Heat Transfer/Heat Exchanger

Transcription

1 Heat ransfer/heat Excanger How is te eat transfer? Mecanism of Convection Applications. Mean fluid Velocity and Boundary and teir effect on te rate of eat transfer. Fundamental equation of eat transfer Logaritmic-mean temperature difference. Heat transfer Coefficients. Heat flux and Nusselt correlation Simulation program for Heat Excanger

2 How is te eat transfer? Heat can transfer between te surface of a solid conductor and te surrounding medium wenever temperature gradient exists. Conduction Convection Natural convection Forced Convection

3 Natural and forced Convection Natural convection occurs wenever eat flows between a solid and fluid, or between fluid layers. As a result of eat excange Cange in density of effective fluid layers taken place, wic causes upward flow of eated fluid. If tis motion is associated wit eat transfer mecanism only, ten it is called Natural Convection

4 Forced Convection If tis motion is associated by mecanical means suc as pumps, gravity or fans, te movement of te fluid is enforced. And in tis case, we ten speak of Forced convection.

5 Heat Excangers A device wose primary purpose is te transfer of energy between two fluids is named a Heat Excanger.

6 Applications of Heat Excangers Heat Excangers prevent car engine overeating and increase efficiency Heat excangers are used in Industry for eat transfer Heat excangers are used in AC and furnaces

7 e closed-type excanger is te most popular one. One example of tis type is te Double pipe excanger. In tis type, te ot and cold fluid streams do not come into direct contact wit eac oter. ey are separated by a tube wall or flat plate.

8 Principle of Heat Excanger First Law of ermodynamic: Energy is conserved. de dt m. ˆ in m. ˆ in out out q w s e generated Q Q c A. m. C. c p A. m. C. c p c m ˆ in. m. ˆ out Control Volume COLD Cross Section Area HO ermal Boundary Layer

9 HERMAL BOUNDARY LAYER Energy moves from ot fluid to a surface by convection, troug te wall by conduction, and ten by convection from te surface to te cold fluid. Region III: Solid Cold Liquid Convection NEWON S LAW OF CCOLING dq x c. ow c.da i,wall o,wall c Region I : Hot Liquid- Solid Convection Q ot NEWON S LAW OF CCOLING dq x. iw.da Region II : Conduction Across Copper Wall FOURIER S LAW Q cold dq x k. d dr

10 Velocity distribution and boundary layer Wen fluid flow troug a circular tube of uniform cross-suction and fully developed, e velocity distribution depend on te type of te flow. In laminar flow te volumetric flowrate is a function of te radius. V r D/ 2 r 0 u2rdr V = volumetric flowrate u = average mean velocity

11 In turbulent flow, tere is no suc distribution. e molecule of te flowing fluid wic adjacent to te surface ave zero velocity because of mass-attractive forces. Oter fluid particles in te vicinity of tis layer, wen attempting to slid over it, are slow down by viscous forces. Boundary layer r

12 Accordingly te temperature gradient is larger at te wall and troug te viscous sub-layer, and small in te turbulent core. q x A q x A( w ) eating cooling ube wall e reason for tis is 1) Heat must transfer troug te boundary layer by conduction. 2) Most of te fluid ave a low termal conductivity (k) 3) Wile in te turbulent core tere are a rapid moving eddies, cold fluid wic tey are equalizing te temperature. c wc Metal wall w Warm fluid q x k A( w )

13 Region I : Hot Liquid Solid Convection Region II : Conduction Across Copper Wall Region III : Solid Cold Liquid Convection U = e Overall Heat ransfer Coefficient [W/m.K] q x c R 1 R 2 R 3 q x U.A. c q x ot. iw.a q x k copper.2l ln r o r i iw o,wall i,wall q x.a i q x.ln r o r i k copper.2l q o,wall c x c o,wall c A o c.a o + 1 c q x.a i q x ln r o r i k copper.2l 1 c.a o U 1 A.R U r o ot. r i r o r.ln o ri k. r copper i 1 cold 1 r i r o

14 Calculating U using Log Mean emperature dq ot dq cold dq c d d c d ( ) p d C m dq.. c c p c c d C m dq.. Hot Stream : Cold Stream: c p c c p C m dq C m dq d.. ) ( da U dq.. c p c p C m C m da U d ) ( ) ( A A c p c p da C m C m U d out c in c out in c q U A q A U... ln ) ( A A c c da q q U d ln. A U q Log Mean emperature

15 1 Log Mean emperature evaluation 2 1 Ln 2 ln 1 CON CURREN FLOW U m Ý. Ý C p. 3 6 A. Ln m Ý. Ý c C c p A. Ln COUNER CURREN FLOW Wall A A A P ara ll e l Fl ow in in 1 c 3 7 out out 2 c Co un t e r - C u r re n t F l ow in out 1 c 3 7 out in 2 c 6 10

16 q A i lm 1 2 lm ( 3 1 ) ( 6 2 ) ln ( 3 1 ) ( 6 2 ) Wall A q c A o lm lm ( 1 7 ) ( 2 10 ) ln ( 1 7 ) ( 2 10 )

