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Corrugated plate heat exchanger review
Renewable and Sustainable Energy Reviews (xxxx) xxxx–xxxx
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Corrugated plate heat exchanger review ⁎
Talal M. Abou Elmaatya, A.E. Kabeelb, , M. Mahgoubc a b c
Mansoura High Inst. of Eng. & Tech.-Mansoura College (MC), Reactors Dept., Egypt Atomic Energy Authority Mechanical Power Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, Tanta, Egypt
A R T I C L E I N F O
A BS T RAC T
Keywords: Heat transfer Heat exchanger Heat transfer enhancement
The developments and the enhancements in all the heat transfer equipments are mainly purposed for energy savings and savings in projects capital investment, through reducing the costs (energy or material). The better heat exchanger is one that transfer's high heat rate at low pumping power with a minimum cost. The spent of money for the research and development in corrugated plate heat exchangers, in last decades, from some companies, offered different and versatile types and models of that heat exchanger. In the current study I made a focus on researcher's efforts in research and developments for corrugated plate heat exchanger. This type of heat exchangers is widely used for different engineering fields and applications. Research reactors represent one of the important engineering fields that extensively use corrugated plate heat exchangers due to their simplicity in assembly/disassembly and their easy maintainability. The corrugated plate heat exchanger has a great flexibility than the other types of heat exchangers; both its heat transfer area and its cooling flow could be increased or decreased easily, so; it is commonly used for enlargement and upgrading works. The current revision incorporated different topics like; the plate heat exchanger structure, thermal performance, heat transfer enhancement mechanisms as well as plate heat exchanger advantages and limitations. The corrugated plate heat exchanger works efficiently in both single phase and two phase flow, while the two phase flow region still needs a lot of research work. Also; the corrugated plate heat exchanger thermal performance and pressure drop behaviours when using nano-fluids were discussed in the current revision.
1. Introduction Heat exchangers are heat transfer devices that exchange thermal energy between two or more mediums. Heat exchangers play a significant role in the operation of many systems such as power plants, nuclear reactors, process industries and heat recovery units. The development of heat exchangers design, reliability and maintainability is always a required matter to enhance the overall systems performance. The heat exchangers have many different types, like; shell and tube (vertical/horizontal), plate heat exchanger (corrugated or flat gasketed or brazed) and micro heat exchangers. Fig. 1 introduces a plate heat exchanger classifications based on their constructions. Two main categories of heat exchangers could be considered, the direct heat exchanger and the indirect heat exchanger. In a direct heat exchanger, the two mediums between which heat is exchanged are in direct contact, e.g. cooling towers. In an indirect heat exchanger, the two mediums between which heat is exchanged are separated by a wall as in plate heat exchanger. The classical method for the heat exchanger design is known as The LMTD (Log Mean Temperature Difference) and
⁎
NTU (Number of Transfer Units) method. These methods are based on iterations and prototype assumptions through the design. Due to these reasons, Computational Fluid Dynamics (CFD) techniques are adopted in the design of heat exchangers. 2. Plate heat exchanger structures and geometry Enhancement of heat transfer surfaces has developed over the years, and is the main focus in the heat exchanger industry. Enhanced surfaces yield higher heat transfer coefficient when compared to unenhanced surfaces. A surface can be enhanced by adding extended surfaces (e.g. fins), or employing interrupted surfaces (e.g. corrugations). The plate type heat exchangers are economic and efficient enough to be widely spread in many markets now days. With it's low cost, flexibility, easy maintenance, and high thermal efficiency. The plate proven design is the main parameter for its high efficiency. In addition to the plate efficiency, corrugation patterns that produce turbulent flows, it is not only cause's unmatched efficiency; it also produces a heat exchanger self-cleaning nature, which in turn reducing
Corresponding author. E-mail addresses: [email protected] (T.M. Abou Elmaaty), [email protected], [email protected] (A.E. Kabeel), [email protected] (M. Mahgoub).
http://dx.doi.org/10.1016/j.rser.2016.11.266 Received 29 August 2015; Received in revised form 3 October 2016; Accepted 29 November 2016 1364-0321/ © 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: Elmaaty, T.A., Renewable and Sustainable Energy Reviews (2016), http://dx.doi.org/10.1016/j.rser.2016.11.266
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Greek symbols
Nomenclature
φ β ϕ ˄ ρ λ μ α ζ
Area (m2) Corrugation depth (m) Corrugation depth (m) Corrugation depth (m) Corrugation depth (m) Diameter (m) Diameter (m) Friction factor Mass flux (Kg/m2 s) Acceleration of gravity (m/s2) Plate length (m) Number of fluid passes Nusselt Number Prandtle Number Prandtle Number Reynolds number Plate width (m) Plate width (m) Plate width (m)
A A A(φ) B(φ) b C(φ) d f G g L N Nu P Pr Re u V W
Plate chevron angle (deg) Plate chevron angle (deg) Surface enlargement factor Plate corrugation pitch m Thermal conductivity (W/m °C) Thermal conductivity (W/m °C) Dynamic viscosity (Pa s) Heat transfer coefficient (W/m2 °C) Moody friction factor
Subscripts b e h p l t w
bulk equivalent hydraulic port Laminar turbulent wall
Fig. 1. Brief classification of heat exchangers [1].
˄=6.9 mm and a corrugation depth of=2 mm generates a surface enlargement factor of =1.189. Commercial plates have commonly surface enlargement factor of ϕ=1.15 to ϕ=1.25 [3].
the fouling effect [2]. The most common surface pattern used is the chevron design Fig. 2. The corrugated plate heat exchanger consists of a number of gasketed plates constrained between an upper carrying bar and a lower guide bar. The plates are compressed between the fixed frame and the movable frame by using many tie bolts. [2]. The Structure of a typical gasketed plate heat exchanger with chevron plates is shown in Fig. 3. The important geometrical parameters for a plate heat exchanger are introduced and defined as in Fig. 4a and b. The following parameters are considered essential parameters in plate heat exchanger simulations, the chevron angle (ϕ ), the corrugation depth (b) and the corrugation pitch (˄) [3]. It has been convenient also to define the parameter “Surface enlargement factor” (ϕ) that calculated from the following relation.
φ =
1 Λ /2
∫0
Λ /2
3. Thermal-hydraulic parameters The hydraulic diameter, Reynolds number, Nusselt number and the friction factor for the corrugated plate heat exchanger are defined in the following section [3]. Two different definitions of the hydraulic diameter are adopted. The most common definition used is similar to
⎛d ⎞2 1 + ⎜ ( y (ζ )) ⎟ dζ ⎝ dζ ⎠
For instance, using a radius of r=1.6 mm, corrugation pitch of
Fig. 2. Chevron plate shape.
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Fig. 3. Structure of a typical gasketed plate heat exchanger with chevron plates.
ρ . u m . de G . de = μ μ
Re = and Nu =
α . de λ
The friction factor of a plate heat exchanger more likely to be defined based on the effective diameter and the projected length between the inlet and the outlet ports, as follows;
f =
ρ . Δp . de 2. L p . G 2
4. Film heat transfer coefficient The film heat transfer coefficient for plate heat exchangers has been investigated by several researchers. Most of them correlate the heat transfer coefficient using Dittus – Boelter equation, where the equation constants are changed [5].
NuD =
a RebD Pr c
Bogaert and Bolcs (1995) introduced experiments to investigate the heat transfer and the pressure drop of plate heat exchanger. This paper introduces explicitly the exponents of both Prandtl number and the viscosity ratio. The Nusselt number was given by Bogaert and Bolcs (1995) [6] as follows; ⎛ 1 ⎞ 64 ⎜ ⎟ e Pr+30
NuD = B1. ReBD2. Pr ⎝ 3 ⎠
A similar expression for the exponent on the viscosity ratio for calculating the friction factor has also been adopted by Shah and Focke (1988) [4]. B1, B2 are empirical constants specific for a certain plate and a certain Reynolds number range. As shown, this purposed correlation is considered a modification to the well known Dittus – Boelter correlation. Muley (1997) [7] developed a similar correlation as Bogaert and Bolcs (1995) correlation. Muley (1997) developed empirical correlations for the parameters B1 and B2. Both parameters are being functions of the chevron angle and the area enlargement factor. The final correlation for Nusselt number at low Reynolds numbers was stated as follows;
Fig. 4. a Corrugated plate geometry parameters. b Corrugated plate geometry parameters.
that defined in a two wide parallel plate flow, with a distance of b between them, hence;
de = 2. b The other definition could be more physically correct as it is defined according to the non – circular tube definition of the hydraulic diameter,
dh =
0.3
⎛ μ ⎞ (Re+6)0.125 . ⎜ ⎟ ⎝ μw ⎠
4. V 2. b = A φ
Nu =
To distinguish between these two definitions the subscripts, e is used for the effective diameter while the subscript h is used for the hydraulic diameter, as suggested by Shah and Focke (1988) [4]. Reynolds and Nusselt numbers may be defined as follow;
0.14 ⎛1⎞ ⎛ ⎛ φ ⎞0.38 ⎜ ⎟ μ⎞ ⎝3⎠ • ⎜ ⎟ 0.44 ⎜ ⎟ • Re0.5 D • Pr ⎝ 30 ⎠ ⎝ μw ⎠
30 ≤ Re≤ 400 and for high Reynolds number; 3
30 o ≤ φ ≤ 60 o
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T.M. Abou Elmaaty et al. ⎛1⎞ 0.14 ⎜ ⎟ ⎛ μ ⎞ A (ϕ) • B (φ)• ReC (φ) • Pr ⎝ 3 ⎠ • ⎜ μ ⎟ ⎝ w⎠
Nu =
transfer is represented by Martin (1996) [8], Fig. 6. is indicated that relation.
