HEAT TRANSFER THROUGH ANNULAR COMPOSITE FINS

Transcription

1 Journal of Mechancal Engneerng and Technology (JMET) Volume 4, Issue 1, Jan-June 2016, pp , Artcle ID: JMET_04_01_001 Avalable onlne at ISSN Prnt: and ISSN Onlne: IAEME Publcaton HEAT TRANSFER THROUGH ANNULAR COMPOSITE FINS T.Kanthmath Assstant Professor: Department of Mechancal Engneerng K L Unversty, Greenfelds, Vaddeswram Guntur, Inda Naga Sa Ram. G U.G Student: Department of Mechancal Engneerng K L Unversty, Greenfelds, Vaddeswram Guntur, Inda ABSTRACT The present paper focuses on the study of the radal composte fns to ncrease the heat transfer rate n may applcatons. By takng the full advantage of the convectve heat transfer equaton. Fns of same thckness wth more than one materals rather than the coatngs are consdered for the steady state thermal analyss s made on those fns and comparson of heat transfer rate s made between the fns of same materal and fns and fns of composte materal when n bonded contact. The overall heat transfer rate wll be ncreased n composte fns of same surface area than that of same materal Key words: Annular Composte Fns, Same Materal Fns, Composte Fns, Bonded Contact, Overall Heat Transfer Rate. Cte ths Artcle: T.Kanthmath and Naga Sa Ram. G. Heat Transfer Through Annular Composte Fns. Journal of Mechancal Engneerng and Technology, 4(1), 2016, pp INTRODUCTION A fn s an extended surface whch s used to ncrease the heat transfer through the body whch s of hgher temperatures. when the surface area ncrease heat conducton ncreases, usng ths prncple fns are used to ncrease the heat transfer rate from the hot body. A fn s generally made of the sngle materal of hgh thermal conductvty say alumnum. There are dfferent types of fns avalable based on the geometry of the fn say Straght, Annular, Longtudnal, Rectangular, Concal, Trapezodal, Parabolc, Cylndrcal (Pns, Splnes), Truncated Concal Splne, Trangular Fns etc. however the basc heat transfer n the fns often follow the one basc equaton but changes n the surface area and the permeter. Many condtons can be made out dependng upon 1 edtor@aeme.com

2 Heat Transfer Through Annular Composte Fns the length of the fns lke long, short etc. The followng equaton shows the basc equaton of the heat transfer rate n the short fns wthout the tp not nsulated. h P h tanh L k A h P k k A Q h P k A ( T T ) b h h P 1 tanh L h P k A k k A (1) The parameters whch change for dfferent materals are k thermal conductvty, A surface area, P PERIMETER, L length of the fn 2. LITERATURE REVIEW The frst approach on the composte materal fn through the coatng of the materals s made by the S Lalot, C Tourner, M Jensen under the ttle of Fn effcency of annular fn made of two materals [1]. The computatonal method of analyzng the Evaluaton of the performance of the annular composte fns usng ANSYS s made by the Ashsh Gr and S.A.K.Jlan whch took the bass of the S Lalot methodology [2]. An numercal approach on the effcency of the composte fns of varable thckness (taper profles) has been made by the Crstbal Cortes and Lus I.Dez and Antono Campo [3]. The effcncy of the extended surfaces along wth the frst formulatons of heat transfer was made by the K.A.Gardner [4] 3. METHEDOLOGY The annular composte fns can be defnded as the fns made of two dfferent materal through the bonded contact. The second materal s not a coatng nstead the whole materal s made added to the basc annular fn. The materal chosen for ths analyss s the hgh thermal conductvty materal lke alumnum and steel, brass, whth the non matalc materal porcelne. The practcal way of dong ths by makng an external case that wll form an jacket on to the base geomentry. Fgure 1 showng the basc geometry of the composte annular fn The parent materal s a base materal whch s the basc host of the fn. The second materal whch s called as chld materal of the same thckness of the base fn. The nner temperature s denoted as T b and the outer ambent temperature s denoted as T. 2 edtor@aeme.com

3 T.Kanthmath and Naga Sa Ram. G The detal geometrc nomenclature of the composte annular materal s used for the dervaton of the expresson s gven as follows Fgure 2 Nomenclature of the composte fn Where L 0 s called as outer radus of the fn. r c s called as the radus of the cylnder. t s called as thckness of the fn. L 1 s called as length of the parent fn. L 2 s called as length of chld fn. r 1 s the radus of the parent fn. 4. DERIVATION OF THE HEAT TRANFER AND TEMPARATURE DISTRIBUTION OF THE COMPOSITE ANNULAR FIN. The followng are the abbrevatons used n the dervaton of the equaton. K 1 s coeffcent of thermal conductvty of parent materal K 2 s coeffcent of thermal conductvty of chld materal P 1 s the permeter of parent materal. P 2 s the permeter of chld materal. h s the convectve coeffcent of materal. A 1 s the surface area of the parent fn. A 2 s the surface area of the chld fn. 3 edtor@aeme.com

