ISSN 00405795, Theoretical Foundations of Chemical Engineering, 2012, Vol. 46, No. 6, pp. 634–111. © Pleiades Publishing, Ltd., 2012.

Heat Transfer and Friction Factor in CrissCross Flow Channels of PlateandFrame Heat Exchangers1 O. P. Arsenyevaa, L. L. Tovazhnyanskyyb, P. O. Kapustenkob, and O. V. Demirskiya a

b

AO SODRUGESTVOT, Kharkiv, Ukraine National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine email: [email protected] Received April 20, 2012

Abstract—The link between heat transfer intensity and hydraulic resistance of plate heat exchangers channels is determined with the use of modified Reynolds analogy of heat and momentum transfer. The formula to estimate the share in total hydraulic resistance of pressure loss due to friction is proposed. The resulting model enables to calculate film heat transfer coefficients in plate heat exchangers channels on a data of hydraulic resistance of the main corrugated heat transfer field. The calculations are compared with the experimental results on heat transfer in channels with cross corrugated walls available in the literature. The good agreement confirms the assumptions made on deriving the equation of the analogy between heat and momentum trans fer in proposed form in plate heat exchanger channels. DOI: 10.1134/S0040579512060024 1

INTRODUCTION New challenges in efficient heat recuperation arise when integrating renewables, polygeneration and combined heat and power (CHP) units with tradi tional sources of heat in industry and the communal sector, as it is shown by Klemes et al. [1]. There is a requirement to consider minimal temperature differ ences in heat exchangers of reasonable size [2]. The plate heat exchanger (PHE) is one of the most effi cient types of modern heat exchange equipment which satisfies this requirement. The design and operation principle of PHE equipment is well described else where, see e.g. Wang et al. [3], Shah and Seculic [4], Tovazhnyansky et al. [5]. The heat transfer processes in this heat exchanger take place in the channels of complex geometry formed by plates pressed from thin metal. The plates’ corrugation form strongly influ ences the heat transfer and hydraulic behaviour of interplate channels; the effect is similar to that in enhanced tubes, see e.g. Kukulka [6], Wang et al. [7]. Plates with straightline corrugations inclined with the certain angle to the plate’s vertical axis are gener ally used in modern PHEs (see Fig. 1). Assembled together in one unit, they form the channels of criss cross flow type which are distinguished by complex geometry and by the existence of contact points between the opposite walls in the sites of corrugations crossing. Geometry of plates with different corruga tion types (sinusoidal and triangular form) are shown in Fig. 2. The comprehensive study of hydraulic resis tance and mass transfer in the models of such channels

with sinusoidal corrugations of height b = 5 mm was reported by Focke et al. [8]. Muley and Manglick [9] published results for hydraulic resistance and heat transfer in channels formed by commercial plates with b = 2.54 mm. More recently Dovich et al. [10] tested the models of channels with corrugations height b = 2 mm. Results of experiments for the models of chan

1 The article is published in the original.

634

1

2 3 2β

4

5

Fig. 1. Schematic drawing of PHE plate: 1—heat carrier inlet and outlet; 2, 5—zones for flow distribution; 3—rub ber gasket; 4—the main corrugated field.

HEAT TRANSFER AND FRICTION FACTOR IN CRISSCROSS FLOW CHANNELS B

(a)

A

635

(c) A

A–A SA S B–B S b β = 90°

S = SA B

2β (d) 2b S

(b) b

Fig. 2. Different corrugation forms: (a, b)—the intersection of the adjacent plates; (c)—channel cross sections for the sinusoidal form of corrugations; (d)—channel cross sections for the triangular form of corrugations.

