRANSFER ENHANCEMENT OVER RECTANGULAR PERFORATED FIN Abstract Kuldeep Rawat*, Ayushman Srivastav* *Assistant Proessor, Shivalik College o Engineering, Dehradun. In this paper, numerical study has been perormed to investigate the heat transer and riction rom a perorated in subjected to orced convection. Thermal and luid dynamic perormances o extended surace having perorations o rectangular cross section are investigated. RANS based k ε turbulence model is used to calculate the luid low and heat transer parameters. Flow and heat transer parameters are presented or ynolds numbers rom to 8 based on the in thickness. Numerical results obtained rom the perorated in geometry are compared with that o a plain in to determine the heat transer enhancement o test in in extracting heat rom its base under similar operating conditions. Keywords: Perorated in; Nusselt number; Friction actor; ynolds number. 1. Introduction Heat sinks are commonly used in many ields o industry as cooling electronic devices, and electronic component cooling becomes a more serious design problem as power densities continue to increase. One o the most common means or cooling electronic modules is a inned heat sink that enhances convection heat transer to the ambient air. There are a many types o heat sinks, with diering in geometries, and operating with orced convection but rectangular plate ins are commonly used or the reason o simplicity in manuacturing. Perormance o three dimensional rectangular blu plates or ins has been studied extensively by many investigators. Rongguang Jia et al. [1] carried out a numerical investigation to determine the velocity and heat transer characteristics o multiple impinging slot jets in rib-roughened channels. He considered dierent size and arrangement o jets and ribs and reported sults show that the ratio (B/W) between the size o the jets and ribs is most important because the ribs inhibit the motion o eddies by preventing them rom coming very close to the surace when B/W is low, e.g. B/W = 1, although the ribs will increase the turbulence intensity. This blockage limited the heat transer enhancement eect o the ribs and impinging jets. intensity. G. Iaccarino et al. [2] investigated the eect o thermal boundary conditions on numerical heat transer predictions in rib-roughened passages. They obtained results using constant heat lux at the walls and conjugate heat transer. Their experimental measurements and data correlations showed that the predicted heat transer is very sensitive to the type o boundary conditions used in the numerical model. It was illustrated that some o the discrepancies observed between experimental and numerical data can be eliminated i conduction heat transer in the rib is taken into account. Meinders et al. [3] experimentally investigated the local convective heat transer on a wall-mounted cube placed in a developing turbulent channel low, Ledezma et al. [4] perormed experimental and numerical studies o heat transer rom a pin in array heat sink in an impinging air stream. They considered pin ins with square cross section and ocused on inding the optimal in spacing. They have proposed the correlations or optimal in-to-in spacing and maximum thermal conductance. Torii and Yang [] studied two dimensional, incompressible thermal-luid low over both sides o a slot-perorated lat surace, which was placed in a pulsating ree stream. Sahin and Demir [6] experimentally investigated the variation o overall heat transer, riction actor and eect o various design parameters on heat transer and riction actor or a heat exchangers equipped with square cross sectional perorated pin ins in a rectangular channel. They considered eects o low and geometrical parameters on heat transer and riction characteristics and also obtained correlations or the eiciency enhancement. Dorignac et al. [7] experimentally investigated the heat transer characteristics o a multi perorated plates. They reported that convective exchange on the upstream side o a multi perorated plate depends on the pitch between perorations. It has been concluded that the mean convective heat exchange rates around perorations can be calculated by deining the Nusselt and ynolds numbers based on characteristics length and upstream velocity. For a large range o perorations spacing s, an empirical relation