A Review on Experimental Analysis for Rectangular Perforated Fin Array
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1 A Review on Experimental Analyi for Rectangular Perforated Fin Array I.N. Wankhede 1, N. P. Salunke 2 1 PG Student, Mechanical Department, RCPIT Shirpur, Maharahtra, India 2 H. O. D., Mechanical Department,RCPIT Shirpur, Maharahtra, India indrajitwankede3@gmail.com 1, ainileh1@gmail.com 2 Abtract:-In thi tudy, variou fin geometrie are referred for teady-tate natural convection heat tranfer. The effect of fin pacing, fin length, fin height, % of perforation, hape ofperforation etc. are tudied from the literature review and come up with a concluion that theheat capacity of material hould be contant for effective analyi of heat tranfer rate.hence, in thi tudy the intention i to do the Experimental analyi for rectangular perforatedfin array and development of Neural Network Model for prediction of heat tranfercoefficient under different boundary condition. Keyword: Perforation, Fin, Steady tate, Natural convection ***** 1. INTRODUCTION While we are working a number of the building framework there i a firt iue of era of warmth. Thi created warmth can aume a part in the diappointment of the framework becaue of overheating. Thi induced warmth in a framework ought to be dieminated in the encompaing in order to hold the framework at it upported working temperature [2].Due to thi the framework can be worked with great proficiency. In advanced electronic framework the wrapping thickne of circuit i much higher [2]; ubequently the iue of warming i not kidding for thi ituation. So a to conquer thi iue, warm framework with agent emitter a balance are fundamental [1]. In the event that we need to fulfill the required warmth decline rate, with minimal meaure of material, the blend of geometry and ituating of the balance ought to be ideal. Between thee varietie of geometry, rectangular blade are the mot often utilized balance geometry in light of their traightforward tructure, leat cot and agent cooling ability [4]. There are two ort of arrangement with affection to rectangular balance coure of action, on a level plane baed vertical blade and vertically baed vertical balance, have been all the more regularly utilized a a part of the application. Be that a it may, the even introduction i not predominant in view of it tolerably econd rate ability to catter heat [2]. The imple mathematical tatement of convection warmth mifortune i given by: "Q" _"c" "=ha T" 1.1 A een from Eq. (1.1), the rate of warmth decadence from the urface can be helped either by expanding the warmth exchange coefficient, h or by expanding the urface territory, A. The etimation of h can be elevated by utilizing legitimate tate of contrained tream over the required urface [2]. In pite of the fact that the contrained convection i proficient, it require an additional pace for fan or blower which limit caue the improvement in tarting and upport cot. Hence, contrained convection i not generally electable. For expanding the warmth exchange, it i more bet, advantageou and imple to utilize the extended urface [1].To build the warmth exchange territory, it i exceptionally effective to utilize the blade over the urface. A a conequence of thi the rate of warmth exchange will be increaed. Be that a it may, if the quantity of balance and the dipering between two balance are not fittingly compoed then the warmth exchange rate can be leened moreover. In pite of the fact that including more number of balance expand the urface territory, they may oppoe the wind current and caue limit layer interruption which influence the warmth exchange unympathetically [3]. The invetigational judgment identified with the warm exhibition of rectangular blade were affirmed in writing. In thi tudy, the enduring tate characteritic convection heat exchange from a punctured vertical rectangular blade compliance jutting from a vertical bae will be invetigated tentatively. 2. LITERATURE REVIEW 2.1 Fin Array (Without Perforation) The point of thi writing audit i to emerge with the comprehenion of the achievement and Natural convection heat exchange rate from balance exhibit up to thi nippet of tudy. Starner and McManu [1] directed one of the underlying learn about the warmth exchange execution of rectangular balance exhibit. In their analye, four arrangement of blade cluter were tried to invetigate free convection heat exchange preentation. The balance cluter were ited with three bae ort, vertical, 45 degree and flat. Other than the principle warmer, watch radiator were locked in to diminih ide warmth mifortune. The average warmth exchange coefficient were gained from all blade tructure for all tet poition. From trial information, it wa found that warmth exchange rate procured from the tet with vertical cluter fell 10 to 30 percent underneath thoe of alo eparated parallel plate. For the 45-degree bae poition, heat exchange rate were 5 to 20 percent underneath from the qualitie taken at vertical poition. With 9