nels with the triangular shape of corrugations of height 5 mm and 10 mm were reported by Tovazhnyansky et al. [11], as also for channels with height down to 1.2 mm by Savostin and Tikhonov [12]. The reviews of these and other works and their results can be found in a book by Wang et al. [3] and papers of Ayub et al. [13] and Khan et al. [14]. All of these authors mainly gen eralize the obtained data in the form of separate empirical correlations for hydraulic resistance calcu lations, which are valid for the investigated channels only in a limited range of hydrodynamic and thermal parameters. Martin [15] tried to generalize all the data for hydraulic resistance by means of an integrated equation on the basis of developed semiempirical mathematical model. He obtained the relation, which in implicit form expresses the dependence of the hydraulic resistance coefficient on Reynolds number and geometrical parameters of plates’ corrugation. But the calculation deviation for this relation from experi mental data of other authors in some cases runs up to 50% and more. In other work [10] similar results in terms of accuracy are obtained. The low accuracy of generalization in the mentioned works can be explained, first of all, by significant differences in experimental PHE models. The plate’s surface of industrial PHE, washed by the fluid (see Fig. 1), consists of the main corrugated field 4 and zones of flow distribution on the inlet 2 and outlet 5. Most of the heat transfer takes place in the

main corrugated field that comes to 80–85% of total plate’s heat transfer surface area. Despite the fact that on the distribution zones considerably less heat is transferred, their influence on the overall hydraulic resistance of the channel can be significantly higher. First, here is the raised velocity of flow movement, which is increasing in following range: from the veloc ity value for the operating field up to the velocity on the outlet from the channel to the gathering collector of PHE due to decrease of channel cross section area (the same is for inlet from the distributing collector of PHE). In addition, the design of distribution parts can considerably vary for different plates, which affects their hydraulic resistance and evenness of flow distri bution. The link between heat and momentum transfer in channels with enhanced heat transfer is very important for the selection of the optimal geometry and correct design of heat exchangers. Dovic et al. [10] and Martin [15] used Leveque equation to generalize heat transfer data for PHEs published by different researchers. The accuracy of prediction is rather good for some cases, but the error in their estimation sometimes reach up to 40–52%. This can be partly explained by attempt to generalize together the data for models of corrugated fields of PHE channels and data for commercial plates which have rather higher pressure losses at inlet and outlet. As it can be judged from the data of Tovazh nyansky et al. [11], the share of pressure drop in

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entrance and exit zones of some PHE channels formed by commercial plates of chevron type, can reach 50% and more especially at lower inclination angles of corrugations to the plate vertical axis. The other reason lays on the accuracy of the employed relation between heat transfer and hydraulic resis tance. In our study we perform data generalization based on the data of hydraulic resistance for PHE channel main corrugated field.

ρWd ρW 0 d e  are Reynolds where Re = e and Re0 =  μ μ numbers for the tube and the PHE channel; μ is the dynamic viscosity, Pa s.

THEORETICAL ANALYSIS

For the turbulent flow of fluid with Pr = 1 in a straight smooth tube the Reynolds analogy holds:

Modification of Reynolds Analogy for PHE Channels The analogy between heat and momentum transfer for flow in channels is a wellestablished fact. The sim plest Reynolds analogy and its different modifications are sufficiently well described in the literature (see e.g. books by Shah and Seculic [4], Kutateladze and Leont’ev [16]). Semiempirical models, developed based on this analogy, proved useful for theoretical analysis of different transport phenomena. For PHE channels of complex geometry the existence of the link between heat and momentum transfer was shown by Kapustenko et al. [17], this link was employed also for the prediction of heat transfer in condensation [18] and fouling [19]. In this paper we establish the link between heat transfer and friction in PHE channels based on a modification to Reynolds analogy and experimental results. Let us assume that the relationship between heat transfer and frictional shear stress on the channel wall of PHE channels is the same as in tubes. In other words, for equal shear stress at the wall the film heat transfer coefficients in PHE channel and straight tube will be equal, supposing that equivalent diameter, tem perature conditions and physical properties of both flows are the same. In dimensionless form it can be written as hd h0 de Nu = e = Nu 0 =  . λ λ

(1)

The shear stress on the wall can be calculated by the following formulas: For the straight tube 2 τ w0 = 1 ζ 0 ρW 0 ; 8

(2)

When shear stresses (2) and (3) are equal, the fol lowing equation can be written: 2

2

Re ζ τ = Re 0 ζ 0 ,

(4)

ζ Nu 0 = Re 0 0 , 8

(5)

where the friction factor ζ0 can be calculated from Blasius equation: – 1/4

ζ 0 = 0.3164Re 0

.