has been developed or heat exchange at windward surace o a perorated lat plate. Shaeri et al. [8] numerically determined the heat transer and rictional losses rom an array o solid and perorated ins mounted on a lat plate. Perorated ins have windows with square cross section and arranged in dierent numbers. sults showed that new perorated ins have higher total heat transer rates with considerable weight reduction in comparison to the solid ins. It was reported that the perorated ins have relatively lesser drag and the drag ratio decreases by increasing the ynolds number. With the increase o ynolds number, the percentage o heat transer enhancement with respect to depreciates in most o the cases. In a similar study, Shaeri et al. [9] investigated the luid low and convective heat transer rom an array o solid and perorated ins that are mounted on a lat plate. Perorations such as small channels with square cross section are arranged stream wise along the in s length and their numbers varied rom 1 to 3. It has been reported that ins with longitudinal pores, have remarkable heat transer enhancement in addition to the considerable reduction in weight by comparison with solid ins. The object o present work is to investigate the heat transer and riction characteristics o perorated in under orced convection using standard numerical techniques. The data pertaining to heat transer and riction at various luid low rates have

2 International Journal o Scientiic & Engineering search, Volume 7, Issue 12, December ISSN been generated by solving the governing equations under the speciied boundary conditions or dierent perorated in geometries. The enhancement in heat transer and riction in dierent cases o perorated ins are compared with that o a at dierent low ynolds number. In order to assess the heat transer perormance o the test in, rate o heat transer enhancement o perorated in is determined with respect to a. Heat transer and riction characteristics o perorated in having dierent height, width and pitch o perorations are discussed with the help o relevant plots. 2. Problem description and computational domain The computational domain chosen or a test in is similar to the study conducted by Shaeri et al. [9]. The ig.1 shows a test in attached to the base plate which is heated by providing uniorm heat lux. The air low is considered to be steady and laminar with constant properties and the air velocities are taken such that orced convection is the dominant heat transer mechanism between perorated in and surrounding air. The aluminium is considered as a in material due to its suitability in the manuacturing o ins. The test in length (L), the height (h ) and thickness (D) are considered as mm, mm and mm, respectively. The computational domain consists o an entry section, an exit section and the upper ree stream surace as planes abcd, ijkl and bckj, respectively. The dimensions o entrance and exit regions are kept as D and D on the upstream and downstream side o in respectively. The domain extends twice the in height in Y direction and D in Z direction. A uniorm low conditions are considered at the inlet section abcd by deining the velocity components at the inlet as: u in = u ; v in = w in = and T in = T. The ree stream conditions are also applied to the upper plane bckj. The exit plane ijkl is suiciently ar rom the plate egh, thereore temperature and pressure gradients are neglected along X direction. All the remaining planes are considered to be solid adiabatic walls with no slip conditions at the suraces. The temperature o in base plane egh (T b ) is kept 7 o C whereas the ree stream temperature o luid (T ) is considered as o C. Perorations Flow L Fig.1: Computational domain. Fig.2: Perorated in geometry. In agreement to the observation o Leung and Probert [], the eect o radiation heat transer is neglected or present work. The geometrical parameters o perorated in is shown in ig.2 in which the rectangular perorations can be seen on the broad surace o the. The perorations o width (W p ) and height (h p ) are separated by peroration pitch (P ). The relative height o peroration (h p /h ) is deined as the ratio o peroration height to the in height. The width o peroration is expressed in a dimensionless orm as relative peroration width (W p /L) which is the ratio o peroration width to the in length. The relative peroration pitch (P /W p ) is given as the ratio o pitch to width o peroration. The results o grid independency study or a plain in are shown in Table 1. It can be noticed that the insigniicant changes in the values o Nusselt number and riction actor are observed due to the reinement in the grid coniguration beyond the grid size o or the in and or the whole domain. Grids in whole domain (X Y Z) Table 1: Grid independency test or a plain in ( = ). Grids in plain in (X Y Z) Nusselt Number (Nu) Friction actor ()