30 o ≤ φ ≤ 60 o
5. Pressure drop
Re≤ 1000
Martin (1996) [8] developed his heat transfer correlation by extending the Leveque theory into turbulent regime. The pressure drop was correlated using the Moody friction factor.
where;
A (ϕ) = 0.2668 − 0.00696 ϕ + 7.244 × 10−5 ϕ2 B (ϕ) = 20.7803 − 50.9372 ϕ + 41.1585 ϕ2 − 10.1507 ϕ3
1 = ζ
C (ϕ) = 0.728 + 0.0543 sin (2. π . ϕ /90 + 3.7) No correlation was predicted in Reynolds number between 400 and 1000. Martin (1996) [8], developed a semi - theoretical correlation for heat transfer and pressure drop in plate heat exchanger. Martin used the hydraulic diameter in defining the Reynolds and Nusselt numbers, thus
1 − cos ϕ 3.8 ζ1, o
for Reh≥ 2000 ζo = (1.8 log10 Reh − 1.5 )−2 39 ζ1, o = Re0.289 h Similar to the heat transfer correlations, Muley (1997) [7] developed an empirical correlation to calculate the pressure drop with dependences on the chevron angle and the surface enlargement factor. For low Reynolds number;
⎛ μ ⎞1/6 0.347 Nuh = 0.122 . Pr1/3 ⎜ ⎟ [ζ . Re2h sin (2 . ϕ)] ⎝ μw ⎠ The range of validity of the correlation is not given in the original reference, however it seems that the Reynolds number was varied between 400 and 10,000. Gaiser and Kottke (1998) [9] also investigated the effect of both the chevron angle (ϕ ) and the corrugation pitch (˄) on heat transfer and pressure drop. A plate with a large chevron angle, small corrugation pitch gave lower heat transfer coefficients than a wider corrugation pitch. There was no significant difference obtained for small chevron angles. Wanniarachchi et al. (1995) [10] investigated the heat transfer in chevron type plate heat exchangers for different chevron angles. They correlated their data with a asymptotic correlation, with two modes, the laminar mode and the turbulent mode. The correlation is described as follows;
1/5 ⎡ ⎛ 30.2 ⎞5 ⎛ ϕ ⎞0.83 ⎛ μ ⎞−0.22 ⎛ 6.28 ⎞5 ⎤ f = ⎢⎜ ⎟ + ⎜ 0.5 ⎟ ⎥ . ⎜ ⎟ . ⎜ ⎟ ⎢⎣ ⎝ Re ⎠ ⎝ 30 ⎠ ⎝ Re ⎠ ⎥⎦ ⎝ μw ⎠
30 o ≤ ϕ ≤ 60 o
2 ≤ Re≤400 For high Reynolds number
⎛ μ ⎞−0.22 f = A (φ) . B (φ) . ReC (φ) . ⎜ ⎟ ⎝ μw ⎠
30 o ≤ ϕ ≤ 60 o Re≥ 1000
where;
3 3 JNu + JNu l t
A (ϕ) = 2.917 − 0.1277 ϕ + 2.016 × 10−3 ϕ2
3.65 JNul = 0.455 β . Re 0.339 dh 12.6 0.646+0.00111 . β JNut = 1.142 Re dh β
B (ϕ) = 5.4742 − 19.0197 ϕ + 18.9338 ϕ2 − 5.3405 ϕ3 C (ϕ ) =
− (0.2 + 0.0577 sin (2. π . ϕ /90 + 2.1))
Lee et al. (2000) [11] investigated the influence of the plate length to the plate width ratio (Aspect Ratio) on the overall heat transfer
and
JNu =
+
for Reh ≺ 2000 64 ζo = Reh 597 ζ1, o = + 3.85 Reh
Martin developed his correlation by extending the Leveque theory into the turbulent region. The final expression for the Nusselt number was given as;
3
0.18 tan ϕ + 0.36 sin ϕ +
ζo cos ϕ
where;
Re = Reh. φ and Nu = Nuh . φ
JNu =
cos ϕ
Nu dh Pr1/3 (μ / μw )0.17
However, if the chevron angle β is smaller than 28°, then the heat transfer coefficient is evaluated using β=28°, the relation between the different chevron angles is
β = 90 − φ The performances of some available correlations were investigated compared to SWEP International Company data for specific plate, as shown in Fig. 5. The adopted correlations were by Martin (1996), Wanniarachchi et al. (1995), and Muley (1997). These correlations to some extant consider the plate geometry effect. The figure showed that, a good agreement was obtained with Martin (1996) and Wanniarachchi et al. (1995). The correlation of Muley (1997) under predicts the heat transfer at low Reynolds numbers. The chevron angle is considered the most important geometrical parameter on heat transfer and pressure drop. The effect of chevron angle on heat
Fig. 5. Different correlations validation w.r.t SWEP.
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The research paper introduced by L. Zhi-jian et al. (2008) did not introduce enough detail about the novel design especially the plate geometry. J.H. Doo et al. (2012) [13] presented a study to develop a novel cross-corrugated primary surface for an intercooler in an aeroengine. Cross-corrugated primary surface heat exchangers are proposed for such applications due to their relatively high ‘‘volume goodness’’ and thus the potential for light weight designs. In their study the recommended surface profiles were analyzed using threedimensional numerical simulation. The fully developed airflow in a cross-corrugated matrix unit cell was modelled with k–e turbulence model. A conventional cross-corrugated surfaces experimental data was used to validate the numerical model. The four different configurated surfaces are illustrated in Fig. 7. The important modelling results introduced by J.H. Doo et al. (2012), presented in Fig. 8, showed that, compared to the conventional sinusoidal model, a pressure drop reduction of approximately −15% was predicted for both the anti-phase and the full wave rectified secondary corrugation models (HC#01 and HC#03) with P/H=2.2 and θ (intersecting angle) =90°, with small changes to the predicted heat transfer capacity. The pressure drop of the in-phase secondary corrugation (HC#02) was predicted to increase by approximately +38%, and heat transfer capacity was enhanced by approximately +7%. J.H. Doo et al. (2012) [14] introduced, in other research paper during the same year (2012) under the title “Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger”, a quantitative assessment of the thermal performance of a crosscorrugated heat exchanger using CFD. This study included the longitudinal heat conduction effect for various design options such as different plate thickness and different corrugation geometry for a typical operating condition. J.H. Doo et al. also predicted the longitudinal heat conduction effect by using the network-of-resistance method’ in the wide range of the heat exchanger design space. They introduced the parameter, λ, that represent the dimensionless longitudinal heat conduction (LHC) effect, it is the ratio of the overall heat transfer coefficient based on CFD calculation to the overall heat transfer coefficient based on the cold side heat transfer coefficient, the hot side heat transfer coefficient, and the transverse heat conduction. They concluded that, when increasing the ratio of pitch of corrugation to the corrugation height, the corrugation becomes flatter. The flatter corrugation results in more uniform local heat transfer coefficient (HTC) distribution, as shown in Fig. 9. The PHE thermal performance is deteriorated by the highly nonuniform heat transfer coefficient (HTC) distribution. This deterioration is reflected on a temperature gradient along the plate. The longitudinal heat conduction (LHC) parameter, λ, is always smaller than unity, as shown in Fig. 10, which is obvious because thermal resistances
Fig. 6. Effect of chevron angle on heat transfer coefficient.
coefficient and pressure drop. They modified the pre mentioned correlation of Muley and Manglik (1999) to account for different aspect ratios. Three different plates, with two different lengths and two different widths, were investigated. They found that, for the aspect ratio 4 and 2.4, the friction pressure drop was the same; these aspect ratios correspond to the smaller plate width. They recommended that, the width of the plate is the main parameter affecting the frictional pressure drop performance, since a large part of the heat exchanger is used for distributing the flow across the width of the plate for a wider plate having the same plate length. The ports pressure drop is also important. Shah and Focke (1988) developed one of the widely used correlations for this pressure drop.
ΔPmanifolds
and ports
⎛ G2 ⎞ = 1.5 ⎜ ⎟ . N ⎝2 ρ⎠
where; N is the number of fluid passes; The following table, Table 1, summarizes the different correlations used for friction factor calculations. 6. Recent developments L. Zhi-jian et al. (2008) [12] introduced a new design for the corrugated Plate Heat Exchanger (PHE). The plates in the new design were compound corrugated plates. The introduced novel design was verified both numerically and experimentally. The results indicated that, the resistance to flow for the modified corrugated plate heat exchanger relative to the ordinary chevron type was decreased by a value more than 50%, while the corresponding heat transfer rate was lowered by a value about 25% approximately. Such a novel plate, consisting of longitudinal and transverse corrugations, can effectively avoid the problem of flow path blockage, which will help to extend the application of PHEs to the situation with unclean working fluids. L. Zhi-jian et al. (2008) introduced a theoretical equation for both the Nusselt number and the Fanning friction factor according to the numerical results obtained with varying inlet velocity.
