Improving the Thermal Efficiency of Gasket Plate Heat Exchangers Used in Vegetable Oil Processing

Abstract

The study investigates, by calculations, some ways to improve the thermal efficiency of plate heat exchangers (PHEs) used in the vegetable oil processing industry. The performance of these heat exchangers is limited by the heat transfer rate of the oil side and by the low thermal conductivity of the plate material. The study starts from a base case with vegetable oils cooled with water in plate heat exchangers, all with a chevron angle of 30° and a different number of channels and plate transfer areas. The change in one geometrical characteristic of the plates, namely the chevron angle, from 30° to 45° then to 60°, led to a significant increase in the overall heat transfer coefficients of 16.0% when changing from 30° to 45° and of 28.1%, on average, when increasing the angle from 45° to 60°. This is a significant increase accompanied by a rise in the pressure drops of the circuits, but the values are acceptable since they do not exceed 1 bar on the oil circuit and 1.4 bar on the cold fluid circuit, respectively. The use of Fe₃O₄–SiO₂/Water hybrid nanofluids with concentrations of 0.5% v/v, 0.75% v/v, and 1% v/v were investigated to replace the cooling water. An increase of 2.2% on average was noticed when using the 1% v/v nanofluid comparatively with water, which is not large but adds to the chevron angle increase. A supplementary 2.6% increase is possible by changing the manufacturing material for plates with aluminum alloy 6060 and also by adding to the performances obtained by previous modifications. The total increase for all sets of modifications can increase the performance by 34.2% on average. Thus, for the design of new PHEs, miniaturization of the equipment becomes possible.

1. Introduction

Plate heat exchangers (PHE) appeared one hundred years ago following the need for compact and more thermally efficient equipment for heat transfer [1]. Now they are widely used in the chemical and food industries, among many other industrial applications [2]. Plate heat exchangers are developed in a range of construction types: gasket plate-and-frame, brazed, welded, and welded plate-and-shell [3]. The gasket plate-and-frame heat exchanger is the oldest type of this category but remains popular for its benefits, such as versatility and easy maintenance [1,4]; it also known for its great thermal efficiency.

Over the years, the geometry of PHEs was improved to enhance heat transfer. Practicing corrugations with chevron angles in plates was widely adopted to increase the heat transfer area per unit volume [5,6], to create supplementary turbulence, or to avoid maldistribution of fluid in the ports [5,6]. Other small improvements were made, with increased effects on thermal efficiency and roughness. For example, wire inserts in the channels [7] led to an increase in longitudinal turbulence with an effect on performance, which enhanced by up to 38% compared with conventional chevron type plates. Modifying the stainless steel of the plates by electrochemical etching with a nitric acid-hydrochloric acid aqueous solution under a voltage of 5 V, Nguyen et al. [8] obtained a rougher surface which produced the effect of an increase in the heat transfer coefficient of 10.5–17.7%, while also increasing the friction coefficient by 21.3%.

Novel configurations of PHEs appeared, such as new geometry corrugates, by repeating a basic half-ellipse cross-section [9] or pillow-plate channels [10]. They bring some advantages. The repeated half-ellipse cross-sections induce transverse disturbances in the fluid, having a positive effect on the heat transfer of up to 37% over the conventional PHEs [9]. The pillow-plate channel, together with an elliptical welding spot in the middle of each unit, improves lateral mixing, leading to superior thermal performances and significantly decreasing the pressure loss in the apparatus [10].

For three decades now, the use of nanofluids as cooling agents was extensively studied [11,12,13,14], aiming to exploit their superior thermal properties. Nanoparticles enhance the conductivity of conventional fluids. Mononanofluids contain a single type of nanoparticle, such as metals, metallic oxides, or graphene. For example, carbon nanotubes (CNT) 1% vol enhance the thermal conductivity of ethylene glycol by 12.4% [15] and CeO₂ dispersed at 0.75% vol in water increased the overall heat coefficient by 28% [16]. Ajeeb et al. [12] reported that nanofluid with 0.2% vol Al₂O₃ in distilled water had an increased heat transfer (Nu number) of 27%. Unavoidably, the pressure drop increases too, by 8%.