2 the utilization of moke fiber, the tream tructure were watched for every bae poition. The impact of blade tature wa additionally thought and it wa comprehended that balance tallne, balance dividing and bae introduction influenced the warmth exchange execution expreively. Leung and Probert [2] executed another invetigational tudy to invetigate conitent tate rate of warmth decline under common convective condition from either vertically baed or evenly baed vertical rectangular blade. They attempted to work out the impact of balance tallne on ideal blade dividing, and ubequently, two balance length were locked in, pecifically 10 mm and 17 mm. The tet were completed with the bae of the blade cluter at either 20 C or 40 C over the mean temperature of the natural air in the workroom. A an aftereffect of et number of tet, it wa ecured that for 150 mm length of balance, the ideal blade dipering qualitie were 9.0 ± 0.5 mm to 9.5 ± 0.5 mm for the vertical balance extended outward from the vertical bae and upward from the flat bae, eparately. It wa likewie gathered that the change of balance tallne and bae-to-urrounding temperature contrat did not diturb ideal blade eparating value for the introduction conidered in the tudy. Leung, Probert and Shilton [3] readie an exploratory invetigation of the warmth exchange rate from an arrangement of vertical rectangular blade on vertical rectangular bae ha been paed on. The blade were made from light aluminium compound. The pacer bar made of the ame material wa made to modify the diviion between neighbouring blade by prearranged um. The wooden cae wa ituated at the back of the tet area to cover warm protection and radiator plate. For different blade coure of action, the analye were controlled at bae temperature 20 C, 40 C, 60 C and 80 C over the mean temperature of urrounding air. It wa firm that the ideal blade dipering, proportionate to the greatet rate of warmth exchange, wa 10 ± 1 mm.welling and Wooldridge [4] performed another experimental tudy to compare actual rectangular fin experiment with thoe of vertical plate, encloed duct and parallel plate data from previou tudie. During the tet, guard heater plate wa utilized to minimize the heat loe from the ide and rear of the et-up. Data obtained from experiment howed that with cloely paced fin, the heat tranfer coefficient were maller compared to wider fin pacing becaue of boundary layer interference, which prevent air inflow. It wa oberved that the heat tranfer coefficient of finned array were maller than thoe of vertical plate and greater than either thoe of encloed duct or thoe of parallel plate. For a given bae-to-ambient temperature difference, an optimum H/ (fin height to fin pacing) ratio at which heat tranfer coefficient i maximum wa determined from the conidered fin configuration. Harahap and McManu [5] oberved the flow field of horizontally baed rectangular fin array for natural convection heat tranfer to determine average heat tranfer coefficient. In the experimental unit, guard heater and guard fin were located near the end fin to eliminate the end effect. To viualize the flow field, chlierenhadowgraph technique and moke injection were ued. Several type of chimney flow were oberved. For equal fin pacing and fin height, two erie of rectangular fin array differing in length wa compared. The reult of comparion indicated that the array having horter fin length (by half) had higher average heat tranfer coefficient becaue of it effective utilization caued by ingle chimney flow. Thi reult revealed that ingle chimney flow pattern wa favourable to high rate of heat tranfer. Uing the average heat tranfer coefficient data, the following correlation were propoed in term of Gr, Pr,, n, h. N ul = G rl P r.n h h L for10 6 <G rl P r.n h N ul = n h G rl P r h L for n <G rl P r h L L Where N ul i the average Nuelt number baed on the half fin length L, G rl i the Grahoff number baed on the half fin length L, n i the number of pacing in the array, i the fin pacing and h i the fin height. All the thermo-phyical propertie of air are evaluated at the wall temperature. Jone and Smith [6] performed an experimental tudy to predict optimum fin pacing in term of fin height and bae-to-ambient temperature difference for natural convection heat tranfer from rectangular fin on horizontal urface ha been reported by. Determination of local heat tranfer coefficient were achieved by meauring local temperature gradient with interferometer. Integrating the meaured local heat tranfer coefficient, the average heat tranfer coefficient for the array wa determined. Since the determined heat tranfer coefficient were for convection only and were independent of the radiation, the interferometry technique wa ued directly. The reult have hown that fin pacing, i primary geometric parameter that affect the heat tranfer coefficient. They alo compared the meaured value with the limited comparable data in literature, and it wa concluded that the agreement between them wa atifactory. The experimental reult were correlated with the following relation: N u = G r P r 1- exp G r P r N u =0.54 (G r P r ) 0.25 for>2 in Where, h = 1.68 h b 24 F3 1- exp F 3 F= S H (G rp r ) for<2 in All the required thermo phyical propertie of air are evaluated at the film temperature. G r i the Grahoff number baed on fin pacing, P r i the Prandtl number. 10