Nu = 0.16 Re0.65
⎛ μ ⎞0.14 Pr 0.33⎜ ⎟ ⎝ μw ⎠
Table 1 Friction factor definition form different researchers work. Definition
Martin (1996) Edwards et al. (1974) Bogaert and Bolcs (1995)
ζ=
400≺ Re ≺18000
The experimental work results were also obtained for the compound corrugated plate heat exchanger with the same geometry as in the numerical simulation
1500≺ Re ≺15000
f = 0.2 Re−0.23
5
Lp=Port centre to centre distance L=A/W ( Flow length)
2 . ρ . Δp . de G 2 . Lp
ρ . Δp . de 2. . L . G 2 . ρ . Δp Fp = 2 2 2 G . b . WP .
f=
ρ . g. . Δp . de ⎛ μb ⎞ ⎜ ⎟ 2. . L . G 2 . ⎝ μw ⎠
ζ=
2 . ρ . Δp . de . Lp . G 2 .
Muley and Manglik (1999)
f=
ρ . Δpcore . . de 2. . Lp . G 2 .
Muley et al. (1999)
f=
ρ . Δpcore . . de 2. . L . G 2 .
Foke (1983) Foke et al. (1985) Talike et al. (1995 a,b)
Length scales
f=
Wanniarachchi et al. (1995)
f = 0.5 Re−0.32
⎛ μ ⎞0.14 Nu = 0.27 Re0.6 Pr 0.33 ⎜ ⎟ ⎝ μw ⎠
Reference
0.17
L=A/W ( Flow length)
L=A/W ( Flow length)
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Fig. 9. Local HTC distributions and standard deviations for four different P/H cases.
Fig. 7. Configurations of four different primary surfaces with; (a) conventional sinusoidal corrugation, (b) anti-phase secondary corrugation, (c) in-phase secondary corrugation and (d) full-wave rectified trough corrugation.
associated with the heat conduction should not be negative. The longitudinal heat conduction increases with increasing the plate temperature and decreasing with increasing the plate thickness (s) due to the proportionality of thermal with plate cross section. H. Lee et al. (2013) [15] analyzed the thermal hydraulic performance of a sinusoidal plate heat exchanger used in heat pump applications at low temperatures (LTLHP). The water-side heat transfer coefficient and pressure drop of the PHX were obtained through the experimental test. The refrigerant-side heat transfer performance was investigated by varying several parameters. H. Lee et al. (2013) stated that, the PHX performance was poor due to low refrigerant mass flux. The PHX needs better balance in two fluids for the LTLHP application. They concluded that, the large pressure drop on the waterside (caused by corrugations) and the low heat transfer coefficient (due to vapour phase) were the factors affect the ordinary plate heat exchanger performance. M. Kim et al. (2010) [16], performed experimental study on cross-flow air-cooled plate heat exchangers (PHEs). They manufactured two prototype PHEs, one with a single-wave plates and the other is a double-wave plates in parallel as shown in Fig. 11 and Fig. 12. Cooling air flows through the PHEs in a crosswise direction against internal cooling water. The heat exchanger aims to substitute open-loop cooling towers with closed-loop water circulation, which guarantees cleanliness and compactness. M. Kim
Fig. 10. Variation of the dimensionless LHC effect parameter λ according to the change of the metal temperature for the P/H=2.2 case.
et al. (2010) were aimed from the experiments to examine the heat transfer performance of the two prototypes. The tests showed that, double-wave PHE shows approximately 50% enhanced heat transfer performance compared to single-wave PHE. However, double-wave PHE costs 30% additional pressure drop. Single-wave plates have the same chevrons design, called primary waves, of ordinary plate heat exchangers. They were manufactured from a sheet of stainless-steel their thickness was 0.6 mm. Double-wave plates were made from titanium alloy, they are 0.5 mm thickness., Additional corrugations, called secondary waves, shaped vertically, were added on double wave plate. A high press deformed force is required for the double –wave
Fig. 8. Friction factor and Nusselet number variation with pitch to corrugation depth ratio.
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Fig. 11. PHE arrangement.
the plate heat exchangers in the transient regime. A wide range of the parametric study has been presented which brings out the effects of NTU and the heat capacity ratio on the response of the plate heat exchanger, subjected flow perturbation. The presented theoretical model is validated by appropriate experiments. Aydın D. (2009) [20], introduced an experimental study that incorporated the effects of surface geometries of three different types heat exchangers, called as PHEflat (Flat plate heat exchanger), PHEcorrugated (Corrugated plate heat exchanger) and PHEasteriks (Asterisk plate heat exchanger) on heat transfer, friction factor and exergy loss. The following figure, Fig. 15, is indicated the Corrugated and the Asterisk types. The experiments were carried out for a single pass heat exchanger with both parallel and counter flow conditions. The experiments were conducted for laminar flow conditions. Reynolds number and Prandtl number were in the range of 50≤Re≤1000 and 3≤Pr≤7, respectively. Heat transfer, friction factor and exergy loss correlations were deduced according to the experimental results. The results indicated that, the efficiency of the heat exchanger increases with increasing the fluids’ contact surface, pressure drop and mass flow rates. Also, it was noticed that the heat gained from the corrugated type heat exchanger is higher than that of the others. Accordingly, pressure drop increases too, the matter that increases the capital costs. The empirical correlations obtained from the experimental results are summarized in the following table, Table 2, for 50≤Re≤1000 and 3≤Pr≤7. Caner Turk et al, [21] performed experimental tests to evaluate the Gasketed plate heat exchanger from thermal and hydraulic point of view. The Reynolds number values during the experiments were ranged from 500 to 5000. Their results were compared with others for the
Fig. 12. Magnified images of the plate surfaces (a) single-wave surface and (b) doublewave surface.
shape due to its complicated shape. Thus the material and the thickness of the double-wave plates were changed to eliminate sheet fracture as well as to eliminate high deformability. T. Abou-El-Maaty and A. Abd-El-Hady (2009) [17] developed a model to study the corrugated plate heat exchanger performance based on Dittus Boelter's correlation for turbulent flow and H. Martin [8] correlations for laminar flow. A set of Alfa Laval data [18] for the heat exchanger type, M30-FG, is used for the model validation. The study proved that, this type of plate heat exchanger can withstand a decrease in its nominal number of plates by 15% without exceeding the pressure limit (100 kPa on primary side) and give a performance near the design performance, Fig. 13. While increasing the number of plates with the same nominal flow does not produce a significant effect. Anil et al. (2007) [19] introduced a predictive model to show the transient response of plate heat exchangers subjected to a step flow variation. The plate heat exchanger port effect on flow misdistribution during flow variations is analyzed and represented in Fig. 14. The results indicated that flow misdistribution affects the performance of
Fig. 13. PHE variation with the number of plates.
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Fig. 14. Temperature response for flow vitiation in both the hot and the cold channels.
showed a wider increase in the superheat region area, in the central part, for parallel flow than that predicted in counter flow by Yang et al. [23]. The counter flow didn’t produce a significant effect. Radia Eldeeb et al., [24] reviewed in their study, the two-phase, heat transfer and pressure drop correlations used for corrugated plate heat exchangers. They held comparisons among some different correlations in the light of their applicability of different refrigerants. K. Sarraf, S., et al., [25] introduced experimental study about the effect of superheated vapour on condensation process inside brazed plate heat exchange. Pentane is used as a working fluid in their study. The geometry and hydraulic parameters of that PHE, used in experiments, are introduced in the literature. The infrared technique is adopted to characterize the different heat transfer, two-phase, regions. The imaging technique showed a significant effect of vapour superheat on flow distribution at the plate heat exchange inlet, depending on the mass flux. The study is carried out at a range of superheat of 5–25 K. The heat transfer coefficient is increased by 70% at low mass flux. The pressure drop recorded 18% increase at that level of increase in heat transfer coefficient.