The hybrid particles synthetized together have a synergistic effect on the thermal conductivity and, consequently, on the heat transfer rate. For example, the aqueous nanofluid containing 1% vol hybrid particles Fe₃O₄–SiO₂ with 47 nm dimension increased the number of transfer units (NTU) by 24.51% and the thermal effectiveness by 13.23% [11]. There is a variety of hybrid particles discovered in the latest years (binary oxides, graphene composites with metals or metal-oxides, graphene-polymer composites, etc.) but some were tested on other types of heat exchangers, so there is a need to focus on the thermal efficiency analysis of PHE applications and to calculate overall heat transfer coefficients since they may vary with the geometrical characteristics’ dimensions of PHE [14].

To improve thermal-hydraulic performance, new materials for plates were developed: polymer-graphene composite [17], coatings with Ni, Cu, and Ag [18], and metallic microporous layers [19], some which also responding to anticorrosion protection requirements.

Among the classic works for the calculation of a PHE’s performance, the book of Kakaç and Liu [20] is nominated as a foundational text. Other authors not only tested this performance in the laboratory but also developed and validated new equations describing thermal efficiency [21,22]. Some up-to-date sources [23,24,25] containing reliable equations, based on extensive experiments and validations, are available for the calculation of the thermal efficiency of PHEs. These equations are usually employed for the dimensioning of industrial equipment. For the present work, we preferred the mathematical model of Dović and co-workers [26], validated and published by us previously for the calculation of heat transfer coefficients [27], because it takes into account a flow profile in the channels that is close to reality, with one main component in the longitudinal direction and a furrow component affecting both the heat transfer rate and the pressure drop in the apparatus.

Higher efficiency and miniaturization are the new challenges for the development of heat exchangers. The overall heat transfer coefficients depend on the convection of fluids on both sides of the separating wall and on the thermal conductivity of the wall’s material. These overall coefficients have lower results than the lowest partial heat transfer coefficients. Any method to enhance the partial heat transfer coefficients is welcome.

Inspired by the works of our forerunners, the present study investigates some solutions for the enhancement of heat transfer in gasket PHEs used in the vegetable oil processing industry: modifying the chevron angle of corrugations, the use of Fe₃O₄–SiO₂ nanoparticles suspended in the cooling water, and a change in the material when making the plates.

2. Materials and Methods/Research Method

2.1. Equipment

Three chevron plate heat exchangers, serving as coolers in different stages of vegetable oil processing, were tested with water in a previous work [27]. Their geometrical characteristics are the same (Figure 1), but differences appear in the effective heat transfer number of plates and the size of some elements (corrugation depth b and channel cross-sectional flow area A_ch) as seen in

Table 1. The size of geometrical characteristics of the PHEs.

Geometrical Characteristics of Chevron Plates	Symbol	Heat Exchanger #1	Heat Exchanger #2	Heat Exchanger #3
Vertical distance between centers of ports	Lv	1070 (mm)	1070 (mm)	1070 (mm)
Plate length between ports (effective length)	Lp (Leff)	858 (mm)	858 (mm)	858 (mm)
Plate width	Lw	450 (mm)	450 (mm)	450 (mm)
Horizontal length between centers of ports	Lh	238 (mm)	238 (mm)	238 (mm)
Port diameter	Dp	212 (mm)	212 (mm)	212 (mm)
Plate thickness	δ	0.6 (mm)	0.6 (mm)	0.6 (mm)
Plate pitch or corrugation wavelength	p or l	3.17 (mm)	3.14 (mm)	3.14 (mm)
Corrugation depth (amplitude of sinusoidal duct)	b	2.57 (mm)	2.54 (mm)	2.55 (mm)
Corrugation inclination angle relative to vertical direction	β	30°	30°	30°
Surface enlargement factor	φ	1.17	1.17	1.17
Hydraulic diameter (=2 b/φ)	dh	4.396 (mm)	4.34 (mm)	4.5 (mm)
Channel cross-sectional free flow area	Ach	1.116 × 10−3 (m2)	1.144 × 10−3 (m2)	1.145 × 10−3 (m2)
Heat transfer total area	Ae	11.2 (m2)	9.2 (m2)	19.7 (m2)
Total number of plates	Nt	35	28	63
Number of fluid passes	Np	1	1	1
Number of channels for one pass	Ncp	17	13.5	31

, so their total heat transfer areas are different.