(6)

Substituting of Equation (6) into Equations (4), (5) and (1) and after rearranging, one can obtain: 6/7

3/7

Nu = 0.065Re ( ζ τ ) .

(7)

Let us assume that the effect of the Prandtl number on heat transfer in the range of 0.5 ≤ Pr ≤ 20 can be taken into account by introducing the factor Pr raised to the power 0.4. To account for temperature change across the channel cross section we introduce the term (μ/μw) raised to the power 0.14. Then the modified Reynolds analogy for PHE channel can be expressed by Eq. (8): 6/7

3/7

0.4

Nu = 0.065Re ( ψζ s ) Pr ( μ/μ w )

(3)

where W and W0 are the flow velocities in PHE chan nel and in tube, m2/s; ρ is the fluid density, kg/m3; ζ0 is the friction factor in straight tube; ζτ is the friction factor in PHE channel, which is accounting for pres sure losses due to friction on the wall.

,

(8)

where ζs is the friction factor for the overall hydraulic resistance which accounts for all pressure losses (due to friction and a form drag); ψ is the share of friction losses in the total pressure loss in the channel (ψ = ζτ/ζs). Prediction of Friction Factor in Crisscross Flow Channels. For the calculation of the friction factor ζ for the main corrugated field of PHE channels we use the correlation proposed by Arsenyeva [20], whose accuracy was confirmed later by Arsenyeva et al. [21]. This expression enables us to predict ζ for a wide range of chevron plates corrugation parameters. This corre lation is as follows:

For the PHE channel 2 1 τ w =  ζ τ ρW , 8

0.14

12 + p 12 1 ζ = 8 ⎛ 2⎞ + 3 ⎝ Re ⎠  2 (A + B) ⎛ ⎞ ⎜ ⎟ p5 A = p 4 ln ⎜  ⎟ 0.9 – 5⎟ ⎜ ⎛ 7p 3⎞ + 0.27 ×10 ⎠  ⎝ ⎝  Re ⎠

1  12

; (9)

16

16

37530p ; B =⎛ 1⎞ , ⎝ Re ⎠

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637

103

Nu/Pr0.4(µ/µω)0.14

1 2 3 4

β = 60° β = 45° β = 30°

100

10 103

104

105 Re

Fig. 3. Dependence of heat transfer on Reynolds number in experimental PHE channels (data from [11, 22]) at γ = 0.556 (lines are calculated by Eq. (8): solid line—ψ = 1; dashed line—ψ by. Eq (11)). 1–4—samples numbers, see Table.

where p1, p2, p3, p4, p5 are parameters defined by the channel corrugation form: p 1 = exp ( – 0.15705β );

2

πβγ p 2 = ; 3

β 1 p 3 = exp ⎛ – π  2⎞ ; ⎝ 180 γ ⎠ π p 4 = ⎛ 0.061 + ⎛ 0.69 + tan ⎛ β ⎞ ⎞ ⎝ ⎝ ⎝ 180⎠ ⎠ × ( 1 + ( 1 – γ ) × 0.9β

0.01

);