Fig. 15. The heat exchanger having the PHE corrugated and PHE asterisk surface structure. Table 2 Experimental results [20]. Nusselt Number
Corrugated
Asterisk
flat
a
b
R- square
sse
7. Nanofluid effects Arun Kumar Tiwari et al., [26] executed experiments to study chevron-type corrugated plate heat exchanger heat transfer characteristics and pressure drop when using CeO2/water nanofluid. The optimum nano particle concentration that leads to maximum heat transfer coefficient was determined. The nanofluid concentration that introduced a maximum heat transfer of 39% was 0.75 vol%. The heat transfer coefficient, under nano particles effects, increases with the increase in the secondary hot water flow rate. The study also showed the enhancement in heat transfer coefficient when the nanofluid temperature was decreased. A.E. Kabeel et al. [27] erected an experimental loop to study heat transfer characteristics and pressure drop for corrugated plate heat exchange. The plate geometry and hydraulic characteristics is cleared in their literature. The experiments were carried out under different nano fluid volumetric concentrations (1–4 vol%). Their experimental results were compared against theoretical model. They concluded that, both the heat transfer and the transmitted power were increased with the nanofluid concentrations. The heat transfer coefficient was increased by 13% at 4% nano fluid concentrations. The uncertainties for their experiments were 9.8%. A heat transfer and hydraulic parameters were investigated experimentally, for corrugated plate heat exchanger, when Al2O3 nano particles are used in a water base fluid by Shive Dayal Pandey, V.K. Nema [28]. Different naofluid concentrations, 2 ,3 and 4 vol%, were used through the experiments. The plate heat exchanger flow arrangement was counter current flow. The exergy loss was also
Parallel flow
Hot side
0.05774
0.8091
0.9983
0.1222
Counter flow
Cold side Hot side Cold side
0.04319 0.0488 0.0443
0.8368 0.8640 0.8709
0.9961 0.9989 0.9996
0.2288 0.1164 0.3828
Parallel flow
Hot side
0.04988
0.7830
0.9962
0.1407
Counter flow
Cold side Hot side Cold side
0.03131 0.03516 0.02928
0.8368 0.8637 0.8713
0.9961 0.9989 0.9996
0.1202 0.06026 0.01667
Parallel flow
Hot side
0.02545
0.8508
0.9991
0.00176
Counter flow
Cold side Hot side Cold side
0.02372 0.02503 0.02228
0.8508 0.8633 0.8717
0.9978 0.9989 0.9962
0.04017 0.03041 0.00990
same plate geometry. They employed the artificial neural network analysis when evaluating the heat exchanger performance. They concluded that, the artificial neural network can be used to predict the thermal and hydraulic performances. Yueh-Hung Lin et al., [22] introduced an experimental study, using Infrared imaging technique, for the observation of evaporation heat transfer during two phase flow. They used R-410A working fluid to pass though the chevron plate heat exchanger. The experiments were carried out in two flow categories, parallel flow and counter flow. Their results 8
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[3] Claesson J. Thermal and hydraulic performance of compact heat exchangers operating as evaporator in domestic heat pumps [Doctoral thesis]. Royal Institute of Technology; 2004. [4] Shah Shah RK, Focke WW. Plate heat exchangers and their design theory, in heat transfer equipment design. Washington D.C: Hemisphere Publishing Corp; 1998. p. 227–54. [5] Winterton RHS. Int J Heat Mass Transf 1998;41:809. [6] Bogaert R, Bolcs A. Global performance of a prototype brazed plate heat exchanger in a large Reynolds number range. Exp Heat Transf 1995;8:293–311. [7] Muley A. Heat transfer and pressure drop in plate heat exchangers [Ph.D. thesis]. Dept Mechanical Industrial and Nuclear Engineering, Div Graduate Studies and Research, University Of Cincinnati; 1997. [8] Martin H. A theoretical approach to predict the performance of chevron type plate heat exchangers. Chem Eng Process 1996;35:301–10. [9] Gaiser G, Kottke V. Effects of wave length and inclination angle on the homogeneity of local heat transfer in plate heat exchangers. Proc 11th Int Heat Transf Con, Kyongju Korea 1998;6:203–8. [10] Wanniarachchi A, Ratnam U, Tilton BE, Dutta-Roy K. Approximate correlation for chevron type plate heat exchangers. ASME 1995;HTD-314. [11] Lee SH, Bai YI, Cho DJ. The effect of aspect ratio on turbulent flow heat transfer and pressure drop in a plate heat exchanger. Int J Heat Exch 2000;i:113–24. [12] Zhi-jian L, Guan-min Z, Mao-cheng T, Ming-xiu F. Flow resistance and heat transfer characteristics of a new type plate heat exchanger. J Hydrodyn 2008;20(4):524–9. [13] Doo JH, Ha MY, Min JK, Stieger R, Rolt A, Son C. An investigation of crosscorrugated heat exchanger primary surfaces for advanced intercooled-cycle aero engines (Part-I: novel geometry of primary surface). Int J Heat Mass Transf 2012;55:5256–67. [14] Doo JH, Ha MY, Min,⇑ JK, Stieger R, Rolt A, Son C. Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger. Int J Heat Mass Transf 2012;55:4129–38. [15] Lee H, Hwang Y, Radermacher R, Chun H. Thermal and hydraulic performance of sinusoidal corrugated plate heat exchanger for low temperature lift heat pump. Int J Refreg 2013;36:689–700. [16] Kim M, Baik Y, Park S, Ra H, Lim H. Experimental study on corrugated cross-flow air-cooled plate heat exchangers. Exp Therm Fluid Sci 2010;34:1265–72. [17] Abou-El-Maaty T, Abd-El-Hady A. Plate heat exchanger – inertia flywheel performance in loss of flow transient. KERNTECHNIK 2009;74:35–41. [18] Laval Alfa. Report for M30 PHEX, Nov 1994. [19] Anil K K, Sarit Das K. Dynamics of plate heat exchangers subject to flow variations. Int J Heat Mass Transf 2007;50:2733–43. [20] Aydın D, Hüseyin D,B, Irfan K, Hasan G. Investigation of heat transfer and pressure drop in plate heat exchangers having different surface profiles. Int J Heat Mass Transf 2009;52:1451–7. [21] Turk Caner, Aradag Selin, Kakac Sadık. Experimental analysis of a mixed-plate gasketed plate heat exchanger and artificial neural net estimations of the performance as an alternative to classical correlations. Int J Therm Sci 2016;109:263–9. [22] Lin Yueh-Hung, Li Guang-Cheng, Yang Chien-Yuh. An experimental observation of the effect of flow direction for evaporation heat transfer in plate heat exchanger. Appl Therm Eng 2015;88:425–32. [23] Yang C-Y, Lin Y-H, Lin F-C. Effect of flow direction for the heat transfer performance of refrigerant R-410A evaporation in plate heat exchanger. Heat Transf Eng 2013;34(13):1133–9. [24] Eldeeb Radia, Aute Vikrant, Radermacher Reinhard. A survey of correlations for heat transfer and pressure drop for evaporation and condensation in plate heat exchangers. Int J Regrig 2016;65:12–26. [25] Sarraf K, Launay S, Tadrist L. Analysis of enhanced vapor desuperheating during condensation inside a plate heat exchanger. Int J Therm Sci 2016;105:96–108. [26] Tiwari Arun Kumar, Ghosh Pradyumna, Sarkar Jahar. Heat transfer and pressure drop characteristics of CeO2/water nanofluid in plate heat exchanger. Appl Therm Eng 2013;57:24–32. [27] Kabeel AE, Abou El Maaty b T, El Samadony Y. The effect of using nano-particles on corrugated plate heat exchanger Performance. Appl Therm Eng 2013;52:221–9. [28] Shive Dayal Pandey VK Nema. Experimental analysis of heat transfer and friction factor of anofluid as a coolant in a corrugated plate heat exchanger. Exp Therm Fluid Sci 2012;38:248–56. [29] Kumar Vikas, Tiwari Arun Kumar, Ghosh Subrata Kumar. Effect of variable spacing on performance of plate heat exchanger using nanofluids. Energy 2016;114:1107–19. [30] Marjan Goodarzi , et al. Investigation of heat transfer and pressure drop of a counter flow corrugated plate heat exchanger using MWCNT based nanofluids. Int Commun Heat Mass Transf 2015;66:172–9.
calculated experimentally. The plate heat exchanger heat transfer characteristics were enhanced by increasing both Reynolds and Peclet numbers. Also; using the AL2O3 nano particles enhance the heat transfer while the pumping power was increased with the increase in non particles concentrations. The study also showed that, a more heat load could be removed for the same plate heat exchanger when using nano fluid. The exergy losses remains constant for pure water while its value is lowered when nano fluid was used (2 vol%). Their study developed new correlations for heat transfer and friction factor for both pure water and naofluid. Vikas Kumar et al., [29] experimentally investigated the corrugated plate spacing effect on energetic and exergetic performance. Different nano particles (TiO2, Al2O3, ZnO, CeO2, hybrid (Cu+Al2O3), grapheme nanoplate (GNP) and multi-walled carbon nanotube (MWCNT)) are used though that experimental investigations. A plate spacing of 5.0 mm introduced the optimum heat transfer characteristics. Their data also showed that, MWCNT/water nanofluid with a plate spacing of 5.0 mm, introduced the maximum heat transfer coefficient. That maximum heat transfer coefficient is 53% higher relative to 0.75 vol % (optimum). The experiments also showed a nominal rise in pressure drop at 0.75 vol%. Marjan Goodarzi et al. [30] experimentally investigated the effect of covalent groups on thermo physical properties of carbon nanotubebase fluid. Multi-Walled Carbon Nano-Tubes (MWCNT) surfaces are covered covalently by silver (Ag) and cysteine (Cys). The MWCNT surface functions and thermal properties were studied by using characterization instruments. Different water base nano fluids are used to investigate the thermal and hydraulic parameters. The adopted flow pattern during the experiments in corrugated plate heat exchanger is counter flow. The Reynolds number was changed from 2500 to 10000 during the study, while the nano fluid volume fraction was from 0–1% by volume. A detailed results and discussion about the thermal and hydraulic performance were shown in the literature. 8. Conclusion This review covered some basic concepts and literatures related to plate heat exchangers. The major contribution of this paper is directed towards introducing a view about the different plate heat exchangers structure, flow arrangements and their using fields. The literature also includes the different enhancement mechanisms for the thermal and hydraulic performance. For a single phase heat transfer and fluid flow, in corrugated plate heat exchanger, considerable amount of data are available but this data still need enhancement and modification. So; an additional experimental and practical studies are required to cover all missing data. Also; The brazed corrugated plate heat exchangers extensively spread in many two phase flow fields, which means, incomplete and insufficient data availability to cover all boiling heat transfer regimes. Additional experimental work and modelling are needed on visualization, calculations and measurements of pressure drop and heat transfer especially when using nanofluids. References [1] Aslam Bhutta M, et al. CFD applications in various heat exchangers design: a review. Appl Therm Eng 2012;32:1e12. [2] www. The wcrgroup.com
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Contents lists available at ScienceDirect
Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser
Corrugated plate heat exchanger review ⁎
Talal M. Abou Elmaatya, A.E. Kabeelb, , M. Mahgoubc a b c
Mansoura High Inst. of Eng. & Tech.-Mansoura College (MC), Reactors Dept., Egypt Atomic Energy Authority Mechanical Power Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, Tanta, Egypt
A R T I C L E I N F O
A BS T RAC T
Keywords: Heat transfer Heat exchanger Heat transfer enhancement
The developments and the enhancements in all the heat transfer equipments are mainly purposed for energy savings and savings in projects capital investment, through reducing the costs (energy or material). The better heat exchanger is one that transfer's high heat rate at low pumping power with a minimum cost. The spent of money for the research and development in corrugated plate heat exchangers, in last decades, from some companies, offered different and versatile types and models of that heat exchanger. In the current study I made a focus on researcher's efforts in research and developments for corrugated plate heat exchanger. This type of heat exchangers is widely used for different engineering fields and applications. Research reactors represent one of the important engineering fields that extensively use corrugated plate heat exchangers due to their simplicity in assembly/disassembly and their easy maintainability. The corrugated plate heat exchanger has a great flexibility than the other types of heat exchangers; both its heat transfer area and its cooling flow could be increased or decreased easily, so; it is commonly used for enlargement and upgrading works. The current revision incorporated different topics like; the plate heat exchanger structure, thermal performance, heat transfer enhancement mechanisms as well as plate heat exchanger advantages and limitations. The corrugated plate heat exchanger works efficiently in both single phase and two phase flow, while the two phase flow region still needs a lot of research work. Also; the corrugated plate heat exchanger thermal performance and pressure drop behaviours when using nano-fluids were discussed in the current revision.