As seen in Table 1, all three heat exchangers have one pass for each fluid; the fluids work in countercurrents. In Figure 2, the construction of such an exchanger and the flow scheme are presented.

2.2. The Research Design

2.2.1. The Base Case

The three PHEs have different technological functions. PHE #1 cools the raw vegetable oil (RO) from 85 °C to 42 °C with cooling water (inlet temperature 30 °C); PHE #2 cools the bleached oil (BO) from 60 °C to 45 °C; and PHE #3 cools the winterized oil (WO) from 110 °C to 40 °C. So, there are differences between their thermal load and fluids properties, which vary with the origin and temperature. However, the physical properties of raw, bleached, and winterized oils are insignificantly different from those of the same vegetal origin.

There are two types of processing oils: sunflower and rapeseed, with density (ρ) and dynamic viscosity (μ) variation shown in Figure 3 and Figure 4. These values were determined in the laboratory with the apparatus Anton Parr SVM 3000 (Ashland, VA, USA), which measures both density and viscosity of a preset range of temperatures.

The specific heat capacity (c_p) and thermal conductivity (λ) values for sunflower oil and rapeseed oil at working temperature were experimentally determined by Hoffmann et al. [28].

The experimental data were collected from three PHEs. In the first part of the experiment, the sunflower oil was processed at four different mass flow rates and, in the second part, the PHEs ran one mass flow rate throughout the campaign for the rapeseed oil. In total, 15 sets of data are available in the base case for the calculations of thermal efficiency and pressure drop, as seen in

Table 2. The base case primary data and calculated similarity criteria (Equations (1)–(5)) for cooling fluid: water and chevron angle β = 30°.

Exp.#	PHE #	Oil Circuit (Hot Fluid)				Water Circuit (Cold Fluid)
		Mass Flowrate, kg/s	Resine	Nusine	Pr	Mass Flowrate, kg/s	Resine	Nusine	Pr
1	1	1.74	17	8.8	211.09	5.25	930	30.7	3.89
2	1	2.05	20	9.5		6.20	1073	34.1
3	1	2.46	24	10.4		7.43	1297	39.2
4	1	2.71	26	10.9		8.21	1437	42.2
5	2	1.94	11	11.6	287.5	2.55	584	21.5	3.89
6	2	2.19	13	12.2		2.88	658	23.4
7	2	2.49	15	12.9		3.27	748	25.7
8	2	2.78	15	12.9		3.62	828	27.7
9	3	1.77	9	5.8	151.0	6.02	600	21.5	3.68
10	3	1.48	10	6.2		7.11	707	24.2
11	3	1.83	12	6.7		8.52	845	27.5
12	3	1.95	14	7.0		9.41	936	29.6
13	1	2.72	18	8.4	202.15	8.23	1443	42.4	3.89
14	2	2.76	17	9.1	267.11	3.62	828	27.6	3.89
15	3	2.72	12	6.0	167.37	9.44	920	29.2	3.68

.

2.2.2. The Change in Corrugation Angles, Cooling Fluid, and Plate Material

The previous studies [29,30] have demonstrated that rising the corrugation angles of the plates causes changes in flow pattern, which led to the increase in heat transfer rate. These studies considered the heat exchange between hot water/cold water (or nanofluid aqueous suspension) and the increase in heat transfer rate impressive in this case. In our case, the hot fluid is vegetable oil with higher thermal resistance, so the heat transfer rate is expected to be lower. We investigated the rise in the corrugation/chevron angle from 30° to 45° and 60°, respectively, by observing the influence of the angle on the heat transfer coefficients and on the pressure drop in the heat exchangers.