17 DIMENSIONLESS ANALYSIS O CHARACERIZE A HEA EXCHANGER Nu f (Re,Pr,L/D, b / o ).D k v.d. C p. k Furter Simplification: Nu a.re b.pr c Can Be Obtained from 2 set of experiments One set, run for constant Pr And second set, run for constant Re Nu D q k A( w )

18 Empirical Correlation For laminar flow Nu = 1.62 (Re*Pr*L/D) For turbulent flow Nu Ln / 3 b.026.re.pr. o 0.14 Good o Predict witin 20% Conditions: L/D > < Pr < 16,700 Re > 20,000

19 Experimental Apparatus Switc for concurrent and countercurrent flow emperature Indicator Cold Flow rotameter Hot Flow Rotameters Heat Controller emperature Controller wo copper concentric pipes Inner pipe (ID = 7.9 mm, OD = 9.5 mm, L = 1.05 m) Outer pipe (ID = 11.1 mm, OD = 12.7 mm) ermocouples placed at 10 locations along excanger, 1 troug 10

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21 ln (Nu) Nus ln (Nu) eoretical trend Examples of Exp. Results y = x eoretical trend y = 0.026x Experimental trend y = x ln (Re) Experimental trend y = x eoretical trend y = x ln (Pr) Experimental trend y = x Pr^X Re^Y Experimental Nu = Re Pr eoretical Nu = 0.026Re 0.8 Pr 0.33

22 Effect of core tube velocity on te local and over all Heat ransfer coefficients i (W/m2K) o (W/m2K) U (W/m2K) Velocity in te core tube (ms -1 )

23 wo-pase Flow Boiling Heat ransfer P M V Subbarao Professor Mecanical Engineering Department Selection of Optimal Parameters for Healty and Safe Furnace Walls wit Frictional Flow..

24 Heat ransfer in Liquid Region q s ( s sat) e liquid in te cannel may be in laminar or turbulent flow, in eiter case te laws governing te eat transfer are well establised. Heat transfer in turbulent flow in a circular tube can be estimated by te wellknown Dittus-Boelter (subcritical ) equation. D k f 0.023Re pr H 0.8 1/ 3 k d

25 Religious to Secular Attitude

26 Specific eat of Supercritical Water

27 Pseudo Critical Line

28 ermo pysical Properties at Super Critical Pressures

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30 Heat ransfer Coefficient d kl Re pr 0.4 k d

31 Actual Heat ransfer Coefficient of SC Water

32 Study of Flow Boiling q s ( s sat)

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35 Single-Pase Liquid Heat ransfer Under steady state one-dimensional conditions te tube surface temperature is given by: wall fluid ( z) ( z) ( z) fluid fluid, i fw q ''. GAC ' q ' fw Pz p, fluid and were q is te eat flux, P is te eated perimeter, G is te mass velocity, A is te flow area. C p is te liquid specific eat. fw is te temperature difference. is te eat transfer coefficient.

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37 e Religious Attitude

38 e Onset of Nucleate Boiling If te wall temperature rises sufficiently above te local saturation temperature pre-existing vapor in wall sites can nucleate and grow. is temperature, ONB, marks te onset of nucleate boiling for tis flow boiling situation. From te standpoint of an energy balance tis occurs at a particular axial location along te tube lengt, Z ONB. For a uniform flux condition, wall, ONB wwi q '' PZ mac ONB We can arrange tis energy balance to empasize te necessary supereat above saturation for te onset of nucleate boiling pl 1 cb wall, ONB sat ONB

39 ONB q '' PZ mac ONB pl 1 cb sat wwi Now tat we ave a relation between ONB and Z ONB we must provide a stability model for te onset of nucleate boiling. one can formulate a model based on te metastable condition of te vapor nuclei ready to grow into te world. ere are a number of correlation models for tis stability line of ONB. Bergles and Rosenow (1964) obtained an equation for te wall supereat required for te onset of subcooled boiling.

40 eir equation is valid for water only, given by '' q 1082 p p W SA ONB ' q ' SA W SA ONB klfgg

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42 Subcooled Boiling e onset of nucleate boiling indicates te location were te vapor can first exist in a stable state on te eater surface witout condensing or vapor collapse. As more energy is input into te liquid (i.e., downstream axially) tese vapor bubbles can grow and eventually detac from te eater surface and enter te liquid. Onset of nucleate boiling occurs at an axial location before te bulk liquid is saturated. e point were te vapor bubbles could detac from te eater surface would also occur at an axial location before te bulk liquid is saturated. is axial lengt over wic boiling occurs wen te bulk liquid is subcooled is called te "subcooled boiling" lengt. is region may be large or small in actual size depending on te fluid properties, mass flow rate, pressures and eat flux. It is a region of inerent nonequilibrium were te flowing mass quality and vapor void fraction are non-zero and positive even toug te termodynamic equilibrium quality and volume fraction would be zero; since te bulk temperature is below saturation.