1. Introduction Heat exchangers are heat transfer devices that exchange thermal energy between two or more mediums. Heat exchangers play a significant role in the operation of many systems such as power plants, nuclear reactors, process industries and heat recovery units. The development of heat exchangers design, reliability and maintainability is always a required matter to enhance the overall systems performance. The heat exchangers have many different types, like; shell and tube (vertical/horizontal), plate heat exchanger (corrugated or flat gasketed or brazed) and micro heat exchangers. Fig. 1 introduces a plate heat exchanger classifications based on their constructions. Two main categories of heat exchangers could be considered, the direct heat exchanger and the indirect heat exchanger. In a direct heat exchanger, the two mediums between which heat is exchanged are in direct contact, e.g. cooling towers. In an indirect heat exchanger, the two mediums between which heat is exchanged are separated by a wall as in plate heat exchanger. The classical method for the heat exchanger design is known as The LMTD (Log Mean Temperature Difference) and
⁎
NTU (Number of Transfer Units) method. These methods are based on iterations and prototype assumptions through the design. Due to these reasons, Computational Fluid Dynamics (CFD) techniques are adopted in the design of heat exchangers. 2. Plate heat exchanger structures and geometry Enhancement of heat transfer surfaces has developed over the years, and is the main focus in the heat exchanger industry. Enhanced surfaces yield higher heat transfer coefficient when compared to unenhanced surfaces. A surface can be enhanced by adding extended surfaces (e.g. fins), or employing interrupted surfaces (e.g. corrugations). The plate type heat exchangers are economic and efficient enough to be widely spread in many markets now days. With it's low cost, flexibility, easy maintenance, and high thermal efficiency. The plate proven design is the main parameter for its high efficiency. In addition to the plate efficiency, corrugation patterns that produce turbulent flows, it is not only cause's unmatched efficiency; it also produces a heat exchanger self-cleaning nature, which in turn reducing
Corresponding author. E-mail addresses: [email protected] (T.M. Abou Elmaaty), [email protected], [email protected] (A.E. Kabeel), [email protected] (M. Mahgoub).
http://dx.doi.org/10.1016/j.rser.2016.11.266 Received 29 August 2015; Received in revised form 3 October 2016; Accepted 29 November 2016 1364-0321/ © 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: Elmaaty, T.A., Renewable and Sustainable Energy Reviews (2016), http://dx.doi.org/10.1016/j.rser.2016.11.266
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Greek symbols
Nomenclature
φ β ϕ ˄ ρ λ μ α ζ
Area (m2) Corrugation depth (m) Corrugation depth (m) Corrugation depth (m) Corrugation depth (m) Diameter (m) Diameter (m) Friction factor Mass flux (Kg/m2 s) Acceleration of gravity (m/s2) Plate length (m) Number of fluid passes Nusselt Number Prandtle Number Prandtle Number Reynolds number Plate width (m) Plate width (m) Plate width (m)
A A A(φ) B(φ) b C(φ) d f G g L N Nu P Pr Re u V W
Plate chevron angle (deg) Plate chevron angle (deg) Surface enlargement factor Plate corrugation pitch m Thermal conductivity (W/m °C) Thermal conductivity (W/m °C) Dynamic viscosity (Pa s) Heat transfer coefficient (W/m2 °C) Moody friction factor
Subscripts b e h p l t w
bulk equivalent hydraulic port Laminar turbulent wall
Fig. 1. Brief classification of heat exchangers [1].
˄=6.9 mm and a corrugation depth of=2 mm generates a surface enlargement factor of =1.189. Commercial plates have commonly surface enlargement factor of ϕ=1.15 to ϕ=1.25 [3].
the fouling effect [2]. The most common surface pattern used is the chevron design Fig. 2. The corrugated plate heat exchanger consists of a number of gasketed plates constrained between an upper carrying bar and a lower guide bar. The plates are compressed between the fixed frame and the movable frame by using many tie bolts. [2]. The Structure of a typical gasketed plate heat exchanger with chevron plates is shown in Fig. 3. The important geometrical parameters for a plate heat exchanger are introduced and defined as in Fig. 4a and b. The following parameters are considered essential parameters in plate heat exchanger simulations, the chevron angle (ϕ ), the corrugation depth (b) and the corrugation pitch (˄) [3]. It has been convenient also to define the parameter “Surface enlargement factor” (ϕ) that calculated from the following relation.
φ =
1 Λ /2
∫0
Λ /2
3. Thermal-hydraulic parameters The hydraulic diameter, Reynolds number, Nusselt number and the friction factor for the corrugated plate heat exchanger are defined in the following section [3]. Two different definitions of the hydraulic diameter are adopted. The most common definition used is similar to
⎛d ⎞2 1 + ⎜ ( y (ζ )) ⎟ dζ ⎝ dζ ⎠
For instance, using a radius of r=1.6 mm, corrugation pitch of
Fig. 2. Chevron plate shape.
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Fig. 3. Structure of a typical gasketed plate heat exchanger with chevron plates.
ρ . u m . de G . de = μ μ
Re = and Nu =
α . de λ
The friction factor of a plate heat exchanger more likely to be defined based on the effective diameter and the projected length between the inlet and the outlet ports, as follows;
f =
ρ . Δp . de 2. L p . G 2
4. Film heat transfer coefficient The film heat transfer coefficient for plate heat exchangers has been investigated by several researchers. Most of them correlate the heat transfer coefficient using Dittus – Boelter equation, where the equation constants are changed [5].
NuD =
a RebD Pr c
Bogaert and Bolcs (1995) introduced experiments to investigate the heat transfer and the pressure drop of plate heat exchanger. This paper introduces explicitly the exponents of both Prandtl number and the viscosity ratio. The Nusselt number was given by Bogaert and Bolcs (1995) [6] as follows; ⎛ 1 ⎞ 64 ⎜ ⎟ e Pr+30
NuD = B1. ReBD2. Pr ⎝ 3 ⎠
A similar expression for the exponent on the viscosity ratio for calculating the friction factor has also been adopted by Shah and Focke (1988) [4]. B1, B2 are empirical constants specific for a certain plate and a certain Reynolds number range. As shown, this purposed correlation is considered a modification to the well known Dittus – Boelter correlation. Muley (1997) [7] developed a similar correlation as Bogaert and Bolcs (1995) correlation. Muley (1997) developed empirical correlations for the parameters B1 and B2. Both parameters are being functions of the chevron angle and the area enlargement factor. The final correlation for Nusselt number at low Reynolds numbers was stated as follows;
Fig. 4. a Corrugated plate geometry parameters. b Corrugated plate geometry parameters.
that defined in a two wide parallel plate flow, with a distance of b between them, hence;
de = 2. b The other definition could be more physically correct as it is defined according to the non – circular tube definition of the hydraulic diameter,
dh =
0.3
⎛ μ ⎞ (Re+6)0.125 . ⎜ ⎟ ⎝ μw ⎠
4. V 2. b = A φ
Nu =
To distinguish between these two definitions the subscripts, e is used for the effective diameter while the subscript h is used for the hydraulic diameter, as suggested by Shah and Focke (1988) [4]. Reynolds and Nusselt numbers may be defined as follow;
0.14 ⎛1⎞ ⎛ ⎛ φ ⎞0.38 ⎜ ⎟ μ⎞ ⎝3⎠ • ⎜ ⎟ 0.44 ⎜ ⎟ • Re0.5 D • Pr ⎝ 30 ⎠ ⎝ μw ⎠
30 ≤ Re≤ 400 and for high Reynolds number; 3
30 o ≤ φ ≤ 60 o
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T.M. Abou Elmaaty et al. ⎛1⎞ 0.14 ⎜ ⎟ ⎛ μ ⎞ A (ϕ) • B (φ)• ReC (φ) • Pr ⎝ 3 ⎠ • ⎜ μ ⎟ ⎝ w⎠
Nu =
transfer is represented by Martin (1996) [8], Fig. 6. is indicated that relation.