The overall heat transfer coefficients in the heat exchangers studied are low due to the vegetable oil fluid partial coefficient, so a solution for increasing the heat transfer rate on the water side is to search for another fluid to replace the water. From the multitude of nanofluids experimented with in the literature, the majority are designed for refrigeration circuits; we chose an aqueous suspension of nanofluid, the Fe₃O₄–SiO₂/Water hybrid nanofluid, which has better physical properties when working at fluid temperatures between 30 and 40 °C. Since some properties of nanofluids are frequently calculated using the laws for common mixtures [11,31], which can introduce big errors in the case of hybrid materials suspensions, it is preferable to have all the physical properties experimentally determined. In the article [32], the density, viscosity, specific heat capacity, and thermal conductivity of Fe₃O₄–SiO₂/Water hybrid nanofluids, the variances in temperature for solid content in suspension in the range of 0–1%, and the volume concentration were determined experimentally. Then, the partial heat transfer coefficients in the hot loop of the heat exchangers and the overall ones were compared between water and nanofluids with 0.5%, 0.75%, and 1% vol. Fe₃O₄–SiO₂. Also, the influence on the pressure drop in the apparatus was quantified as a function of the solid concentration in the nanofluid.

Usually, the plates of PHEs are manufactured from stainless steel, a cheap and corrosion/erosion resistant material with small thermal conductivity (cca. 15 W/m K) compared with plain carbon steel (cca. 70 W/m K) at the working temperatures of the heat exchangers. It is desirable to find an affordable material with consistently higher conductivity to positively influence the heat transfer. The aluminum alloy 6060, with λ = 207 W/m K, possesses other attractive qualities: good processability and good weldability, making it prone to complex cross-sectional manufacturing. The calculation of the overall heat transfer coefficients was made for this material at the optimum case (corrugation angle, nanofluid) considered so far, and the coefficients were compared with those in case of stainless steel.

3. Model

An approach frequently found in the literature of heat transfer efficiency [25,27] is to plot Nu vs. Re, where Nu and Re are Nusselt and Reynolds, respectively. According to Dović and co-authors’ model (Equation (1)), Nu and Re are redefined as Nu and Re are redefined as Nu_sine and Re_sine by taking into account the cell’s sine ducts [26]. This model was validated by us in previous work on 27 sets of data [27] and proved to be reliable. Previously, Dović and co-authors [26] validated the model on their own experimental data on channels with β = 28° and β = 65° and on other data in the literature where the authors provided the exact geometric dimensions of the plates tested [33,34,35]. The model is valid for 28° < β < 65°.

Nu_sine numbers serve to calculate the partial heat transfer coefficients on each fluid side (Equation (1)):

$${Nu}_{sine}=0.38·0.40377·{(4·f_{app}{Re}_{sine}^2·{\displaystyle \frac{d_{h,sine}}{L_{furr}}})}^{0.375}{Pr}^{1/3}{\left({\displaystyle \frac{\mu }{{\mu }_w}}\right)}^{0.14}$$

(1)

where L_furr = b/sin(2β) is the furrow characteristic length.

-

d_h,sine is the hydraulic diameter of the sine duct, calculated with Equation (2) being related to the independent variable x—the ratio corrugation depth: corrugation wavelength (x = b/l), in Equation (2):

$${\displaystyle \frac{d_{h,sine}}{l}}=0.1429x^3-0.623x^2+1.087x-0.0014$$

(2)

-

f_app is the apparent friction factor, which takes into account the flow through sine duct. f_app is calculated with Equation (3):

$$f_{app}={\displaystyle \frac{C}{{Re}_{sine}}}+B$$

(3)

B and C are constants depending on the channel geometry.

Equations (4) and (5) serve the calculation of Re_sine number:

$${Re}_{sine}={\displaystyle \frac{u_{sine}{d}_{h,sine}}{\nu }}$$

(4)

$$u_{sine}={\displaystyle \frac{\dot{m_{ch}}}{\rho ·A_{ch,sine}}}$$

(5)

where u_sine is the average velocity in the cell’s sine duct in furrow direction [m/s], υ is the kinematic viscosity [m²/s], ${\dot{m}}_{ch}$ is the mass flowrate in the channel [kg/s], and A_ch,sine is the channel cross-section area transverse to the furrow [m²].

