Augmentation of Plate-Fin Heat Exchanger Performance with Support of Various Types of Fin Configurations

Fins are surface augmentations that are frequently employed in different types of heat exchangers to increase the efficiency of heat transfer between a solid surface and nearby fluid. The heat exchanger's surface area density was occasionally raised by combining geometrically better fins, which also helped to develop the convection heat transfer factor. These increased surface compact cores have several instances like OSF, Louvered fins, Wavy fins, Plain fins, and Pin fins [1]. Plate fins, pin fins, offset strip fins, louvered fins, and wavy fins are some of the different types of finned surfaces that are used in plate fin type of dense heat exchangers, where the finned surfaces actually offer a huge surface area density. These finned surfaces are used in several automotive, refrigeration, and air conditioning, propulsion system, waste heat recovery, cryogenic, and other heat recuperative uses. The fin geometry made the implementation of a (PFHE) unnatural as well [2]. The most prevalent fin configurations were interrupted fins and simple fins with rectangular, trapezoidal, or triangular channels. The investigation of "laminar and turbulent" flow and fluid dynamics in OSF fin designs has attracted a lot of research attention. Numerous scholars have investigated the features of fluid flow and heat transmission both numerically and experimentally.

Plain Fins:

Simple fins were continuous and in a line. The cross-sections of plain fins were typically triangular and rectangular. Compared to other designs of fins, the manufacture of triangular fins was straightforward. The plain fins, on the other hand, had weak structural integrity and limited heat transmission during laminar flow. Plain fins were typically utilized for pressure dips that could be harmful [3].

In order to evaluate the heat transfer factor (j) and the heat exchanger core pressure drop characteristic f-factor as functions of the heat exchanger geometry and Re number, Bose et al. (2019) presented a comprehensive mathematical research of the rectangular (PFHE). They examined the execution of the plain rectangular model using the finite volume approach (PFHE). They came to the conclusion that the (f) and (j) factors differ nonlinearly inside the boundaries of fin geometry, which are (1 h/s 4) and (0.04 t/s 0.14), and the laminar area of 200 Re 800. Additionally, they saw that (f) and (j) both decreased as Re and (t/s) increased, but increased with h/s [4].

The heat transfer correlations for rectangular plain fins were published by Bala et al. in 2013. The "heat transfer coefficient" could be calculated for all Re number magnitudes, including laminar and turbulent zones, using the formulas provided in terms of j-factor and f-factor. On the flat plate channel, there were installed rectangular fins. By comparing the correlations for the (f) and (j), it had been determined that they were accurate. For a compacted plate type HE, the parameters for heat transmission and friction-coefficient are presented, and they are in excellent agreement with the experimental data [5].

The heat transmission and f-factor correlations for plate-fin compact HE's triangular plain fin surfaces were presented by Bala et al. in 2015. The fluent software application was used to finish the numerical calculations. For a range of Re numbers, the coefficients (j) and (f) were calculated. These magnitudes were compared to the (j) and (f) coefficient data from previous, relevant investigations. Two different equations covering the low and high Re areas, as well as geometrical dimensionless elements, had been used to express the correlations [6].

By using the program COMSOL 4.3, Jia and Hu [7] created a numerical model to simulate a counter flows parallel HE. On the flat plate channel, there were installed rectangular fins. To replicate the heat transfer and fluid flow pattern in a unit cell of one cold channel and one hot channel, the researchers' study built a three-dimensional model of a multilayered counter flow parallel heat exchanger. Water and oil are both functioning fluids. The optimum HE design can be guided by the precise temperature, velocity, and pressure distributions in the channels.

Offset Strip Fins (OSF):

One of the greatest parts for improving heat transfer in airplanes, cryogenics, and other industrial processes that don't require mass production is OSF. The highest heat transfer performance surfaces are OSF surfaces. This was accomplished by reattaching the new, thin boundary layer to the fin plate of each (OSF) fin module and periodically disturbing it. Their heat transmission efficiency was 1.5 to 4 times greater than that of simple fins. If the study's focus had been on analyzing the pressure drop and heat transfer typical of (PFHE), concentrating on the (OSF) kind of (PFHE) [8].