30 o ≤ φ ≤ 60 o
5. Pressure drop
Re≤ 1000
Martin (1996) [8] developed his heat transfer correlation by extending the Leveque theory into turbulent regime. The pressure drop was correlated using the Moody friction factor.
where;
A (ϕ) = 0.2668 − 0.00696 ϕ + 7.244 × 10−5 ϕ2 B (ϕ) = 20.7803 − 50.9372 ϕ + 41.1585 ϕ2 − 10.1507 ϕ3
1 = ζ
C (ϕ) = 0.728 + 0.0543 sin (2. π . ϕ /90 + 3.7) No correlation was predicted in Reynolds number between 400 and 1000. Martin (1996) [8], developed a semi - theoretical correlation for heat transfer and pressure drop in plate heat exchanger. Martin used the hydraulic diameter in defining the Reynolds and Nusselt numbers, thus
1 − cos ϕ 3.8 ζ1, o
for Reh≥ 2000 ζo = (1.8 log10 Reh − 1.5 )−2 39 ζ1, o = Re0.289 h Similar to the heat transfer correlations, Muley (1997) [7] developed an empirical correlation to calculate the pressure drop with dependences on the chevron angle and the surface enlargement factor. For low Reynolds number;
⎛ μ ⎞1/6 0.347 Nuh = 0.122 . Pr1/3 ⎜ ⎟ [ζ . Re2h sin (2 . ϕ)] ⎝ μw ⎠ The range of validity of the correlation is not given in the original reference, however it seems that the Reynolds number was varied between 400 and 10,000. Gaiser and Kottke (1998) [9] also investigated the effect of both the chevron angle (ϕ ) and the corrugation pitch (˄) on heat transfer and pressure drop. A plate with a large chevron angle, small corrugation pitch gave lower heat transfer coefficients than a wider corrugation pitch. There was no significant difference obtained for small chevron angles. Wanniarachchi et al. (1995) [10] investigated the heat transfer in chevron type plate heat exchangers for different chevron angles. They correlated their data with a asymptotic correlation, with two modes, the laminar mode and the turbulent mode. The correlation is described as follows;
1/5 ⎡ ⎛ 30.2 ⎞5 ⎛ ϕ ⎞0.83 ⎛ μ ⎞−0.22 ⎛ 6.28 ⎞5 ⎤ f = ⎢⎜ ⎟ + ⎜ 0.5 ⎟ ⎥ . ⎜ ⎟ . ⎜ ⎟ ⎢⎣ ⎝ Re ⎠ ⎝ 30 ⎠ ⎝ Re ⎠ ⎥⎦ ⎝ μw ⎠
30 o ≤ ϕ ≤ 60 o
2 ≤ Re≤400 For high Reynolds number
⎛ μ ⎞−0.22 f = A (φ) . B (φ) . ReC (φ) . ⎜ ⎟ ⎝ μw ⎠
30 o ≤ ϕ ≤ 60 o Re≥ 1000
where;
3 3 JNu + JNu l t
A (ϕ) = 2.917 − 0.1277 ϕ + 2.016 × 10−3 ϕ2
3.65 JNul = 0.455 β . Re 0.339 dh 12.6 0.646+0.00111 . β JNut = 1.142 Re dh β
B (ϕ) = 5.4742 − 19.0197 ϕ + 18.9338 ϕ2 − 5.3405 ϕ3 C (ϕ ) =
− (0.2 + 0.0577 sin (2. π . ϕ /90 + 2.1))
Lee et al. (2000) [11] investigated the influence of the plate length to the plate width ratio (Aspect Ratio) on the overall heat transfer
and
JNu =
+
for Reh ≺ 2000 64 ζo = Reh 597 ζ1, o = + 3.85 Reh
Martin developed his correlation by extending the Leveque theory into the turbulent region. The final expression for the Nusselt number was given as;
3
0.18 tan ϕ + 0.36 sin ϕ +
ζo cos ϕ
where;
Re = Reh. φ and Nu = Nuh . φ
JNu =
cos ϕ
Nu dh Pr1/3 (μ / μw )0.17
However, if the chevron angle β is smaller than 28°, then the heat transfer coefficient is evaluated using β=28°, the relation between the different chevron angles is
β = 90 − φ The performances of some available correlations were investigated compared to SWEP International Company data for specific plate, as shown in Fig. 5. The adopted correlations were by Martin (1996), Wanniarachchi et al. (1995), and Muley (1997). These correlations to some extant consider the plate geometry effect. The figure showed that, a good agreement was obtained with Martin (1996) and Wanniarachchi et al. (1995). The correlation of Muley (1997) under predicts the heat transfer at low Reynolds numbers. The chevron angle is considered the most important geometrical parameter on heat transfer and pressure drop. The effect of chevron angle on heat
Fig. 5. Different correlations validation w.r.t SWEP.
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The research paper introduced by L. Zhi-jian et al. (2008) did not introduce enough detail about the novel design especially the plate geometry. J.H. Doo et al. (2012) [13] presented a study to develop a novel cross-corrugated primary surface for an intercooler in an aeroengine. Cross-corrugated primary surface heat exchangers are proposed for such applications due to their relatively high ‘‘volume goodness’’ and thus the potential for light weight designs. In their study the recommended surface profiles were analyzed using threedimensional numerical simulation. The fully developed airflow in a cross-corrugated matrix unit cell was modelled with k–e turbulence model. A conventional cross-corrugated surfaces experimental data was used to validate the numerical model. The four different configurated surfaces are illustrated in Fig. 7. The important modelling results introduced by J.H. Doo et al. (2012), presented in Fig. 8, showed that, compared to the conventional sinusoidal model, a pressure drop reduction of approximately −15% was predicted for both the anti-phase and the full wave rectified secondary corrugation models (HC#01 and HC#03) with P/H=2.2 and θ (intersecting angle) =90°, with small changes to the predicted heat transfer capacity. The pressure drop of the in-phase secondary corrugation (HC#02) was predicted to increase by approximately +38%, and heat transfer capacity was enhanced by approximately +7%. J.H. Doo et al. (2012) [14] introduced, in other research paper during the same year (2012) under the title “Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger”, a quantitative assessment of the thermal performance of a crosscorrugated heat exchanger using CFD. This study included the longitudinal heat conduction effect for various design options such as different plate thickness and different corrugation geometry for a typical operating condition. J.H. Doo et al. also predicted the longitudinal heat conduction effect by using the network-of-resistance method’ in the wide range of the heat exchanger design space. They introduced the parameter, λ, that represent the dimensionless longitudinal heat conduction (LHC) effect, it is the ratio of the overall heat transfer coefficient based on CFD calculation to the overall heat transfer coefficient based on the cold side heat transfer coefficient, the hot side heat transfer coefficient, and the transverse heat conduction. They concluded that, when increasing the ratio of pitch of corrugation to the corrugation height, the corrugation becomes flatter. The flatter corrugation results in more uniform local heat transfer coefficient (HTC) distribution, as shown in Fig. 9. The PHE thermal performance is deteriorated by the highly nonuniform heat transfer coefficient (HTC) distribution. This deterioration is reflected on a temperature gradient along the plate. The longitudinal heat conduction (LHC) parameter, λ, is always smaller than unity, as shown in Fig. 10, which is obvious because thermal resistances
Fig. 6. Effect of chevron angle on heat transfer coefficient.
coefficient and pressure drop. They modified the pre mentioned correlation of Muley and Manglik (1999) to account for different aspect ratios. Three different plates, with two different lengths and two different widths, were investigated. They found that, for the aspect ratio 4 and 2.4, the friction pressure drop was the same; these aspect ratios correspond to the smaller plate width. They recommended that, the width of the plate is the main parameter affecting the frictional pressure drop performance, since a large part of the heat exchanger is used for distributing the flow across the width of the plate for a wider plate having the same plate length. The ports pressure drop is also important. Shah and Focke (1988) developed one of the widely used correlations for this pressure drop.
ΔPmanifolds
and ports
⎛ G2 ⎞ = 1.5 ⎜ ⎟ . N ⎝2 ρ⎠
where; N is the number of fluid passes; The following table, Table 1, summarizes the different correlations used for friction factor calculations. 6. Recent developments L. Zhi-jian et al. (2008) [12] introduced a new design for the corrugated Plate Heat Exchanger (PHE). The plates in the new design were compound corrugated plates. The introduced novel design was verified both numerically and experimentally. The results indicated that, the resistance to flow for the modified corrugated plate heat exchanger relative to the ordinary chevron type was decreased by a value more than 50%, while the corresponding heat transfer rate was lowered by a value about 25% approximately. Such a novel plate, consisting of longitudinal and transverse corrugations, can effectively avoid the problem of flow path blockage, which will help to extend the application of PHEs to the situation with unclean working fluids. L. Zhi-jian et al. (2008) introduced a theoretical equation for both the Nusselt number and the Fanning friction factor according to the numerical results obtained with varying inlet velocity.