After calculating Nu_sine for the cell sine duct with Equation (1), Nu number for the whole cell is calculated with Equation (6):

$$Nu={\displaystyle \frac{{Nu}_{sine}\times dh}{{dh}_{sine}}}$$

(6)

Hence, the partial heat transfer coefficients on hot circuit (h_h) and on cold circuit (h_c) respectively, are as follows:

$$h_h={\displaystyle \frac{{Nu}_h\times {\lambda }_h}{dh}};h_c={\displaystyle \frac{{Nu}_c\times {\lambda }_c}{dh}}$$

(7)

A more detailed presentation of this model is made in work [26].

Then, the overall coefficient U is calculated with Equation (8):

$${\displaystyle \frac{1}{U}}={\displaystyle \frac{1}{h_h}}+{\displaystyle \frac{\delta }{{\lambda }_{plate}}}+{\displaystyle \frac{1}{h_c}}$$

(8)

where δ is plate thickness [m] and λ is metal thermal conductivity [W/m K].

For the calculation of the total pressure drop, one has to take into consideration the pressure drop in the cells (Δp_c) and the pressure drop in the ports (Δp_r), summed up to give the total pressure drop (Δp). Since the cells work in parallel, the pressure drop in the cells equals the pressure drop in one cell. Equations (9)–(12) are used to calculate the pressure drop on both fluids sides [20].

$$\Delta p=\Delta p_c+\Delta p_r$$

(9)

$$\Delta p_c=4\times f\times {\displaystyle \frac{L_{ef}\times N_p}{dh}}\times {\displaystyle \frac{G_{ch}^2}{2\rho }}\times {\left({\displaystyle \frac{\mu }{{\mu }_w}}\right)}^{-0.17}$$

(10)

where G_ch is the mass flow in the channel (kg m⁻²s⁻¹), μ is the fluid dynamic viscosity at the average temperature in the apparatus, μ_w is the viscosity at the wall, and L_ef, N_p, dh are geometrical characteristics (Table 1).

$${\Delta p}_r=1.4\times N_p\times G_p^2/2\rho$$

(11)

where G_p is the mass flow in the ports (kg m⁻²s⁻¹); Δp_r is negligible (units or dozens N/m²) in relation to Δp_c, (bar); however, it is common to take into consideration this term for the accuracy of the calculation [36,37,38]. By considering Δp_r as recommended in the literature, an increase of $\Delta p$ by 0.026–0.138% was obtained in our case, comparable to the situation in which Δp_r is neglected, depending on the fluid, turbulence, and corrugation angle.

The friction factor f is correlated by Dović [26] with the apparent friction factor f_app (Equation (2)) by Equation (12).

$$f={\displaystyle \frac{f_{app}\times dh}{2{(\cos \mathsf{\beta })}^3\times {dh}_{sine}}}$$

(12)

4. Results and Discussion

4.1. Changing the Chevron Angle of Plates

The Nu_sine and Re_sine were calculated with Equation (1), respectively, with Equation (3) on both fluid sides, for water as cooling fluid, at β = 30°, then 45° and 60°. The results were compared for the three chevron angles in the graph of Nu_sine vs. Re_sine (Figure 5). Then, the partial heat transfer coefficients, h, were calculated with Equations (4)–(6) and plotted versus Re_sine (Figure 6).

Figure 5a,b and Figure 6a,b indicate that the heat transfer rate increases with Re_sin, confirming that turbulence favors heat transfer. Also, it can be observed that increasing the chevron angle leads to an increase in both the Nu_sine number and the partial heat transfer coefficient h at the same Re_sine numbers. This could be explained by the influence of the plate geometry favoring the good mixing and uniformity of flow and temperature in the channel section. At Re_sine numbers corresponding to the flow on the oil side, at each Re_sine point, it is obvious that Nu_sine and h_h increase with the chevron angles (Figure 5a and Figure 6a); overall, there are no linear correlations for Nu_sine vs. Re_sine or h_h vs. Re_sine. This can be explained by the very different average temperatures of the oil in the exchangers of the close values of Re_sine. Instead, on the water side, the cooling water has close average temperatures in all exchangers, so the linearity is good with correlation coefficients R² = 0.9702–0.9969, as seen in Figure 5b and Figure 6b.

The overall heat transfer coefficients U were calculated with Equation (8) and the results are presented in

Table 3. The increase of overall heat transfer coefficients U with increasing the chevron angle *.