3 International Journal o Scientiic & Engineering search, Volume 7, Issue 12, December-16 ISSN Numerical method 3.1 RNG k-ε turbulent model The RNG k-epsilon (k- ε) model is used to model the turbulent low in the present work to compliment the conditions that the low is incompressible with constant thermal conductivity, no heat dissipation, no compression work and no heat generation. The turbulence is assumed to be homogeneous and isotropic and thereore, the turbulence kinetic energy (k), and its rate o dissipation (ε), are given by ollowing two equations k k k µ ( ) [( t k k k ρ u + v + w = µ + )( + + )] + G x y z k ρε (1) σ k x y z And turbulent energy dissipation rate equation is ε ε ε µ ( u v w ) [( t ε ε ε ε ε (2) ρ + + = µ + )( + + )] + C ε Gk C2ερ x y z σε x y z k k Where G k represents the generation o turbulent kinetic energy due to mean velocity gradients, and can be calculated using Boussinesq hypothesis as G k = µ t S 2, where S is the modulus o the mean rate-o-strain tensor, deined as S (2S ij S ij ) and Sij can be deined as 1 u u i j = + (3) Sij 2 x j xi The turbulent (or eddy) viscosity μ t is computed by combining k and ε as ollows: 2 k (4) µ t = ρcµ ε The model constants or the two transport equations C 1Ɛ, C 2Ɛ, C μ, σ k and σ Ɛ have the ollowing values C 1Ɛ = 1.42; C 2Ɛ =1.68; C μ =.8; σ k =1.; σ Ɛ = Solution method FLUENT 13. is used to solve the incompressible RANS equations using a second order upwind scheme chosen or energy and momentum equations and the SIMPLE pressure velocity coupling technique. 4. Validation To validate the present numerical scheme the results o computational model are compared with correlations proposed by Shaeri Nu p.32 () et al.[9] or large size windows: = 1.296( D ) ( 1 ϕ ).269 Nu s where ϕ=.6 and the ratio o Nusselt number or perorated in to that o a Nu p Nu s have been calculated with respect to dierent ynolds number. In order to compare the heat transer data obtained by the present numerical scheme with the data obtained rom the correlations suggested by Shaeri et al.[9], the values o Nusselt number enhancement ratio are plotted as unction o ynolds number. The comparative plot in Fig.3 shows that the present numerical data is in good agreement with the corresponding data ound rom correlations. The average absolute deviation o the present numerical data rom the correlation data is ound to be 3.7% which conirms the accuracy o the data. 1.8 % Average absolute deviation: 3.7% M.R. Shaeri et al[2] present study Fig.3: Comparison o present numerical data to Nusselt number enhancement ratio or a perorated in.

4 International Journal o Scientiic & Engineering search, Volume 7, Issue 12, December ISSN sults and discussion The validated numerical scheme is used to generate the heat transer and riction data pertaining to the perorated in under orced convection. The heat transer and riction characteristics o perorated in are discussed with the help o plots o heat transer, Nusselt and riction actor at the in suraces as unction o in and operating parameters. The heat transer perormance o perorated in is also discussed by estimating the heat transer enhancement due to perorations or dierent in conigurations while low ynolds number is varied rom to 8. The temperature and velocity counters o solid and perorated in are discussed to understand the eect o peroration parameters o test in on heat transer and riction. Hp/H=.4, Wp/L=.6 Hp/H=.8, Wp/L=.6 P/Wp= P/Wp= Hp/H=.4,P/Wp=2 Hp/H=.8,P/Wp=2 Wp/L=.2 Wp/L=.4 Wp/L= Wp/L=.2 Wp/L=.4 Wp/L=.6 Fig.4: Variation o in heat transer rate with ynolds number or dierent relative peroration pitch (P / W p ) and dierent relative peroration width (W p /L). It is evident that the heat transer rate rom a in under orced convection is highly sensitive to the luid