3 Bar-Cohen [7] analytically invetigated the effect of fin thickne on free convection heat tranfer performance of rectangular fin array. The reult of analyi have hown that for each ditinct combination of environmental, geometric and material contraint, an optimum fin thickne that maximize the thermal performance of an array exit. It wa uggeted that in air, the optimum fin thickne value of an array can be taken approximately equal to optimum fin pacing value for the bet thermal performance. Baed on hi analyi, the following equation which give the fin height aociated with the optimum fin pacing wa propoed: H opt =1.7 k 0.5 t 0.5 k 0.25 air R a Where R a i the Rayleigh number baed on fin pacing, k i the thermal conductivity of the fin material and t i the fin thickne. Leung, Probert and Shilton [8] tudied the thermal performance of rectangular fin on vertical and horizontal rectangular bae, experimentally. Experiment were performed for three different cae; horizontally baed vertical fin, vertically baed vertical fin and vertically baed horizontal fin. Optimum fin pacing value were predicted for each cae. For contant bae temperature of 40 C, 60 C and 80 C, the experiment were conducted to reveal the effect of bae poition on heat tranfer recital of fin array. For three different fin height, namely 32 mm, 60 mm and 90 mm, and for a bae temperature of 60 C, the trial were alo executed. The reult have hown that for vertical fin on a vertical bae, fin pacing i the mot effective contraintprompting the heat tranfer rate. It wa alo determined that unlike fin pacing, the variation in fin height did not caue an operative change in heat tranfer rate for vertical fin on both vertical bae and horizontal bae. It wa clinched that between the all conidered bae poition vertical fin on a vertical bae wa the bet olution for better heat tranfer routine. The impact of changing balance length from 250 to 375 mm on the recurrence of warmth exchange and the ideal blade dipering of vertical rectangular balance expanded from a flat or a vertical rectangular bae have been conidered by Leung,Probert and Shilton [9], tentatively. But blade length, other geometric parameter of variou balance arrangement were kept altered for thought introduction. Trial were directed at a conitent bae temperature, 40 C over that of the urrounding environment. The trial amount for vertical bae demontrated that the expanion in blade length brought about rebate in the rate of warmth decline per unit bae region from the balance exhibit. Alo, the bo blade dividing range from 10 ± 1 mm to 11 ± 1 mm a an aftereffect of balance length increment. Then again, with level bae, expanive decreae in the rate of warmth exchange per unit territory emerged when the balance length wa expanded. The finet blade dipering of on a level plane baed balance cluter expanded from 11 ± 1 mm to 14 ± 1 mm a the balance length wa expanded from 250 mm to 375 mm. Every one of thee ignificance advertied that the impact of blade length on warmth exchange execution of balance exhibit i imperative. Leung and Probert [9] invetigated aet of changing balance thickne on the rate of warmth exchange from vertical duralumin blade welling oppoitely outward from a vertical rectangular bae, tentatively with the expectation of complimentary convection condition. The examination were executed with five divere blade thicknee, in particular 1, 3, 6, 9 and 19 mm, for bae temperature of 20 C and 40 C over that of the urrounding environment, which wa kept up at 20 C. It wa een that the normal ideal uniform blade thickne wa 3 ± 0.5 mm, for amazing rate of warmth exchange, when the uniform parting between the neighbouring balance urpaed 20 mm and for 20 mm 50 mm, the ideal balance thickne diminihed to ome degree a either the balance detachment or the bae temperature wa leened. Yüncü and Anbar [10] achieved an experimental tudy of free convection heat tranfer from rectangular fin array on a horizontal bae. 15 different fin array and a bae plate were verified. The effect of fin height, fin pacing and bae-to-ambient temperature difference on heat tranfer recital were inpected. It wa found that the rate of convective heat tranfer from the fin array mainly be contingent on thee bound. The experimental reult howed that optimal fin pacing, for maximum heat tranfer rate from fin array, diminihed a the fin height amplified. The effect of bae-to-ambient temperature on the optimal fin pacing wa alo dicued and it