Data set #	U30°	U45°	U60°	(%) 30–45	(%) 45–60
1	301	349	412	15.8	20.8
2	325	377	447	15.9	21.4
3	356	414	492	16.2	22.1
4	373	435	518	16.4	22.4
5	377	403	469	7.0	17.3
6	399	432	491	8.3	14.9
7	423	471	517	11.3	11.0
8	427	469	562	10.0	21.7
9	199	208	267	4.5	30.0
10	213	223	288	4.9	30.6
11	230	242	314	5.0	31.3
12	241	253	329	5.0	31.6
13	298	341	440	14.5	33.4
14	320	363	474	13.3	34.8
15	209	258	319	23.9	28.8
Average increase, %				11.5	24.8

* Legend: chevron angle 30°; chevron angle 45°; chevron angle 60°.

. The increase in the heat transfer rate with the chevron angle is significant due to the 11.5% average when passing from 30° to 45°, and the 24.8% average when passing from 45° to 60°. This is an indication that building plates with a larger chevron angle in the range 30°–60° may improve substantially based on the performance of the heat exchanger. Sadeghianjahromi and co-authors [29] demonstrated this by experiment, in the range of 35°–50°–65°, with the mention that the increase from 50 to 65° is larger than the difference between 35° and 50°, a tendency confirmed by our data.

The overall heat transfer coefficients are smaller than the partial coefficients in Equation (8), namely smaller than the smallest value between h_c, and h_r. Also, the difference for the overall coefficients when passing from angle 30° to 60° is slightly lower than that for the partial coefficients. However, an important increase in the overall heat transfer coefficients is noticed, which can account for the better thermal performance of the apparatus.

The influence of the chevron angle on the pressure drop in the apparatus can be evaluated, at first glance, by comparing the friction factors at 30°, 45°, and 60°, both on water and oil circuits (Figure 7a,b). The plot f vs. Re_sin shows that values of f on oil circuits are larger than those for water circuits. It is explained by Re_sin, which is smaller for the laminar flow as it comes across the oil flow. According to Equation (3), corroborated by Equation (12), the smaller Re_sine is, the bigger f_app is and, by consequence, the bigger f is. Both family curves respect the exponential trend with correlation coefficients 0.93–0.95 for oil and >0.90 for water. The friction coefficients for water are in the asymptotic zone of the exponential curve, this is why their variation appears linear. In Figure 7a,b, it is obvious that increasing the chevron angle will lead to a rise in f values.

We compared Nu vs. Re at different chevron angles (30°–45°–60°) with data obtained in the literature for conditions as close as we could find. Working in the laboratory with shorter plates (L_v = 300 mm compared with our 1070 mm long plates) and with close corrugation angles (35°–50°–65°), Saderghianjahromi et al. [29] obtained higher Nu numbers at the same Re, and implicitly higher heat transfer coefficients. Their Nu numbers are 5.7% higher for plates with β = 35°, 20.8% higher for β = 50° compared with ours for β = 45°, and 16.0% higher for β = 65° compared with ours for β = 60°.

From the literature data collected in their review, Zhu and Haglind [39] built a general diagram of f vs. Re for different corrugation angles β, analogous to Moody’s diagram. By comparing our data with the diagram, for the steady laminar flow in oil circuits, our f values were an average of 6.4% lower for β = 30°, 20.3% lower for β = 45°, and 37.1% lower for β = 60°. Our data differ from Dović’s diagram [26] by a 19.46% increase for β = 30° and a 43% increase for β = 60°. For turbulent water flow, our values were 10.48% lower compared with the Zhu and Haglind diagram [39], but compared with Muley and Manglik [34], ours were 11.3% higher. Also, they were 19.4% higher than the values reported by Dović et al. [26]. Differences of that magnitude are frequently encountered in the literature since the experimental conditions differ, especially from PHE dimensions point of view.

The calculated pressure drops also indicate the increase in the values with the corrugation angle, both on water and oil circuits, as seen in Figure 8a,b. The pressure drops are larger on the water circuit than on the oil’s, even though the friction factors are smaller in water channels. This is due to the mass flow square $G_{ch}^2$ being much larger for the water circuit (see Equation (10)).