(10) – 2.63

⎞ ⎠

p 5 = 1 + β. 10

The friction factor in Eq. (2) assumes that the equivalent diameter of the channel is defined as de = 2b and the characteristic length is the length of the channel L. The Reynolds and Nusselt numbers in Eq. (8) must be determined at de = 2b and the friction factor from Equation (9) must be divided by the ratio Fx of the actual surface area to the projected one: ζs = ζ/Fx. This accounts for the distribution of shear stresses around all effective heat transfer surface area, similar to the distribution of the film heat transfer coefficient. For an accurate comparison with experi mental data it should be taken into consideration that some researchers are taking hydraulic diameter of the channel dh in reduction of their experimental data. The Share of Friction Losses in Total Hydraulic Resistance of Crisscross Flow Channels. The main parameter, which is not determined in Eq. (8) is the share of pressure loss due to friction on the wall in total loss of pressure ψ. Its value can be estimated from experimental data on heat transfer in models of PHE channels. Figure 3 shows the experimental data of Tovazhnyansky et al. [11] and Tovazhnyansky and Kapustenko [22] for four experimental samples of PHE channel. The parameters of the samples are given

in Table. The Nusselt and Reynolds numbers are recalculated for de = 2b. The analysis of the data presented in Fig. 3 leads to the following conclusion: the discrepancies between the calculations using Eq. (8) for ψ = 1 with experi mental data increase with the increase of the corruga tions angle β and Reynolds number. The analysis of flow patterns in PHE channels by Dovic et al. [10] has shown a stronger mixing at higher β and Reynolds numbers. The mixing is associated with flow disrup tions which contribute to the rise of form drag and consequent decrease in the share ψ of pressure loss due to friction on the wall. Correlating the values of y cal culated from Eq. (8) using experimental values of Nu, the expression describing its dependence on ψ and Reynolds number is A = 380/ [ tan ( β ) ]

1.75

;

– 0.15 sin ( β )

at Re > A ψ = ( Re/A ) at Re ≤ A ψ = 1.

(11)

;

The model composed by Eqs. (8) and (11) corre lates experimental data of Fig. 3 with a mean square error of 6.2%. This model describes the influence of the corrugations geometrical parameters on heat transfer. Geometrical parameters of the experimental plates Sam Pitch Height β, Length Width dh, ple no. S, mm b, mm deg L, m W, mm mm 1 2 3 4

18 36 18 18

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5 10 5 5

60 60 45 30

No. 6

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225 225 225 225

9.6 19.3 9.3 9.0

Fx 1.15 1.15 1.15 1.15

638

ARSENYEVA et al. ζ

100 Nu/Pr0.4(µ/µω)0.14

10 1 0.1 10

0

20

40

60

80 β, deg

Fig. 4. The influence of corrugation inclination angle β on friction factor. Comparison of data from Zimmerer et al. [23] with calculations by Eq. (9).

Nu 103 100

β = 72° β = 48° β = 33° β = 18° β = 14° β = 10°

1 2 3 4 5 6

103

104 Re

30

50

70 β, deg

Fig. 5. The influence of corrugation inclination angle β on heat transfer. Comparison of data from Zimmerer et al. [23] with calculations by Eq. (8).

Nu 103

100

10

100

10 10

10 100

1 2 3 4 5 1 2 3 4 5

103

104 Re

Fig. 6. The influence of Reynolds number on heat transfer for plates with different inclination angles calculated by Eq. (8) (curves) and for data published by Savostin and Tikhonov [12] (points): 1—β = 72°, γ = 0.872; 2—β = 48°, γ = 0.926; 3—β =33°, γ = 0.911; 4—β = 18°, γ = 0.926; 5—β = 14°, γ = 1.460; 6—β = 10°, γ = 0.934.

Fig. 7. The influence of Reynolds number on heat transfer for plates with different inclination angles calculated by Eq. (8) (curves) and for data published by Heavner et al. [24] (points): 1—β = (90° + 45°)/2; 2—β = (90° + 23°)/2; 3—β = 45°; 4—β = (23°+45°)/2; 5—β = 23°.