Tiwari et al. [9] used the calculating approach of fluent simulation software to assess the performance factors of a counter flow HE. The results show that efficiency increased with mass flow rate, and both the theoretical and actual total heat transfer factors rise as mass flow rate increases. The overall thermal conductance increased as the j-factor grew, which was proportional to the heat transfer factor. Finally, they came to the conclusion that the pressure drop swiftly grew because the pressure drop in the HE varies with the shifting mass flow rate. There were numerous deviations.

By using numerical analysis, Bhowmik and Lee [10] investigated a steady-state three-dimensional mathematical model to assess the heat transmission and pressure drop properties of an OSF-HE. The (f_cor) and (j_cor) factors could be used to investigate flow and heat transfer in laminar, turbulent, and even transitional zones thanks to a common correlation known as the derivative. Using the correlated jcor, the effect of Prandtl numbers was determined and the Nusselt number was projected. For various fluids, three alternative performance criteria for HEs were evaluated.

Yang and Li [11] employed numerical analysis to examine the heat transmission and flow f-factors for offset strip fins (OSF) used in (PFHE)s. Comprehensive analysis of the geometrical effects on the thermal hydraulic performance s for OSF fins was conducted. According to the findings of the experimental research, the proposed correlation may be calculated using 92.5% of the (j) data and 90.3% of the (f) data within 20%, with RMS errors under 15%. Comparing the suggested correspondences to the existing ones reveals that they provide calculations for OSF fins of various thicknesses covering a wide range of blockage ratios, whereas the earlier correspondences only adjust for the thinner fins and actually depart from practice at higher blockage ratios [11].

Plain and Offset Strip Fins:

Yang et al. [12] looked at the conformist fin's qualities, including efficacy and efficiency. They employed an offset strip fin (OSF) and a plain fin, which was mathematically, examined using 3D models with strong validation. The analysis's findings demonstrated that the thermal performance of the fin surface increased with actual fin efficiency. In areas with relatively low Re, the OSF fin's fin performance was higher than the plain fin's with the same cross section, however plain fins perform better in areas with Re > 1000. Additionally, the OSF fins with big (d) were well chosen in the low Re zone, whilst those with small (d) are better suited for use in conditions with a relatively high Re number.

In one-side heated vertical channels with plain fins, serrated fins, and perforated fins, Yang et al. [13] investigated the evaluation of heat transfer and flow friction qualities using experimental and mathematical analysis. The heating situation and Prandtl number influences caused the experimental j-factor of the serrated fin to be equal to 20% less than the values of "Manglik and Bergles" correlation, whereas the friction-coefficient (f) showed a well agreement with the results of "Manglik and Bergles" correlation with a relative error of 10%. This is because the friction-coefficient (f) was primarily influenced by Re number.

Four fundamental (PFHE) fins were computer generated by Zhu and Li [14] using 3-dimensional numerical simulations of the flow and heat transfer in the laminar flow domain. The (PFHE)s, rectangular plain fins, strip offset fins, perforated fins, and wavy fins were all included in the model geometry. The analysis' findings indicate that there was good agreement between the computations and the experimental analysis. Additionally, a data-decreasing method for calculating the local Nusselt numbers, (j) coefficient, and (f) coefficient was provided. Using this method, the properties of the four fins' pressure drop and heat transfer were obtained and thoroughly examined.

Yang et al. [15] evaluated the offset strip fins' improved heat transfer utilizing in (PFHE). To accurately depict the thermodynamic performance of various path architectures, they suggested a method of solution known as a relative entropy generation distribution coefficient (PFHE). A typical offset strip (OSF) and a plain fin model are the model geometries. According to the analysis's findings, the relatively small results in better implementation, while the parameter or, which contribute to the greatest degree of OSF fin heat transfer enhancement, should be computed after the other two geometric parameters have been selected.

The goals of this study can be summarized as investigating how the OSF fin configuration affects heat transfer to a single-phase fluid in PFHE and gaining a better and more quantitative understanding of the heat transfer process that takes place when a fluid passes through the OSF fin configuration as follows:

• Inspect the hydro-dynamics and thermal performance of different fin configuration.

• Analysis the effect of using the OSF fin configuration on flow field, heat transfer enhancement and friction losses.