low conditions near the in suraces. It is believed that the application o turbulators in the orm o perorations promotes disturbance near the wall and thereby yields higher heat transer rates at the cost o additional pressure drop, Fig.4 shows the plot o in heat transer rate as a unction o the low ynolds number or dierent relative peroration pitch (P /W p ) and relative peroration width (W p /L) corresponding to two dierent relative peroration heights (H p / H ). It can be observed rom the plots that the heat transer rate increases as the value o ynolds number is increased or all in conigurations. The plot reveals that the perorated in yields substantial enhancement in heat transer than that o a irrespective o the dimensions o peroration. It can be seen that the heat transer rates are equally sensitive to the relative peroration width (W p /L) and relative peroration pitch (P /W p ), irrespective o the height o peroration and ynolds number. Fig.. Temperature contour around a in with peroration at = (H p /H =.8, W p /L=.2, P /W p =2). 16

5 International Journal o Scientiic & Engineering search, Volume 7, Issue 12, December ISSN With a view to understand the heat transer characteristics o a perorated in, temperature contours or perorated in is shown in Fig.. It can be observed that the temperature o the perorated in surace towards the leading end is on the lower side when a slot is cut along the length o the in. This is due to the act that the cold air stream experiences a higher temperature gradient at the entry section o the slot. As a result o which higher heat transer rates are achieved near the leading end o the slot. Careul study o temperature contours unolds that the air stream progresses along the length also helps to lush out the hot air vortices trapped inside the perorations. The accelerated air movement in the perorations leads to better luid mixing and enhanced heat transer rates 4 3 Hp/H=.4, Wp/L=.6 3 Hp/H=.8, WP/L=.6 Nu Nu P/Wp= P/Wp= Hp/H=.4,P/Wp=2 4 3 Hp/H=.8, P/Wp=2 Nu Nu Wp/L=.2 Wp/L=.2 Wp/L=.4 Wp/L=.4 Wp/L=.6 Wp/L= Fig.6. Variation o Nusselt number with ynolds number or dierent relative peroration pitch (P / W p ) and dierent relative peroration width (W p /L). The relative contribution o heat transer by convection to that o conduction across the boundary layer developed over the in surace is usually represented by Nusselt number. To acilitate the understanding o Nusselt number variation over the entire range o ynolds number, Fig.6 shows the Nusselt number plot or dierent values o peroration pitch and peroration width. It is interesting to note that the maximum values o Nusselt number are obtained or the perorated in, ollowed by the and perorated in without slot at all the values o the ynolds number. It can be noticed that the peroration width has a substantial eect on the Nusselt number at all the values o the low ynolds number. The maximum values o Nusselt number are observed at relative peroration pitch (P /W p ) o 2, relative peroration width (W p /L) o.6, and relative peroration height (H p / H ) o.8 irrespective o the values o low ynolds number. Heat transer enhancements attained by way o turbulence promoters like perorations are usually accompanied by the rise in rictional losses. It is thereore necessary to study the eect o the geometrical parameters o the perorated in on the riction actor under varied low ynolds number. Fig.7 shows the eect o low ynolds number on the riction actor with regard to dierent peroration parameters. The plot shows that the riction actor decreases as the low ynolds number is increased or all in geometries. Notable reduction in riction can be observed or the perorated in as compared to a subjected to similar operating conditions. A relatively greater all in the rictional losses can be observed with the larger height o peroration, at all the ynolds number. It can be seen that the eect o peroration pitch on riction is insigniicant in comparison to the eect o peroration width or both types o in conigurations. Fig.8 the velocity streamlines revealed that the perorated in has relatively lesser orm drag in comparison to the as the low coninement within the perorations decreases the length o a recirculation region on the downstream side o the in and consequently reduces the pressure drop caused by the wake ormation.