COMPARISON OF THE MODEL WITH EXPERIMENTS AND DISCUSSION To validate the model and establish the limits of its application we have compared its results with different experimental data available in literature. The experi mental study of the influence of corrugation inclina tion angle β on heat transfer and friction factor was reported by Zimmerer et al. [23]. The experiments were made on the models of channels with corrugated walls, so the influence of inlet and outlet zones is min imal. The data for friction factor of Fig. 4 are in good agreement with the calculations obtained from Equa tion (9), which are presented by the solid line (biggest discrepancy is 20%). The change of β from 18° to 68° results in 30 times increase on the friction factor. At the same time the film heat transfer coefficient, characterized by Nu in Fig. 5, increases about three times. The accuracy of calculations by the proposed model is fairly good for β up to 60° (deviation less than 2%), but for β = 68° discrepancy increases up to 20%. It can be concluded that β = 68° is outside the upper limit of model application. In any way the corrugation inclination angle affects friction factor and heat trans

fer to a considerable extent and can be used as one of the main variables when optimizing the geometry of heat exchanger plates. The data for models of crisscross flow channels were published by Savostin and Tikhonov [12]. These data are presented in Fig. 6. The experiments were conducted with air at 368 and 463 K. For these condi tions Pr = 0.69 and (μ/μw)0.14 = 1. The corrugations had triangular shape with radii (about 0.6 mm) at the edges. The height of the corrugations for the cases pre sented in Fig. 6 was in the range of 1.12 to 1.22 mm. The experimental Nu and Re were multiplied on 2b/dh, for a comparison to be made based on the same definition of equivalent diameter. The discrepancies for β =14°, 18°, 33° and 48° do not exceed 15%. For β = 10° the error is up to 25% and it can be concluded that the lower limit for the application of the model β =14°. The upper limit is certainly below 72°, as dis crepancies at β =72° go up to 50% at Re < 800. Another comprehensive study of heat transfer with extended set of mixed commercial plates (produced by APV) of different corrugations was reported by Heavner et al. [24]. These data are presented in Fig. 7

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HEAT TRANSFER AND FRICTION FACTOR IN CRISSCROSS FLOW CHANNELS Nu 104 103 1 2

100 10 1 100

103

104 Re

Fig. 8. The influence of Reynolds number on heat transfer for different plates. Comparison of data calculated by Eq. (8) (curves) with heat transfer data published by Dovic et al. [10] (points): 1—β = 65°, 2—β = 28° (γ = 0.52, Fx = 1.19).

Nu 103

1 2 3

100

1 2 3

100

103

104 Re

Fig. 9. The influence of Reynolds number on heat transfer for different plates. Comparison of data calculated by Eq. (8) (curves) with data from Muley and Manglik [9] (points): 1—β = 60°, 2—β = (60° + 30°)/2, 3—β = 30° (γ = 0.556, Fx = 1.29).