For an apparatus keeping all geometrical characteristics except the corrugation angle, in the oil circuits, the pressure drops Δp increase by 133.2% on average when changing the angle from 30° to 45°, and by 462.6% from 30° to 60°. The figures are comparable for the water circuit Δp increasing by 86.4% from 30° to 45°, and 414.3% from 30° to 60°, respectively. It is important to note that the pressure drop values are acceptable even for the corrugation angle of 60°, where the maximum values are below 1.0 bar for oil and below 1.4 bar for water. These data corroborated the important gains in heat transfer rate when changing the chevron angle from 30° to 60°, suggesting that this solution should be given further consideration.

4.2. Changing Water with Nanofluids as a Cooling Medium

A nanofluid with good physical properties is able to increase P_r numbers (=${\displaystyle \frac{c_p\mu }{\lambda }}$) and should be the preferred method to improve the performance of PHEs. The Fe₃O₄–SiO₂/Water hybrid nanofluids were selected from other aqueous suspensions since they have very good thermal conductivity and a higher viscosity than water at working temperatures, even if the specific heat coefficient c_p is slightly poorer. P_r numbers increased with the concentration of solids in suspension; in our case, up to 16.9% for the suspension with 1% Fe₃O₄–SiO₂. The concentration of these nanofluids is limited to 1% [33] due to the sharp increase in the viscosity over this concentration which can produce disturbances in the flow through the apparatus.

The partial heat transfer coefficients for the cold fluid h_c, as well as the overall coefficients for the PHEs with chevron angles 30°, 45°, 60° and fluids with 0.5%, 0.75%, and 1% Fe₃O₄–SiO₂ nanofluids (nf) were calculated and then compared with water as a cooling fluid. The results are summarized in Figure 9, Figure 10 and Figure 11 for all 15 sets of data in the base case.

The results in Figure 9, Figure 10 and Figure 11 show a significant increase in the partial heat transfer coefficients of the cooling circuit with the concentration of Fe₃O₄–SiO₂ in the nanofluid: up to 8.4% for the angle 30°, 22.8% for 45°, and 46,9% for 60°. However, the effect on the overall transfer coefficient is much smaller but not negligible: 2.2% for 30°, 2.3% for 45°, and 2.1% for 60° when increasing the concentration of Fe₃O₄–SiO₂ from 0 to 1%. This adds to the increase in the overall coefficients obtained when increasing the chevron angle.

The effect of replacing water with the Fe₃O₄–SiO₂/Water hybrid nanofluid on the pressure drop is illustrated in Figure 12a–c. As seen, the pressure drop in PHE increases moderately with the concentration of Fe₃O₄–SiO₂. By increasing the concentration from 0% to 1%, the pressure drops increases by 6.6% for the PHEs having chevron angles 30°, 4.7% for angle 45°, and with 5.8% for 60°. The rise of the pressure drop because of using nanofluid is much lower when compared with the increase because of changing the chevron angle and adds to that, without affecting it decisively.

One can raise the question of particulate fouling; as Ponticorvo et al. showed, this phenomenon can be caused by the interaction between nanoparticles and the base fluid or with heat transfer surfaces, but also by the temperature difference within the fluid. Therefore, nanoparticles can lose their stability in the suspension and stick to the surface [40]. We do not have experimental data related to this but know from theory that, in the case of the Al₂O₃–SiO₂ hybrid nanofluid, there is a strong interaction between particles and water favoring maintenance in suspension. Also, the temperature difference within the cooling agent is less than 10.5 °C from inlet to outlet, such that this factor is unlikely to cause suspension instability. Moreover, the turbulent flow prevents the deposition of nanoparticles.

4.3. Changing the Plate Material

When choosing the aluminum alloy 6060 for further calculations, the main reason was its very good thermal conductivity λ = 207 W/m K compared with stainless steel (λ = 15 W/m K), the material from which are made the plates of PHEs. In addition, it is appropriate for the manufacturing of the plates considering its good processability when embossed in thin sheets, it supports our process pressures, and it is resistant to corrosion and oxidation.