Nu = 0.16 Re0.65
⎛ μ ⎞0.14 Pr 0.33⎜ ⎟ ⎝ μw ⎠
Table 1 Friction factor definition form different researchers work. Definition
Martin (1996) Edwards et al. (1974) Bogaert and Bolcs (1995)
ζ=
400≺ Re ≺18000
The experimental work results were also obtained for the compound corrugated plate heat exchanger with the same geometry as in the numerical simulation
1500≺ Re ≺15000
f = 0.2 Re−0.23
5
Lp=Port centre to centre distance L=A/W ( Flow length)
2 . ρ . Δp . de G 2 . Lp
ρ . Δp . de 2. . L . G 2 . ρ . Δp Fp = 2 2 2 G . b . WP .
f=
ρ . g. . Δp . de ⎛ μb ⎞ ⎜ ⎟ 2. . L . G 2 . ⎝ μw ⎠
ζ=
2 . ρ . Δp . de . Lp . G 2 .
Muley and Manglik (1999)
f=
ρ . Δpcore . . de 2. . Lp . G 2 .
Muley et al. (1999)
f=
ρ . Δpcore . . de 2. . L . G 2 .
Foke (1983) Foke et al. (1985) Talike et al. (1995 a,b)
Length scales
f=
Wanniarachchi et al. (1995)
f = 0.5 Re−0.32
⎛ μ ⎞0.14 Nu = 0.27 Re0.6 Pr 0.33 ⎜ ⎟ ⎝ μw ⎠
Reference
0.17
L=A/W ( Flow length)
L=A/W ( Flow length)
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Fig. 9. Local HTC distributions and standard deviations for four different P/H cases.
Fig. 7. Configurations of four different primary surfaces with; (a) conventional sinusoidal corrugation, (b) anti-phase secondary corrugation, (c) in-phase secondary corrugation and (d) full-wave rectified trough corrugation.
associated with the heat conduction should not be negative. The longitudinal heat conduction increases with increasing the plate temperature and decreasing with increasing the plate thickness (s) due to the proportionality of thermal with plate cross section. H. Lee et al. (2013) [15] analyzed the thermal hydraulic performance of a sinusoidal plate heat exchanger used in heat pump applications at low temperatures (LTLHP). The water-side heat transfer coefficient and pressure drop of the PHX were obtained through the experimental test. The refrigerant-side heat transfer performance was investigated by varying several parameters. H. Lee et al. (2013) stated that, the PHX performance was poor due to low refrigerant mass flux. The PHX needs better balance in two fluids for the LTLHP application. They concluded that, the large pressure drop on the waterside (caused by corrugations) and the low heat transfer coefficient (due to vapour phase) were the factors affect the ordinary plate heat exchanger performance. M. Kim et al. (2010) [16], performed experimental study on cross-flow air-cooled plate heat exchangers (PHEs). They manufactured two prototype PHEs, one with a single-wave plates and the other is a double-wave plates in parallel as shown in Fig. 11 and Fig. 12. Cooling air flows through the PHEs in a crosswise direction against internal cooling water. The heat exchanger aims to substitute open-loop cooling towers with closed-loop water circulation, which guarantees cleanliness and compactness. M. Kim
Fig. 10. Variation of the dimensionless LHC effect parameter λ according to the change of the metal temperature for the P/H=2.2 case.
et al. (2010) were aimed from the experiments to examine the heat transfer performance of the two prototypes. The tests showed that, double-wave PHE shows approximately 50% enhanced heat transfer performance compared to single-wave PHE. However, double-wave PHE costs 30% additional pressure drop. Single-wave plates have the same chevrons design, called primary waves, of ordinary plate heat exchangers. They were manufactured from a sheet of stainless-steel their thickness was 0.6 mm. Double-wave plates were made from titanium alloy, they are 0.5 mm thickness., Additional corrugations, called secondary waves, shaped vertically, were added on double wave plate. A high press deformed force is required for the double –wave
Fig. 8. Friction factor and Nusselet number variation with pitch to corrugation depth ratio.
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Fig. 11. PHE arrangement.
the plate heat exchangers in the transient regime. A wide range of the parametric study has been presented which brings out the effects of NTU and the heat capacity ratio on the response of the plate heat exchanger, subjected flow perturbation. The presented theoretical model is validated by appropriate experiments. Aydın D. (2009) [20], introduced an experimental study that incorporated the effects of surface geometries of three different types heat exchangers, called as PHEflat (Flat plate heat exchanger), PHEcorrugated (Corrugated plate heat exchanger) and PHEasteriks (Asterisk plate heat exchanger) on heat transfer, friction factor and exergy loss. The following figure, Fig. 15, is indicated the Corrugated and the Asterisk types. The experiments were carried out for a single pass heat exchanger with both parallel and counter flow conditions. The experiments were conducted for laminar flow conditions. Reynolds number and Prandtl number were in the range of 50≤Re≤1000 and 3≤Pr≤7, respectively. Heat transfer, friction factor and exergy loss correlations were deduced according to the experimental results. The results indicated that, the efficiency of the heat exchanger increases with increasing the fluids’ contact surface, pressure drop and mass flow rates. Also, it was noticed that the heat gained from the corrugated type heat exchanger is higher than that of the others. Accordingly, pressure drop increases too, the matter that increases the capital costs. The empirical correlations obtained from the experimental results are summarized in the following table, Table 2, for 50≤Re≤1000 and 3≤Pr≤7. Caner Turk et al, [21] performed experimental tests to evaluate the Gasketed plate heat exchanger from thermal and hydraulic point of view. The Reynolds number values during the experiments were ranged from 500 to 5000. Their results were compared with others for the
Fig. 12. Magnified images of the plate surfaces (a) single-wave surface and (b) doublewave surface.
shape due to its complicated shape. Thus the material and the thickness of the double-wave plates were changed to eliminate sheet fracture as well as to eliminate high deformability. T. Abou-El-Maaty and A. Abd-El-Hady (2009) [17] developed a model to study the corrugated plate heat exchanger performance based on Dittus Boelter's correlation for turbulent flow and H. Martin [8] correlations for laminar flow. A set of Alfa Laval data [18] for the heat exchanger type, M30-FG, is used for the model validation. The study proved that, this type of plate heat exchanger can withstand a decrease in its nominal number of plates by 15% without exceeding the pressure limit (100 kPa on primary side) and give a performance near the design performance, Fig. 13. While increasing the number of plates with the same nominal flow does not produce a significant effect. Anil et al. (2007) [19] introduced a predictive model to show the transient response of plate heat exchangers subjected to a step flow variation. The plate heat exchanger port effect on flow misdistribution during flow variations is analyzed and represented in Fig. 14. The results indicated that flow misdistribution affects the performance of
Fig. 13. PHE variation with the number of plates.
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Fig. 14. Temperature response for flow vitiation in both the hot and the cold channels.
showed a wider increase in the superheat region area, in the central part, for parallel flow than that predicted in counter flow by Yang et al. [23]. The counter flow didn’t produce a significant effect. Radia Eldeeb et al., [24] reviewed in their study, the two-phase, heat transfer and pressure drop correlations used for corrugated plate heat exchangers. They held comparisons among some different correlations in the light of their applicability of different refrigerants. K. Sarraf, S., et al., [25] introduced experimental study about the effect of superheated vapour on condensation process inside brazed plate heat exchange. Pentane is used as a working fluid in their study. The geometry and hydraulic parameters of that PHE, used in experiments, are introduced in the literature. The infrared technique is adopted to characterize the different heat transfer, two-phase, regions. The imaging technique showed a significant effect of vapour superheat on flow distribution at the plate heat exchange inlet, depending on the mass flux. The study is carried out at a range of superheat of 5–25 K. The heat transfer coefficient is increased by 70% at low mass flux. The pressure drop recorded 18% increase at that level of increase in heat transfer coefficient.