wa concluded that thi effect i not ignificant. A correlation relating the ratio of convective heat tranfer rate from a fin array to that of a bae plate a a function of number of fin n, fin height H and fin pacing wa etimated and propoed a: Q fc =0.923 exp n n H Q pc Yüncü and Güvenc [11] invetigated the performance of rectangular fin on a vertical bae in free convection heat tranfer, experimentally. During experiment, the length, width and thickne of fin on array were kept fixed, but other parameter uch a fin pacing and fin height were varied. The effect of fin height, fin pacing and bae-to-ambient temperature difference on the heat tranfer performance of fin array wa oberved for everal heat input. According to the experimental reult, it wa deduced that fin pacing i the mot important parameter in the thermal performance of fin array and an optimum fin pacing can be found for every fin height, for a given bae-to-ambient temperature difference. Thi reult revealed that optimum fin pacing depend on two main parameter, fin height and bae-to-ambient temperature difference. The experimental reult were compared with thoe of obtained from horizontally baed fin array in Ref. [13]. It wa concluded that for vertically baed fin array, higher heat tranfer enhancement can be achieved. Yüncü and Mobedi [12] performed a three dimenional numerical tudy on natural convection heat tranfer from longitudinally hort horizontal rectangular fin array. The governing equation, momentum and energy, were olved by uing a finite difference code baed on 11
4 vorticity-vector potential approach. For variou geometric parameter, fin length, fin height and fin pacing, flow configuration occurring in the channel of the fin array were analyzed. Two type of flow were defined a a reult of obervation. In firt type flow configuration; with mall fin pacing, air enter from the end of the channel move along the fin length and flow out at the center of the channel. On the other hand, in the econd cae, with large fin pacing, freh air can alo enter into the channel from the middle part ince the pace between two fin i ufficiently large. Then, it turn 180 degree at the bae and flow up along the fin height while it move to the central part of the channel. The effect of fin length and fin height on the heat tranfer rate of horizontal fin array were alo examined and it wa concluded that an increae in thee geometric parameter caue reduction in the rate of heat tranfer from array. Thi i due to more boundary layer interference along the channel which lower the amount of intake cold air in the channel. Yüncü and Yildiz [13] invetigated natural convective heat tranfer from annular fin experimentally. 18 et of annular fin array were teted to oberve their heat tranfer performance. The fin array were heated with everal heat input and correponding bae and ambient temperature difference were recorded. Uing the meaured data, total heat tranfer rate from fin configuration were evaluated. A radiation analyi wa applied to etimate the rate of radiation heat tranfer. Then, radiation contribution were ubtracted from total heat diipation to obtain eential convection heat tranfer rate. It wa concluded that the convection heat tranfer rate from the fin array depend on fin diameter, fin pacing and bae-to-ambient temperature difference. A cale analyi wa alo performed in order to etimate a correlation which evaluate order-ofmagnitude of optimum fin pacing at a given fin diameter and bae-to-ambient temperature difference. The correlation i: opt D =3.38 R a 2.2 Fin Array (With Perforation) Guei-Jang Huang et al. [14] planned Natural convection heat exchange rate from penetrated balance cluter ha been aeed for variou geometrie. The hypothetical and trial tudy wa teered to locate the finet geometric requirement in order to accomplih greatet warmth exchange from the finned urface. An invetigational tudy wa made to ae the impact of blade eparating, balance tallne and meaure of warmth flux on blended convection heat exchange from rectangular balance exhibit. To acquire the mot extreme warmth exchange ideal balance dipering ha been evaluated. Amid the trial conitent warmth flux boondock condition wa perceived and air wa utilized a the working liquid. The peed of liquid entering channel wa kept verging on teady (0.156win m/) utilizing a tream rate control valve with the goal that Reynold number wa contantly about Re= Experimentation were led for altered Rayleigh number 3x107<Ra*<8x108and Richardon number 0.4 <Ri< 5. Balance eparating wa changed from S/H= 0.04 to S/H= and blade tature wa differed from Hf/H= 0.25 to Hf/H= For blended convection heat exchange, the reult obtained from tet tudy demontrate that the ideal balance dividing which yield the mot extreme warmth exchange i S= 8 9 mm and ideal balance eparating relie on upon the etimation of Ra* Rigan Jain and M.M.Sahu [15] examined the relentle tate common convection heat exchange from vertical