In previous calculations, the best overall heat transfer coefficients were obtained for plates with a corrugation angle of 60° and when replacing the water as cooling fluid with 1% v/v Fe₃O4–SiO₂ nanofluid. The pressure drops in PHEs under the new conditions were acceptable, with values under 1.5 bar. So, the overall heat transfer coefficients were recalculated with Equation (7), where only the λ_plate was replaced. The results are presented in

Table 4. The overall heat transfer coefficients for β = 60° nanofluid 1% v/v and plate manufactured from alloy 6060 compared with the base case.

Data Set #	U [W/m2 K] β = 30° Fluid: Water Stainless Steel Plate Base Case	U [W/m2 K] β = 60° Nanofluid 1%, Stainless Steel Plate	U [W/m2 K] β = 60° Nanofluid 1% Alloy 6060 Plate Final choice	U Increasing for Changing the Material β = 60° Nanofluid 1%	U Increasing From the Base Case to Final Choice %
1	301	427	435	2.0	44.5
2	325	461	471	2.3	44.8
3	356	510	523	2.6	46.8
4	373	533	547	2.7	46.5
5	377	490	501	2.3	33.0
6	399	514	526	2.5	32.0
7	423	540	554	2.6	30.9
8	427	378	555	2.7	30.1
9	199	273	278	1.5	39.8
10	213	296	301	1.7	41.3
11	230	323	329	1.9	42.6
12	241	348	355	2.0	47.2
13	298	455	404	4.1	35.7
14	320	532	456	4.5	42.3
15	209	330	333	3.0	59.7
Average increase:				2.6%	41.2%

.

The average increase in U by only changing the material is 2.6%. As calculations went, by adopting the chevron angle β = 60°, the hybrid nanofluid Al₂O₃–SiO₂ with 1% v/v concentration and the aluminum alloy 6060 as manufacturing material, the overall heat transfer coefficients increased by 30.1–59.7% for each PHE, with an average of 41.2%. This is an important increase, considering the resistance that vegetable oil imposes on the heat transfer rate.

Switching stainless steel with aluminum alloy will raise the problem of the new material’s cost compared with the old one. The price of metallic materials is volatile both in the domestic and international markets; however, a comparation can be made at the present time. Stainless steel SS316 at a manufacturer in China costs 980–1680 USD/t, depending on the quantity ordered [41]; aluminum alloy, according to the London Metal Exchange, is 2255 USD/t [42]. Even if shipping costs are added to the manufacturing price, it is clear that aluminum alloy is two or three times more expensive. However, due to the difference in density (8000 kg/m³ for stainless steel compared with 2700 kg/m³) and considering that the same material volume is employed in heat exchanger manufacturing, it is expected that a PHE would cost approximately the same amount.

5. Conclusions

When looking for solutions to improve the heat transfer of PHEs used in the vegetable oil processing industry, the following ways were searched: changing the corrugation inclination angle relative to vertical direction, replacing the water as cooling medium with appropriate nanofluid, and replacing the material for plate manufacture with an alloy with better thermal conductivity.

The findings of our study are the following:

The biggest influence on the PHEs’ performances was increasing the corrugation angle from β = 30° to β = 45°, then to β = 60°. Since the rise in partial heat transfer coefficients h_c was spectacular, the overall coefficients (U) increased less, but this was a significant increase of 11.5% when changing from 30° to 45° and by 24.8% from 45° to 60°. When increasing the corrugation angle from β = 30° to β = 60°, the pressure drops increased by 462.6% on average in the oil circuit and by 414.3% on average in the cooling fluid circuit. The values of pressure drops are acceptable on both fluids’ sides since they did not exceed 1 bar in oil and 1.4 bar in cold fluid circuit, respectively.

The use of Al₂O₃-SiO₂/Water hybrid nanofluid as cooling medium also improves the thermal efficiency of the PHEs by 2.2% on average, also increasing with the concentration of solid in fluid, but this is limited to 1% v/v because of the sharp increase in the fluid viscosity over this concentration.

Changing the manufacturing material for plates with aluminum alloy improves the heat transfer coefficients by 2.6% on average and the total increase for all the modifications can increase the performance by 45.0% on average. For the design of new PHEs, the miniaturization of the equipment is possible.