6 International Journal o Scientiic & Engineering search, Volume 7, Issue 12, December ISSN Hp/H=.4,Wp/L=.2.16 Hp/H=.8,Wp/L= P/Wp=2 P/Wp=3 P/Wp= P/Wp= Hp/H=.4,P/Wp=2. Hp/H=.8,P/Wp= Wp/L=.2 Wp/L=.3 Wp/L= Wp/L=.2 Wp/L=.4 Wp/L= Fig.7. Variation o riction actor with ynolds number or dierent relative peroration pitch (P / W p ) and dierent relative peroration width (W p /L). Fig.8. Velocity streamline around a in without slot, p/h=.4,w p /L=.2, P/Wp=4 (=) 6. Conclusions The present work deals with the study o heat transer and riction characteristics o a perorated in by using computational approach.on the basis o present study, ollowing conclusions is drawn: The perorated in has slightly better heat transer perormance with the notable reduction in rictional losses than that o a. The heat transer increases and riction actor decreases with an increase in the values o ynolds number or all in conigurations. 16

7 International Journal o Scientiic & Engineering search, Volume 7, Issue 12, December ISSN The relative peroration width (W p / L) o.4 has been ound suitable or attaining higher heat transer rates rom a perorated in with relative peroration height (H p / H ) o.8 whereas relative peroration width (W p / L) o.2 and.4 yield comparable heat transer rates in case o relative peroration height (H p / H ) o.4. The heat transer rates rom perorated in are intensiied when peroration height is increased. However, riction decreases by increasing the height o peroration when perorated in has no slot. Nomenclature A b Cross-section area o the base plate T Temperature A Cross-section area o the in T in = T Mean plate temperature C p Speciic heat W p Width o peroration C p,al Speciic heat o aluminium u in = u Inlet velocity o air D Fin thickness X,Y,Z rectangular coordinate D h Equivalent hydraulic diameter o duct P/e lative rib pitch Friction actor h Convective heat-transer coeicient Greek symbols h Fin height α Under-relaxation actor h p Height o peroration Δ Dierence k Al Thermal conductivity o aluminium µ Dynamic viscosity k Turbulent kinetic energy ρ Density o air at bulk mean air L Fin length temperature Nu s Nusselt number o Φ General variable Nu p Nusselt number o perorated in The vector dierential operator Pr Prandtl number ε turbulent dissipation rate Heat transer rate to air η Thermo hydraulic perormance ynolds number t Time erences [1] Rongguang Jia, Masoud Rokni and Bengt Sunde n Impingement cooling in a rib-roughened channel with cross-low, International Journal o Numerical Methods or Heat & Fluid Flow, Vol. 11; No. 7, pp (1). [2] Iaccarino G., Ooi A. and Durbin P.A., Behnia M. Conjugate heat transer predictions in two-dimensional ribbed passages, International Journal o Heat and Fluid Flow, Vol. 23; pp (2). [3] Meinders E.R, Hanjalic K, Martinuzzi R.J, "Experimental study o the local convection heat transer rom a wall-mounted cube in turbulent channel low", J Heat Transer;121:64 73, (1999). [4] Ledezma G, Morega AM, Bejan A, "Optimal spacing between pin ins with impinging low". ASME J Heat Transer,118:7 7, (1996). [] Torii S, Yang W.J., "Thermal transport phenomena over a slot-perorated lat surace in pulsating ree stream". Int J Therm Sci, 41:241 2, (2). [6] Sahin, B., Demir, A., "Perormance analysis o a heat exchanger having perorated square ins. Appl". Therm. Eng. 28, , (8). [7] Dorignac E, Vullierme J.J, Broussely M, Foulon C, Mokkadem M., "Experimental heat transer on the windward surace o a perorated lat plate" Int J Therm Sci, 44:88 93, (). [8] M.R. Shaeri, M. Yaghoubi., "Numerical analysis o turbulent convection heat transer rom an array o perorated ins",international Journal o Heat and Fluid Flow , (9). [9] Shaeri, M.R., Yaghoubi, M., Heat transer analysis o lateral perorated in heat sinks, Applied Energy 86, 19 29, (9). [] Leung C.W, Probert S.D., "Heat exchanger perormance: eect o orientation". Appl Energy, 33:3 2, (1989).