trapezoidal blade augment upright from vertical rectangular bae with Computational liquid element (CFD). The impact of warmth burden on temperature ditinction in the middle of bae and encompaing on the warmth exchange preentation of trapezoidal balance cluter for the ideal blade dipering value ha been meaured with the aitance of reproduction model. The warmth input going from 25 W to 125 W ha been upplied for blade arrangement, and ubequently, the bae and the urrounding temperature are meaured keeping in mind the end goal to get the warmth exchange rate from balance exhibit. The outcome are egregate with thoe acquired tentatively and factually for rectangular blade with ame urface region, balance tip thickne and bae plate extent. Yazicioğlu B.[16] examined the enduring tate normal convection heat exchange from vertical rectangular blade dragging out upright from vertical rectangular bae tentatively. The impact of geometric limitation and baeto-urrounding temperature ditinction on the warmth exchange preentation of balance cluter were een and the ideal blade diviion qualitie were reolved. Two comparative trial et-up were locked in amid trial o a to take limit from30 divere balance coure of action having balance length of 250 mm and 340 mm. Balance thickne wa maintained altered at 3 mm. Balance tature and balance eparating were dotted from5 mm to 25 mm and 5.75 mm to 85.5 mm, eparately. 5 heat input fluctuating from25 W to 125 W were accommodated all balance development, and conequently, the bae and the urrounding temperature were honourable keeping in mind the end goal to ae the warmth exchange rate from balance exhibit. Mohamad I. Al-Widyan and Amjad Al-Shaarawi [17] begin a rectangular balance having unvarying cro egment with roundabout puncturing on a urface at a conitent temperature. The punctured balance wa purpoeful under regular convection utilizing familiar any for warmth exchange expanion imilar to it trong partner conidering ditinctive level of Grahoff number and two geometric limit: a dividing between gap, x, and opening meaurement, D. It i found that, over the deciion conidered, heat exchange from the penetrated balance enhanced with Grahoff number. Alo, warm exchange opened up a the dipering between gap dwindled. Concerning the opening meaurement, about all cae diplayed an upurge in warmth exchange with width barring for the intance of high Grahoff number and high dividing proportion, ε, where a greatet etimation of warmth exchange advancement i touched then begun to fall again with the ditance acro calling for further 12
5 invetigation that incorporate the balance thickne. Thi tudy think about a olitary rectangular blade with an even warm conductivity, undeviating cro area with length L, thickne of 0.1L, and i endlely wide. The blade i punched with roundabout gap along the balance length and balance width. Every puncturing (opening) ha a width D and i liced vertically through the blade' body (thickne). The egment of opening are diengaged from each other by a eparation Sx in the heading upright to the blade length. In the ame egment, opening are conitently cattered toward L and are incoherent by a eparation Sy=L/4. The blade i given to a vertical urface at a relentle temperature T and work under common convection circumtance where the beiding liquid i required to have teady propertie with a uniform temperature, T. " A=πDt-2" ("π" "D" ^"2" )/"4" ΔA communicate the adjutment in the urface zone of a balance with thickne t becaue of entering a vertical gap with a ditance acro D through it. Abdullah H. AlEa, ET. Al. [18] think the expanion of normal convection heat exchange from a level rectangular balance having rectangular opening with angle proportion of two utilizing limited component procedure. The outcome for pricked blade have been connected with it relating trong one. For geometrical meaurement and warm aet of a blade and the opening one ought to do a parametric tudy. The tudy urvey the addition in blade region and of warmth exchange coefficient in light of hole. It wa found that, for certain deciion of rectangular meaurement and pace between hole, there i an enlargement in warmth intemperance and a leening in weight over that of the comparing trong one. Likewie, the warmth exchange elevating of the punctured blade upurge with the expanion in balance thickne and warm conductivity. The punctured blade reult are connected with trong one to dicover the expanion in warmth exchange brought on by embedding the hole. It i expected that both balance have the ame ize (the balance length i L= 50 mm and it width i W = 200 mm), ame warm conductivity, ame bae temperature (T_b= 100 ^0 c) and ame encompaing temperature (T_ = 20 ^0 c). The tudy mirrored the addition in blade territory and of warmth exchange coefficient becaue of puncture. The outcome uncovered that, for pecific etimation of rectangular aperture meaurement, the hole lead to an expanion in warmth exceivene of the punctured blade over that of the reporter trong one. The ize of warmth liberality upgrade relie on the balance thickne, it warm conductivity, and the aperture meaurement, horizontal and longitudinal dividing. At lat, the tudy uncovered that, the puncture preented in the blade upport rate of warmth decline and in the meantime decreae the heavine of the balance. 