4 Heat Transfer Through Annular Composte Fns Form the equaton 1 the followng expresson can be wrtten as Q Q Q c. f PARENT CHILD As referred form the equaton (1) h tanh( ml) m k R h 1 tanh( m L) m k (2) (3) h P k A J (4) ( T T ) T (5) b c. f 1 n Q T R J (6) Q n cf. R J (7) T 1 Snce there are two materals n ths analyss the equaton (7) s wrtten as Q 2 cf. R J (8) T 1 Q 2 cf. R J (9) T 1 Q cf. R J R J T Where (10) m h P k A (11) A 2 ( r t rt r r ) (12) c 1 1 c A 2 ( rt L t L r ) (13) P 2 r (14) 1 1 P 2 L (15) 2 0 A. TEMPARATURE DISTRIBUTION EQUATION OF THE COMPOSITE FIN cosh( m ( L X )) C snh( m ( L X )) U cosh( m L ) C snh( m L ) From the equaton 16 the temperature dstrbuton can be wrtten as (16) T T T n U (17) b T edtor@aeme.com

5 T.Kanthmath and Naga Sa Ram. G T T n U (18) T 1 b. EFFICIENCY OF THE COMPOSITE ANNULAR FIN cf. Q Q cf. (19) Q cf. cf. T h ( P 1 l 1 P 2 l2) (20) By subsstng the equaton (6) n equaton (20) we can wrte as P l G R J 1 n cf. h 1 G 1 n cf. h 1 G R J For stagnant ar of smplfed case h s 5W/m 0 C then 1 R J n cf. 5 1 G (21) (22) (23) (24) 5. FEA OF THE ANNULAR COMPOSITE FIN S The fnte element analyss s carred for the valdaton of the composte fns and the procedure s carred n ANSYS 12.1 student s verson and the steady state thermal module s used. The followng s the CAD model of the annular composte fns Fgure 3 3D CAD model of the annular composte fn The materals are appled to the CAD model n two ways wth same materal s appled to whole geometry frst and then the followng materal parng are appled and the analyss s conducted. 5 edtor@aeme.com

6 Heat Transfer Through Annular Composte Fns Parent materal Chld materal Attrbute Alumnum Alumnum A Brass Brass B Porcelan porcelan C Steel Steel D Alumnum Porcelan E Alumnum Brass F Alumnum Steel G Porcelan Steel H Porcelan Brass I Porcelan Alumnum J The dmensons used to model the composte annular fns s as follows. Fgure 4 The dmensons of the composte annular fn Meshng s made by the refnement of 2 n order to capture the hgh curvatures around the fn geometry and the trangular method s used to patch up the body. The total number of the nodes are and total number of the elements are Fgure 5 The mesh model of the composte annular fn 6 edtor@aeme.com

7 T.Kanthmath and Naga Sa Ram. G 6. BOUNDARY CONDITIONS The boundary condtons are appled for the analyss wth Temperatures of 50 0 s appled on the nner surface of the cylnder and rest of the body s made to expose to envronment so convectve heat transfer take place so stagnate ar of smplfed case s appled on the all other surfaces. The ambent temperatures are 25 0 C s appled Fgure 6 The boundary condtons of the Analyss 7. REULTS AND DISCUSSIONS The analyss s made to run for 1s and the followng results are obtaned. The followng are the result s obtaned and the followng table bref up the analyss wth respect to attrbute. Attrbute Image A B C 7 edtor@aeme.com

8 Heat Transfer Through Annular Composte Fns D E F G H 8 edtor@aeme.com

9 T.Kanthmath and Naga Sa Ram. G I J Table 1 Temperature dstrbuton of the composte annular fn at dfferent attrbute The followng plot gves the mmmum and temparatures wth respect to the attrbute. Fgure 7 the mnmum temperatures of the sorted attrbutes 8. CONCLUSION The above study nfer that the usage of the metallc annular fns has shown no sgnfcant change n the heat transfer. But the mplementaton of the non-metallc materals wth the metallc has gven the sgnfcant results n the heat transfer and another mprovement n the heat transfer s made by usng the total nonmetallc materals n the fns has gven a profound and large change n the heat transfer, though the manufacturng of ths knd of fns s easy wth the castngs and the composte materal based fns can also be made wth the slurry based castng technque and by makng a jacket 9 edtor@aeme.com

10 Heat Transfer Through Annular Composte Fns REFERENCES [1] Lalot. S. et.al. Fn effcency of annular fns made of two materals Internatonal Journal, Heat and Mass Transfer, Vol. 42, 1999, pp [2] Ashsh Gr, S.A.K.Jlan. Evaluaton of the Performance of Annular Composte Fns usng ANSYS. [3] L.I. Díez, A. Campo, C. Cortés, Quck desgn of truncated pn fns of hyperbolc profle for heat-snk applcatons by usng shortened power seres, Appled Thermal Engneerng (2008) [4] K.A. Gardner Effcency of extended surface, Transactons of the ASME Nov Pp