FORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER

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1 FORCED CONVECION HEA RANSFER IN A DOUBLE PIPE HEA EXCHANGER Dr. J. Mchael Doster Department of Nuclear Engneerng Box 7909 North Carolna State Unversty Ralegh, NC

2 Introducton he convectve heat transfer coeffcent h c s defned accordng to Newton's Law of Coolng as q hc As ( w where q s the surface heat transfer rate, w the wall temperature, A s the surface area and the bulk flud temperature. he value of h c s governed by operatng parameters (geometrcal shape of the channel, mass flux, pressure, etc. as well as physcal propertes of the flud (densty, specfc heat, vscosty, and thermal conductvty. he complex nature of the conservaton equatons governng heat transfer and flud flow make analytc solutons possble n only very lmted cases of lttle or no practcal nterest. hs forces us to rely heavly on emprcal correlaton's based upon expermental data. Utlzng expermental data effectvely however, presents ts own specal problems n terms of what varables to examne and how to meanngfully correlate the data. o allevate many of these problems, expermental data s often correlated n terms of dmensonless groups, the number and nature of whch are determned by dmensonal analyss. In most reactor work, the flow s forced and turbulent. Under these condtons, the convectve heat transfer coeffcent s usually formulated n terms of three dmensonless groups as 08. n Nu C Re Pr where the dmensonless groups are defned as Nu Nusselt Number hd c e k Re Reynolds Number ρ vde GDe µ µ Pr Prandtl Number C pµ k and the constants C and n are n general functons of the flow condtons and geometry. A classc correlaton for convectve heat transfer n condut and annul s the Dttus-Boelter correlaton for whch C.023 and n 0.4 or 0.3 dependng on whether the surface s beng heated or cooled, respectvely. hs experment wll utlze the Hlton Double-Ppe Heat Exchanger to nvestgate the nfluence of velocty (Reynolds Number on the convectve heat transfer coeffcent.

3 heory A double-ppe heat exchanger operatng n con-current flow s llustrated below Local emperature Dfference emperature 5 3 Metal Poston It can be shown, that the heat transfer n ths devce can be descrbed by the relatonshp &Q UA m where U s the Overall Heat ransfer Coeffcent and for the double-ppe arrangement s gven by UA + ln ( Ro / R + 2πkL ha o o where the subscrpts and o refer to the nner and outer tube wall surfaces respectvely. he temperature dfference m n the total heat transfer rate s called the Log Mean emperature Dfference (LMD and represents the approprate average temperature dfference between the hot and cold fluds over the length of the heat exchanger. For the double-ppe arrangement, the LMD s gven by m ( 1 5 ( hs expresson for the LMD s vald for both con-current and counter-current flow. As the metal wall offers very lttle resstance to heat transfer n ths devce, we can approxmate the Overall Heat ransfer Coeffcent n terms of just the convectve heat transfer coeffcents as 1

4 1 1 UA + hoao and the wall temperature as essentally a constant radally as ndcated n the above fgure. We may then rewrte the LMD n terms of the nner and outer surface heat transfer coeffcents as 1 + ( 1 5 ( 2 6 hoao ( ( 3 5 ( 2 4 ( or recognzng that we can rewrte the LMD n terms of those varables assocated wth the nner wall and outer wall heat transfer rates as + ( 1 3 ( ( 3 5 ( 4 6. hoao Snce the frst terms on the left and rght hand sde of the equatons contan only varables assocated wth the heat transfer rate to the nner wall surface and the second terms on the left and rght hand sdes contan only terms assocated wth the heat transfer rate from the outer wall surface, we can equate these components to gve ( 1 3 ( 2 4 ha and o ( 3 5 ( 4 6 ha o o such that we may obtan the heat transfer coeffcents drectly from the measured temperatures and heat transfer rates by h ( A 1 3 ( ho ( A 3 5 ( 4 6 o

5 INVESIGAION OF HE RELAIONSHIP BEWEEN REYNOLDS NUMBER AND NUSSEL NUMBER (Convectve Heat ransfer Coeffcent We wsh to examne the relatonshp EXPERIMENAL PROCEDURE Nu C Re a Pr b as a functon of Reynolds number. Snce the Prandtl Number s a functon of temperature, t s necessary to obtan a set of measurements from tests n whch the mean hot water temperature s constant Connect the heat exchanger unt H950 for counter-current flow. 2 Fully open the "hgh flow" water control valve, swtch on the man power swtch, set the heater nput to maxmum and rase the hot water temperature to about 70 C. 3 Adjust the cold water flow rate to brng the mean hot water temperature to about 70 C. 4 Allow the system to reach steady-state and record nner and outer tube temperatures and flow rates. 5 Reduce the hot water flow rate to about 90% of maxmum and wthout changng the cold water flow rate use the heater control to brng the mean hot water temperature back to ts orgnal value. 6 Allow condtons to stablze and repeat the measurements. 7 Repeat ths procedure for hot water flow rates of approxmately 10 % ncrements of the ntal value. DAA ANALYSIS he heat transfer rate from the hot sde to the cold sde of the heat exchanger s gven by mc & ( p and 1 2 m& C ( o o p 5 6. Note, Q & and Q & o should be equal except for heat losses from the system, measurement error, and falure of the system to reach steady-state. In the remanng analyss, Q & s preferred as t s ndependent of heat losses to the envronment. Gven ( 1 3 ( the convectve heat transfer coeffcent on the nner wall surface s gven by

6 h A he Nusselt Number and Reynolds Number may then be calculated drectly as hd Nu k Re Gd µ For constant Prandtl Number, plot Nusselt Number versus Reynolds Number on a Log-Log scale. Perform a least squares ft to the data to fnd the coeffcent a n the expresson and compare your results to those n the lterature. Nu C Re a Pr b HEA EXCHANGER DAA Inner ube Materal External Dameter (d o Internal Dameter (d Length Outer ube Materal External Dameter Internal Dameter Copper 9.5 mm 7.9 mm 870 mm Copper 12.7 mm 11.1 mm

7 COMPARISON OF CON-CURREN AND COUNER-CURREN FLOW IN A HEA EXCHANGER EXPERIMENAL PROCEDURE 1 Connect the heat exchanger unt H951 for counter-current flow. 2 Fully open the "hgh flow" water control valve, swtch on the man power swtch, set the heater nput to maxmum and rase the hot water nlet temperature to about 90 C. 3 Adjust the cold water flow rate to brng the system to steady state. If the cold water supply s nsuffcent to brng the system to steady state, then the heater nput can be reduced. 4 Allow the system to reach steady-state and record hot and cold water nlet temperatures, outlet temperatures and flow rates. 5 Wthout changng the system settngs, swtch the heat exchanger from counter flow to parallel flow. Adjust the heater output to acheve the same hot water nlet temperature as n the counter-flow case. When the system has reached steady state, record the temperatures and flows. 6 Repeat the experment at hot water flow rates of 80%, 60%, 40% and 20% of maxmum holdng the hot water nlet temperature constant. 7 Repeat the experments by reducng hot water nlet temperatures n ncrements of 10 C. DAA ANALYSIS 1 Calculate the heat transfer rates to and from the hot and cold fluds, and compare to those when operatng n parallel versus counter flow at the same nlet temperatures and flow rates. 2 Compute and compare the LMD's for the two operatng modes.

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