103 Nu/Pr0.4(µ/µω)0.14

by points calculated from correlations presented by Wang et al. [3]. The equations were obtained for the exponent of Pr equal to 1/3. To account for differences with exponent in Equation (8), which is equal to 0.4, the data for Nu were calculated at average Pr number equal to 4.6. The estimation for geometrical parame ters was taken from the paper of Dovic et al. [10]: γ =0.7, Fx = 1.26. The results of the application of mathematical model (8)–(11) are presented by solid lines in Fig. 7. The agreement with experiments is rather good for β from 23 to 23+90 degrees. The dis crepancies not exceed 10%. For the highest β at com bination of plates with β = 90° and β = 45° (average β = 67.5°) the experimental data are 14 to 23% lower than predicted by the model. The research for β = 65° was reported by Dovic et al. [10]. The authors have performed tests with two models of PHE channels having corrugations with angles at β = 65° and β = 28°. The tests were made with water and waterglycerol solutions. The water data corresponds to Re numbers higher than 200. The heat transfer results of these authors are presented in Fig. 8. As the hydraulic diameter they used is dh = 2b/Fx, the values of Nu and Re were corrected by Fx = 1.19. The data for Nu were calculated at Pr = 3.54 (water 50°C) to account for the difference in the exponent of Pr. The data were taken from a graph, so the accuracy is limited, but for Re > 100 the model prediction (solid lines on Fig. 8) is fairly good. The error for β = 65° does not exceed 10%. So we define the upper β limit of the model as 65°. The lower limit for Reynolds number can be considered 100. The heat transfer and friction factor data for differ ent arrangements of two plates with β = 60° and β = 30° are from Muley and Manglik [9]. The authors studied the cooling of hot water (2 < Pr < 6) and used an equivalent diameter of de = 2b. The exponent of the Pr number was taken to be 1/3, so we performed cal culations for Pr = 4 to exclude the influence of Pr. The predictions of the model (solid lines in Fig. 9) are rather good for β = 60° and combination of plates with β = 60° and β = 30° (average β = 45°), the error is not bigger than 10%. But for a low angle β = 30° the model underestimates data by up to 30%. This can be explained based on the influence of the inlet and outlet distribution zones of the short tested plates (the dis tance between the ports is 392 mm, the length of the main corrugated field is approximately Lp = 280 mm). While the area of the distribution zones is about 20% of the total heat transfer area, the higher level of turbu lence generated at the entrance has an influence on the heat transfer of all plate, especially at low β, when there is about 15 cells formed by the corrugations along the length of a channel. For β = 60° the number of such cells is 27 and 23 cells for β = 45°. For this plate the ratio Lp/de = 55, but we can expect that such effect will be eliminated at Lp/de > 100. The data for heat transfer of longer plates were reported by Arsenyeva et al. [25]. These data for the commercial plates M10B

639

1 2 3

100

100

100

103

104

105 Re

Fig. 10. The influence of Reynolds number on heat trans fer for different plates. Comparison of data calculated by Eq. (8) (curves) with data from Arsenyeva et al. [21] (points): 1—β = 61°, 2—β = (61°+ 31°)/2, 3—β = 31° (γ = 0.588, Fx = 1.21).

of AlfaLaval are presented in Fig. 10. The length Lp is 720 mm and Lp/de is about 120. The error of the model does not exceed 10% for all the β analyzed: 1—β =

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Nu 60 50 40 30 20 10 0 200

600

1000

1400

Re

Fig. 11. The influence of Reynolds number on heat trans fers for different plates. Comparison of data calculated by Eq. (8) (curves) with data reported by Gherasim et al. [26] (points) with γ = 0.556, Fx = 1.

61°, 2—mixed β = 61° and β = 31° (average 46°), 3— β = 31°. Another study of PHE consisting of commercial plates with β = 60° was reported by Gherasim et al. [26]. The corrugations on the plates are of triangular cross section, but with small, about 1 mm flat zones at the edges. The pitch is 9 mm and the corrugation height is b = 2.5 mm, with an aspect ratio of γ = 0.556. The comparison of data calculated from the empirical correlation of the paper [26] (represented by the dot ted line) with our model results (solid line) at Pr = 3.54 are presented in Fig. 11. The error is not more than 5%. This confirms the applicability of the model for corrugations of different shapes: sinusoidal, triangular and even triangular with flat zones about 12% of the corrugation pitch. This paper shows the comparison of experimental results for heat transfer in PHE channels of various geometrical forms, reported in eight papers published by different authors. The natures of heat and momen tum transfer phenomena in flows at all these channels are similar. The average values of friction factors and film heat transfer coefficients can be calculated by the same equations of proposed dimensionless form. These equations account for the main parameters that characterize the geometrical form of the channel, but they are not sensitive to the size of the channel in the range of channel spacing from 1.12 to 10 mm. The range of applicability for these equations includes the possible range of geometrical parameters for commer cial plates. These equations can be used for the opti mization of PHEs geometrical parameters that meet the required process conditions. CONCLUSIONS The semiempirical mathematical model intro duced enables us to predict the film heat transfer coef ficients in PHE channels based on the geometrical parameters, such as corrugation angle β, profile aspect

