CORRELATION EQUATIONS: FORCED AND FREE CONVECTION

Transcription

1 CHAPER 0 0. Inroducion CORREAION EQUAIONS: FORCED AND FREE CONECION A ey facor in convecion is e ea e ea ransfer coefficien. Insead of deermining we deermine e ssel number, wic a dimensionless ea ransfer coefficien. Wenever i is difficul or no possible o deermine e ssel number analyically, we searc for a correlaion equaion wic gives e ssel number. Correlaion equaions are usually based on eperimenal daa. is caper gives correlaion equaions for: () Eernal forced convecion over plaes, cylinders, and speres. (2) Inernal forced convecion roug cannels. (3) Eernal free convecion over plaes, cylinders and speres. (4) free convecion in enclosures. 0.2 Eperimenal Deerminaion of Hea ransfer Coefficien Newon's law of cooling is used o deermine eperimenally: q s s (0.) Measure surface emperaure s, surface ea flu q s, and free sream emperaure, and use (0.) o deermine. Eample: Deermining q s. In Fig. 0. e cylinder is eaed elecrically, curren and volage give power (ea) dissipaed, ea flu qs is power divided by surface area Eperimenal daa is correlaed in erms of dimensionless variables and parameers. Eample: Forced convecion for consan properies and no dissipaion, local ssel number is correlaed as - q s s Δ Fig. 0. i = f ( * ; Re, Pr) (2.52) 0.3 imiaions and Accuracy of Correlaion Equaions

2 All correlaion equaions ave IMIAIONS. ey MUS be carefully noed. Eamples of limiaions: Geomery: An equaion for eac configuraion. Range of parameers, suc as e Reynolds, Prandl and Grasof numbers, for wic a correlaion equaion is valid, are deermined by e availabiliy of daa and/or e een o wic an equaion correlaes e daa. 0.4 Procedure for Selecing and Applying Correlaion Equaions 2 ere are many, many correlaion equaions. Eac is for a specific applicaion and is valid under specified condiions. Presening all correlaion equaions and discussing eir applicaions and limiaions is no e mos effecive and efficien approac o sudying and learning e maerial. Insead, we will describe a sysemaic procedure for searcing, idenifying and selecing correlaion equaions. Some of e common applicaions will be presened as eamples. Selecing correlaion equaions for applicaions no discussed in is caper follow e same procedure described below. () Idenify e geomery under consideraion. Is i flow over a fla plae, over a cylinder, roug a ube, or roug a cannel? (2) Idenify e classificaion of e ea ransfer process. Is i forced convecion, free convecion, eernal flow, inernal flow, enrance region, fully developed region, boiling, condensaion, micro-graviy? (3) Deermine if e objecive is finding e local ea ransfer coefficien (local ssel number) or average ea ransfer coefficien (average ssel number). (4) Cec e Reynolds number in forced convecion. Is e flow laminar, urbulen or mied? (5) Idenify surface boundary condiion. Is i uniform emperaure or uniform flu? (6) Eamine e limiaions on e correlaion equaion o be used. Does your problem saisfy e saed condiions? (7) Esablis e emperaure a wic properies are o be deermined. For eernal flow properies are usually deermined a e film emperaure f f ( ) / 2 (0.2) s and for inernal flow a e mean emperaure m. However, ere are ecepions a sould be noed. (8) Use a consisen se of unis in carrying ou compuaions. (9) Compare calculaed values of wi ose lised in able.. arge deviaions from e range of in able. may mean a an error as been made.

3 3 0.5 Eernal Forced Convecion Correlaions 0.5. Uniform Flow over a Fla Plae: ransiion o urbulen Flow Boundary layer flow over a semi-infinie fla plae. Mied flow: laminar and urbulen. ransiion or criical Reynolds number Re (0.3) () Plae a Uniform Surface emperaure. alid for: e local ea ransfer coefficien is deermined from e local ssel number. In e urbulen region, Re : / ( Re (0.4a) Average ea ransfer coefficien for mied flow: consider bo laminar and urbulen: fla plae, consan s Re (0.4b) ( ) d ( ) d ( ) d (0.5) 0 0 Use (4.72) for () and (0.4a) for () P r 60 properies a f,, inegrae laminar urbulen ransiion Fig. 8.2 Fig. 0.2 / ( Re ) ( Re ) ( Re (0.7a) / 3 imiaions: see limiaions on e respecive correlaions for e ssel numbers. Epressed in erms of e average ssel number : / 2 / ( Re ) ( Re ) ( Re (0.7b) (2) Plae a Uniform Surface emperaure wi an Insulaed eading Secion. urbulen flow o ( Re (0.8) 9 /0 / 9 ( / ) /3 insulaion o Fig. 0.3 s

4 4 imiaions: see (0.4b) and review limiaions on (4.72) (3) Plae wi Uniform Surface Flu. 4/5 / ( Re ) Pr (0.9) Properies f ( s ) / 2, were s is e average surface emperaure Eernal Flow Normal o a Cylinder Average ssel number Fig. 0.5 / 2 / 3 D 0.62ReD Pr ReD N ud 0.3 (0.0a) 2 / 3 / 4 282, Pr alid for: 5 / 8 flownormal ocylinder PeRe D Pr 2.0 properies a f (0.0b) For Pe < 0.2, use D D ln Pe (0.a) alid for: flownormal ocylinder PeRe D Pr 2.0 properies a f (0.b) e above gives eamples of correlaion equaions and eir limiaions. Correlaion equaions for oer configuraions will be lised wiou deails. imiaions and condiions on eir use sould be noed Eernal Flow over a Spere 0.6 Inernal Forced Convecion Correlaions

5 Enrance Region: aminar Flow roug ubes a Uniform Surface emperaure () Fully Developed elociy, Developing emperaure: aminar Flow. (2) Developing elociy and emperaure: aminar Flow. is case is given by [5, 7] Fully Developed elociy and emperaure in ubes: urbulen Flow () e Colburn Equaion (2) e Gnielinsi Equaion Non-circular Cannels: urbulen Flow 0.7 Free Convecion Correlaions 0.7. Eernal Free Convecion Correlaions () erical Plae: aminar Flow, Uniform Surface emperaure. (2) erical Plaes: aminar and urbulen, Uniform Surface emperaure. (3) erical Plaes: aminar Flow, Uniform Surface Hea Flu. (4) Inclined Plaes: aminar Flow, Uniform Surface emperaure. (i) Heaed upper surface or cooled lower surface (ii) Heaed lower surface or cooled upper surface (6) erical Cylinders. (7) Horizonal Cylinders. (8) Speres Free Convecion in Enclosures () erical Recangular Enclosures. (2) Horizonal Recangular Enclosures. (3) Inclined Recangular Enclosures. 0.8 Oer Correlaions Keep in mind a is caper presens correlaion equaions for very limied processes and configuraions. ere are many oer correlaion equaions for opics suc as: Condensaion Boiling Hig speed flow Je impingemen Dissipaion iquid meals Hea ransfer enancemens Finned geomeries Irregular geomeries Micro-graviy Non-Newonian fluids Ec. Consul eboos, andboos and journals.