Fig. 15. The heat exchanger having the PHE corrugated and PHE asterisk surface structure. Table 2 Experimental results [20]. Nusselt Number
Corrugated
Asterisk
flat
a
b
R- square
sse
7. Nanofluid effects Arun Kumar Tiwari et al., [26] executed experiments to study chevron-type corrugated plate heat exchanger heat transfer characteristics and pressure drop when using CeO2/water nanofluid. The optimum nano particle concentration that leads to maximum heat transfer coefficient was determined. The nanofluid concentration that introduced a maximum heat transfer of 39% was 0.75 vol%. The heat transfer coefficient, under nano particles effects, increases with the increase in the secondary hot water flow rate. The study also showed the enhancement in heat transfer coefficient when the nanofluid temperature was decreased. A.E. Kabeel et al. [27] erected an experimental loop to study heat transfer characteristics and pressure drop for corrugated plate heat exchange. The plate geometry and hydraulic characteristics is cleared in their literature. The experiments were carried out under different nano fluid volumetric concentrations (1–4 vol%). Their experimental results were compared against theoretical model. They concluded that, both the heat transfer and the transmitted power were increased with the nanofluid concentrations. The heat transfer coefficient was increased by 13% at 4% nano fluid concentrations. The uncertainties for their experiments were 9.8%. A heat transfer and hydraulic parameters were investigated experimentally, for corrugated plate heat exchanger, when Al2O3 nano particles are used in a water base fluid by Shive Dayal Pandey, V.K. Nema [28]. Different naofluid concentrations, 2 ,3 and 4 vol%, were used through the experiments. The plate heat exchanger flow arrangement was counter current flow. The exergy loss was also
Parallel flow
Hot side
0.05774
0.8091
0.9983
0.1222
Counter flow
Cold side Hot side Cold side
0.04319 0.0488 0.0443
0.8368 0.8640 0.8709
0.9961 0.9989 0.9996
0.2288 0.1164 0.3828
Parallel flow
Hot side
0.04988
0.7830
0.9962
0.1407
Counter flow
Cold side Hot side Cold side
0.03131 0.03516 0.02928
0.8368 0.8637 0.8713
0.9961 0.9989 0.9996
0.1202 0.06026 0.01667
Parallel flow
Hot side
0.02545
0.8508
0.9991
0.00176
Counter flow
Cold side Hot side Cold side
0.02372 0.02503 0.02228
0.8508 0.8633 0.8717
0.9978 0.9989 0.9962
0.04017 0.03041 0.00990
same plate geometry. They employed the artificial neural network analysis when evaluating the heat exchanger performance. They concluded that, the artificial neural network can be used to predict the thermal and hydraulic performances. Yueh-Hung Lin et al., [22] introduced an experimental study, using Infrared imaging technique, for the observation of evaporation heat transfer during two phase flow. They used R-410A working fluid to pass though the chevron plate heat exchanger. The experiments were carried out in two flow categories, parallel flow and counter flow. Their results 8
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[3] Claesson J. Thermal and hydraulic performance of compact heat exchangers operating as evaporator in domestic heat pumps [Doctoral thesis]. Royal Institute of Technology; 2004. [4] Shah Shah RK, Focke WW. Plate heat exchangers and their design theory, in heat transfer equipment design. Washington D.C: Hemisphere Publishing Corp; 1998. p. 227–54. [5] Winterton RHS. Int J Heat Mass Transf 1998;41:809. [6] Bogaert R, Bolcs A. Global performance of a prototype brazed plate heat exchanger in a large Reynolds number range. Exp Heat Transf 1995;8:293–311. [7] Muley A. Heat transfer and pressure drop in plate heat exchangers [Ph.D. thesis]. Dept Mechanical Industrial and Nuclear Engineering, Div Graduate Studies and Research, University Of Cincinnati; 1997. [8] Martin H. A theoretical approach to predict the performance of chevron type plate heat exchangers. Chem Eng Process 1996;35:301–10. [9] Gaiser G, Kottke V. Effects of wave length and inclination angle on the homogeneity of local heat transfer in plate heat exchangers. Proc 11th Int Heat Transf Con, Kyongju Korea 1998;6:203–8. [10] Wanniarachchi A, Ratnam U, Tilton BE, Dutta-Roy K. Approximate correlation for chevron type plate heat exchangers. ASME 1995;HTD-314. [11] Lee SH, Bai YI, Cho DJ. The effect of aspect ratio on turbulent flow heat transfer and pressure drop in a plate heat exchanger. Int J Heat Exch 2000;i:113–24. [12] Zhi-jian L, Guan-min Z, Mao-cheng T, Ming-xiu F. Flow resistance and heat transfer characteristics of a new type plate heat exchanger. J Hydrodyn 2008;20(4):524–9. [13] Doo JH, Ha MY, Min JK, Stieger R, Rolt A, Son C. An investigation of crosscorrugated heat exchanger primary surfaces for advanced intercooled-cycle aero engines (Part-I: novel geometry of primary surface). Int J Heat Mass Transf 2012;55:5256–67. [14] Doo JH, Ha MY, Min,⇑ JK, Stieger R, Rolt A, Son C. Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger. Int J Heat Mass Transf 2012;55:4129–38. [15] Lee H, Hwang Y, Radermacher R, Chun H. Thermal and hydraulic performance of sinusoidal corrugated plate heat exchanger for low temperature lift heat pump. Int J Refreg 2013;36:689–700. [16] Kim M, Baik Y, Park S, Ra H, Lim H. Experimental study on corrugated cross-flow air-cooled plate heat exchangers. Exp Therm Fluid Sci 2010;34:1265–72. [17] Abou-El-Maaty T, Abd-El-Hady A. Plate heat exchanger – inertia flywheel performance in loss of flow transient. KERNTECHNIK 2009;74:35–41. [18] Laval Alfa. Report for M30 PHEX, Nov 1994. [19] Anil K K, Sarit Das K. Dynamics of plate heat exchangers subject to flow variations. Int J Heat Mass Transf 2007;50:2733–43. [20] Aydın D, Hüseyin D,B, Irfan K, Hasan G. Investigation of heat transfer and pressure drop in plate heat exchangers having different surface profiles. Int J Heat Mass Transf 2009;52:1451–7. [21] Turk Caner, Aradag Selin, Kakac Sadık. Experimental analysis of a mixed-plate gasketed plate heat exchanger and artificial neural net estimations of the performance as an alternative to classical correlations. Int J Therm Sci 2016;109:263–9. [22] Lin Yueh-Hung, Li Guang-Cheng, Yang Chien-Yuh. An experimental observation of the effect of flow direction for evaporation heat transfer in plate heat exchanger. Appl Therm Eng 2015;88:425–32. [23] Yang C-Y, Lin Y-H, Lin F-C. Effect of flow direction for the heat transfer performance of refrigerant R-410A evaporation in plate heat exchanger. Heat Transf Eng 2013;34(13):1133–9. [24] Eldeeb Radia, Aute Vikrant, Radermacher Reinhard. A survey of correlations for heat transfer and pressure drop for evaporation and condensation in plate heat exchangers. Int J Regrig 2016;65:12–26. [25] Sarraf K, Launay S, Tadrist L. Analysis of enhanced vapor desuperheating during condensation inside a plate heat exchanger. Int J Therm Sci 2016;105:96–108. [26] Tiwari Arun Kumar, Ghosh Pradyumna, Sarkar Jahar. Heat transfer and pressure drop characteristics of CeO2/water nanofluid in plate heat exchanger. Appl Therm Eng 2013;57:24–32. [27] Kabeel AE, Abou El Maaty b T, El Samadony Y. The effect of using nano-particles on corrugated plate heat exchanger Performance. Appl Therm Eng 2013;52:221–9. [28] Shive Dayal Pandey VK Nema. Experimental analysis of heat transfer and friction factor of anofluid as a coolant in a corrugated plate heat exchanger. Exp Therm Fluid Sci 2012;38:248–56. [29] Kumar Vikas, Tiwari Arun Kumar, Ghosh Subrata Kumar. Effect of variable spacing on performance of plate heat exchanger using nanofluids. Energy 2016;114:1107–19. [30] Marjan Goodarzi , et al. Investigation of heat transfer and pressure drop of a counter flow corrugated plate heat exchanger using MWCNT based nanofluids. Int Commun Heat Mass Transf 2015;66:172–9.
calculated experimentally. The plate heat exchanger heat transfer characteristics were enhanced by increasing both Reynolds and Peclet numbers. Also; using the AL2O3 nano particles enhance the heat transfer while the pumping power was increased with the increase in non particles concentrations. The study also showed that, a more heat load could be removed for the same plate heat exchanger when using nano fluid. The exergy losses remains constant for pure water while its value is lowered when nano fluid was used (2 vol%). Their study developed new correlations for heat transfer and friction factor for both pure water and naofluid. Vikas Kumar et al., [29] experimentally investigated the corrugated plate spacing effect on energetic and exergetic performance. Different nano particles (TiO2, Al2O3, ZnO, CeO2, hybrid (Cu+Al2O3), grapheme nanoplate (GNP) and multi-walled carbon nanotube (MWCNT)) are used though that experimental investigations. A plate spacing of 5.0 mm introduced the optimum heat transfer characteristics. Their data also showed that, MWCNT/water nanofluid with a plate spacing of 5.0 mm, introduced the maximum heat transfer coefficient. That maximum heat transfer coefficient is 53% higher relative to 0.75 vol % (optimum). The experiments also showed a nominal rise in pressure drop at 0.75 vol%. Marjan Goodarzi et al. [30] experimentally investigated the effect of covalent groups on thermo physical properties of carbon nanotubebase fluid. Multi-Walled Carbon Nano-Tubes (MWCNT) surfaces are covered covalently by silver (Ag) and cysteine (Cys). The MWCNT surface functions and thermal properties were studied by using characterization instruments. Different water base nano fluids are used to investigate the thermal and hydraulic parameters. The adopted flow pattern during the experiments in corrugated plate heat exchanger is counter flow. The Reynolds number was changed from 2500 to 10000 during the study, while the nano fluid volume fraction was from 0–1% by volume. A detailed results and discussion about the thermal and hydraulic performance were shown in the literature. 8. Conclusion This review covered some basic concepts and literatures related to plate heat exchangers. The major contribution of this paper is directed towards introducing a view about the different plate heat exchangers structure, flow arrangements and their using fields. The literature also includes the different enhancement mechanisms for the thermal and hydraulic performance. For a single phase heat transfer and fluid flow, in corrugated plate heat exchanger, considerable amount of data are available but this data still need enhancement and modification. So; an additional experimental and practical studies are required to cover all missing data. Also; The brazed corrugated plate heat exchangers extensively spread in many two phase flow fields, which means, incomplete and insufficient data availability to cover all boiling heat transfer regimes. Additional experimental work and modelling are needed on visualization, calculations and measurements of pressure drop and heat transfer especially when using nanofluids. References [1] Aslam Bhutta M, et al. CFD applications in various heat exchangers design: a review. Appl Therm Eng 2012;32:1e12. [2] www. The wcrgroup.com
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