ratio γ and the surface area enlargement factor Fx. The comparison with data available in the literature has shown that the error on the heat transfer prediction by proposed model is not larger than 15% in the following range of corrugations parameters: β from 14° to 65°; γ from 0.5 to 1.5; Fx from 1.14 to 1.5. This applies for Reynolds numbers from 100 to 25000 for both shapes of individual corrugations: sinusoidal and triangular. The model can be used for the optimization of the PHEs geometrical parameters that best meets the required process specifications of heat exchangers in the chemical and other industries. ACKNOWLEDGMENTS The financial support of EC Project INTHEAT (FP7SME20101262205INTHEAT) is sincerely acknowledged. NOTATIONS b—corrugation height, m; de—equivalent diameter, m; dh—hydraulic diameter, m; Fx—the ratio of actual surface area to projected one; h—heat transfer coefficient, W/(m2 K); p1, p2, p3, p4, p5—parameters defined by channel corrugation form; S—pitch of corrugations, m; W—flow velocities in channel, m2/s. β—the corrugation angle to the plate longitudinal axis, deg; γ—the corrugation profile aspect, γ = 2b/S; ζ—friction factor; λ—heat conductivity, W/(m K); μ—dynamic viscosity, Pa s; ρ—fluid density, kg/m3; τ—shear stress, Pa; ψ—the share of friction losses in total pressure loss in channel; hd Nu = e —Nusselt number; λ ρWd e Re =  —Reynolds number in PHE channel. μ SUBSCRIPTS AND SUPERSCRIPTS 0—tube; s—overall hydraulic resistance, accounting for all pressure losses; τ—accounting for pressure losses due to friction on the wall; w—on the wall.

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REFERENCES 1. Klemeš, J., Friedler, F., Bulatov, I., and Varbanov, P., Sustainability in the Process Industry. Integration and Optimization, New York: McGrawHill, 2010. 2. Fodor, Z., Varbanov, P. and Klemeš, J., Total Site Tar geting Accounting for Individual Process Heat Transfer Characteristics, Chem. Eng. Trans., 2010, vol. 21, p. 49. 3. Wang, L., Sunden, B., and Manglik, R.M., PHEs: Design, Applications and Performance, Southampton: WIT, 2007. 4. Shah, R.K. and Seculic, D.P., Fundamentals of Heat Exchanger Design, New York: Wiley, 2003. 5. Tovazshnyansky, L.L., Kapustenko, P.O., Khavin, G.L., and Arsenyeva, O.P., PHEs in Industry, Kharkiv: NTU KhPI, 2004. 6. Kukulka, D.J., Smith, R., and Fuller, K.G., Develop ment and Evaluation of Enhanced Heat Transfer Tubes, Appl. Therm. Eng., 2011, vol. 31, p. 2141. 7. Wang, Q.W., Lin, M., and Zeng, M., Effect of Lateral Fin Profiles on Turbulent Flow and Heat Transfer Per formance of Internally Finned Tubes, Appl. Therm. Eng., 2009, vol. 29, p. 3006. 8. Focke, W.W., Zacharadies, J. and Olivier, I., The Effect of the Corrugation Inclination Angle on the Thermo hydraulic Performance of Plate Heat Exchangers, Int. J. Heat Mass Transfer, 1985, vol. 28, p. 1469. 9. Muley, A. and Manglik, R.M., Experimental Study of Turbulent Flow Heat Transfer and Pressure Drop in a Plate Heat Exchanger with Chevron Plates, ASME J. Heat Transfer. 1999, vol. 121, p. 110. 10. Dovic’, D., Palm, B., Švaic’, S., Generalized Correla tions for Predicting Heat Transfer and Pressure Drop in Plate Heat Exchanger Channels of Arbitrary Geometry, Int. J. Heat Mass Transfer, 2009, vol. 52, p. 4553. 11. Tovazhnyansky, L.L., Kapustenko, P.A., and Tsibulnic, V.A., Heat Transfer and Hydraulic Resistance in Chan nels of Plate Heat Exchangers, Energetika, 1980, vol. 9, p. 123. 12. Savostin, A.F. and Tikhonov, A.M., Investigation of the Characteristics of PlateType Heating Surfaces, Therm. Eng., 1970, vol. 17, no. 9, p. 113. 13. Ayub, Z.H., Plate Heat Exchanger Literature Survey and New Heat Transfer and Pressure Drop Correlations for Refrigerant Evaporators, Heat Transfer Eng., 2003, vol. 24, no. 5, p. 3. 14. Khan, T.S., Khan, M.S., Chyu, MC., and Ayub, Z.H., Experimental Investigation of Single Phase Convective Heat Transfer Coefficient in a Corrugated Plate Heat