3. CONCLUSION If we ee the overall pread of the above literature urvey, it i clearly oberved that the whole tudy i limited to the certain parameter like fin with perforation, fin without perforation, fin orientation, fin length, fin height, bae to ambient temperature difference, % of perforation etc. But in the tudy of heat tranfer heat capacity of the material alo play an important role. So there i wide cope of tudy w.r.t thi parameter. We will brought forward the above tudy By comparing the reult of two different material with and without perforation by keeping the heat capacity of both material contant and accordingly other propertie can be varied. Alo we can develop a prediction model for the value of heat tranfer coefficient by uing Neural Network (MATLAB). The above two objective can be achieved with contant pacing at optimum level a mentioned in the above literature. The preent work i primarily for rectangular fin and fin array. It may be further extended for other type of fin profile wherever neceary. Maximum work i done on tall fin which are generally ued for experimental purpoe only. Actual application baed hort fin are till require more development. REFERENCES [01] Starner K.E. and McManu H.N., An Experimental Invetigation of Free Convection Heat Tranfer from Rectangular Fin Array, Journal of Heat Tranfer, , (1963) [02] Leung C.W. and Probert S.D., Thermal Effectivene of Short-Protruion Rectangular, Heat-Exchanger Fin, Applied Energy, 1-8, (1989) [03] Leung C.W., et al., Heat Exchanger: Optimal Separation for Vertical Rectangular Fin Protruding from a Vertical Rectangular Bae, Applied Energy, 77-85, (1985) [04] Welling J.R. and Wooldridge C.N., Free Convection Heat Tranfer Coefficient from Vertical Fin, Journal of Heat Tranfer, , (1965) [05] Harahap F. and McManu H.N., Natural Convection Heat Tranfer from Horizontal Rectangular Fin Array, Journal of Heat Tranfer, 32-38, (1967) [06] Jone C.D. and Smith L.F., Optimum Arrangement of Rectangular Fin on Horizontal Surface for Free Convection Heat Tranfer, Journal of Heat Tranfer, 6-10, (1970) [07] Bar-Cohen A., Fin Thickne for an Optimized Natural Convection Array of Rectangular Fin, Journal of Heat Tranfer, , (1979) [08] Leung C.W., et al., Heat Exchanger Deign: Thermal Performance of Rectangular Fin Protruding from Vertical or Horizontal Rectangular Bae, Applied Energy, , (1985) [09] Leung C.W. and Probert S.D., Heat-Exchanger Deign: Optimal Uniform Thickne of Vertical Rectangular Fin Protruding Perpendicularly Outward, at Uniform 13
6 Separation, from a Vertical Rectangular Bae, Applied Energy, , (1987) [10] Yüncü H. and Anbar G., An Experimental Invetigation on Performance of Rectangular Fin on a Horizontal Bae in Free Convection Heat Tranfer, Heat and Ma Tranfer, , (1998) [11] Yüncü H. and Güvenc A., An Experimental Invetigation on Performance of Rectangular Fin on a Vertical Bae in Free Convection Heat Tranfer, Heat and Ma Tranfer, , (2001) [12] Yüncü H. and Mobedi M., A Three Dimenional Numerical Study on Natural Convection Heat Tranfer from Short Horizontal Rectangular Fin Array, Heat and Ma Tranfer, (2003) [13] Yüncü H. and Yildiz Ş., An Experimental Invetigation on Performance of Annular Fin on a Horizontal Cylinder in Free Convection Heat Tranfer, Heat and Ma Tranfer, , (2004) [14] Guei-Jang Huang et al., Enhancement of natural Convection heat tranfer from horizontal rectangular fin array with perforation in fin bae, Int. Journal of Thermal Science, 84(2014) [15] Rigan Jain and M.M.Sahu., Comparative Study of performance of Trapezoidal and Rectangular fin on a Vertical bae under free convection heat tranfer IJERT vol.2 (2013) [16] Yazicioğlu B., Performance of Rectangular Fin on a Vertical Bae in Free Convection Heat Tranfer, M.S. Thei in Mechanical Engineering, Middle Eat Technical Univerity, Ankara (2005). [17] Mohamad I. Al-Widyan, Amjad Al-Shaarawi, Numerical Invetigation of Heat Tranfer Enhancement for a Perforated Fin in Natural Convection IJERA, Vol. 2, Iue 1, Jan-Feb 2012, pp [18] Abdullah H. AlEa et.al. Enhancement of natural convection heat tranfer from afin by rectangular perforation with apect ratio of two International Journal of Phyical Science Vol. 4 (10), pp , October, 2009 [19] Kakaç S., Convective Heat Tranfer, METU, Ankara, (1980) [20] Incropera F.P. and DeWitt D.P., Fundamental of Heat and Ma Tranfer, John Wiley & Son, New York, (1990) [21] McAdam W. H., Heat Tranmiion, McGraw-Hill, New York, (1954) [22] Bejan A., Convection Heat Tranfer, John Wiley & Son, New York, (1984) 14
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