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

641

Exchanger for Multiple Plate Configurations, Appl. Therm. Eng., 2010, vol. 30, p. 1058. Martin, H., Theoretical Approach to Predict the Per formance of ChevronType Plate Heat Exchangers, Chem. Eng. Process., 1996, vol. 35, p. 301. Kutateladze, S.S. and Leont’ev, A.I., Heat Transfer, Mass Transfer, and Friction in Turbulent Boundary Lay ers, New York: Hemisphere, 1990. Kapustenko, P., Arsenyeva, O., and Dolgonosova, O., The Heat and Momentum Transfers Relation in Chan nels of Plate Heat Exchangers, Chem. Eng. Trans., 2011, vol. 25, p. 357. Arsenyeva, O., Tovazhnyansky, L., Kapustenko, et al., Investigation of the New Corrugation Pattern for Low Pressure Plate Condensers, Appl. Therm. Eng., 2011, vol. 31, p. 2146. Gogenko, A.L., Anipko, O.B., Arsenyeva, O.P., and Kapustenko, P.O., Accounting for Fouling in Plate Heat Exchanger Design, Chem. Eng. Trans., 2007, vol. 12, p. 207. Arsenyeva, O., The Generalized Correlation for Calcu lation of Hydraulic Resistance in Channels of PHEs, Integr. Technol. Energy Saving, 2010, no. 4, p. 112. Arsenyeva, O., Tovazhnyansky, L., Kapustenko, and P., Khavin, G., The Generalized Correlation for Fric tion Factor in Crisscross Flow Channels of Plate Heat Exchangers, Chem. Eng. Trans., 2011, vol. 25, p. 399. Tovazhnyansky, L.L. and Kapustenko, P.A., Intensifi cation of Heat and Mass Transfer in Channels of Plate Condensers, Chem. Eng. Trans., 1984, vol. 31, no. 6, p. 351. Zimmerer, C., Gschwind, P., Gaiser, G., and Kottke, V., Comparison of Heat and Mass Transfer in Different Heat Exchanger Geometries with Corrugated Walls, Exp. Therm. Fluid Sci., 2002, vol. 26, p. 269. Heavner, R.L., Kumar, H., and Wanniarachchi, A.S., Performance of an Industrial Plate Heat Exchanger: Effect of Chevron Angle, AIChE Symp. Ser., 1993, vol. 89, no. 295, p. 262. Arsenyeva, O., Tovazhnyansky, L., Kapustenko, P., and Khavin, G., Optimal Design of PlateandFrame Heat Exchangers for Efficient Heat Recovery in Process Industries, Energy, 2011, vol. 36, p. 4588. Gherasim, I., Taws, M., Galanis, N., and Nguyen, C.T., Heat Transfer and Fluid Flow in a Plate Heat Exchanger: Part I. Experimental Investigation, Int. J. Therm. Sci., 2011, vol. 50, p. 1492.

THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING Vol. 46

No. 6

2012