• Using a novel fin shapes (OT and ORT) and examining them hydrodynamics and thermal performance.

Paper's Layout:

2. Model description: Illustrates the model geometry and the boundary conditions.

3. Demand to capacity ratio results: Explains the numerical method.

4. Results and discussion: Illustrates results and discussion.

5. Conclusions: Provides a set of conclusions drawn from this study.

3.1 Assumptions

The proposed model solution is simplified on the following presumptions:

(1) Three-dimensional model;

(2) The air is the working fluid;

(3) A constant properties fluid;

(4) Steady state flow;

(5) The flow is incompressible;

(6) The gravity effect is neglected;

(7) Non slip flow is assumed;

(8) The airflow is laminar, and laminar model was used;

(9) Neglecting the dissipation of heat is assumed;

(10) The wall thickness is neglected.

3.2 Governing equations

By resolving the average differential equation of mass (continuity) and momentum equation, the laminar incompressible stable equations may be used to describe the fluid motion in the plate fin heat exchanger for the laminar state:

3.2.1 Continuity equation

The mass conservation is mathematically represented by the continuity equation. Its form is [17]:

$\frac{\partial U}{\partial x}+\frac{\partial V}{\partial y}+\frac{\partial W}{\partial z}=0$          (1)

$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$           (2)

3.2.2 Momentum equations (NSEs)

Equations of momentum are a group of equations that derived throughout Newton second law of momentum to conserve the fluid momentum in the three directions of fluid motion; x, y and z [18]. These equations are known as Navier-Stokes equations (NSE), named after Navier and Stokes [19]:

Momentum equation in x-direction:

$\rho\left(u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y}+w \frac{\partial u}{\partial z}\right)=-\frac{\partial p}{\partial x}+\left(\frac{\partial^2 u}{\partial x^2}\right)+\left(\frac{\partial^2 u}{\partial y^2}\right)+\left(\frac{\partial^2 u}{\partial z^2}\right)$          (3)

Momentum equation in y-direction:

$\rho\left(u \frac{\partial v}{\partial x}+v \frac{\partial v}{\partial y}+w \frac{\partial v}{\partial z}\right)=-\frac{\partial p}{\partial x}+\left(\frac{\partial^2 v}{\partial x^2}\right)+\left(\frac{\partial^2 v}{\partial y^2}\right)+\left(\frac{\partial^2 v}{\partial z^2}\right)$          (4)

Momentum equation in z-direction:

$\rho\left(u \frac{\partial w}{\partial x}+v \frac{\partial w}{\partial y}+w \frac{\partial w}{\partial z}\right)=-\frac{\partial p}{\partial x}+\left(\frac{\partial^2 w}{\partial x^2}\right)+\left(\frac{\partial^2 w}{\partial y^2}\right)+\left(\frac{\partial^2 w}{\partial z^2}\right)$          (5)

3.2.3 Energy equation

$u \frac{\partial T}{\partial x}+v \frac{\partial T}{\partial y}+w \frac{\partial T}{\partial z}=\frac{k}{\rho C_p}\left[\frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial y^2}+\frac{\partial^2 T}{\partial z^2}\right]$          (6)

3.3 Boundary conditions

The inlet velocity for air (cold fluid) was uniform with a temperature of 300 k and an outlet pressure equal to zero. Furthermore, the upper and lower plates of the plate fin heat exchanger were kept at a constant heat flux of (q=3,000W/m²). To facilitate simulation, periodic boundary conditions were adopted for the left and right sides of the computational domain. Finally, the velocity at the walls is assumed to be zero (no-slip).

3.4 Hydrodynamic parameters

The required outcomes have been found by using the "Area Weighted Averaged", "wall flux", and "interfaces" in a sequence for calculating Nu, Q, h, Δp.

For pressure drop, since the outlet is set to pressure zero, the pressure drop equal to the pressure at the inlet.

Pin-Pout=ΔP

While volume weighted Averaged, mass, and fluid are used in a sequence to calculate the mean velocity (u) and density ($\rho a v$).

The Reynolds number, which is normally used to describe the flow phenomena depend on the four quantities: The diameter of the flow and the viscosity, density, and average liner velocity of the fluid. The Reynolds number is defined by equation [20]:

Re=inertial forces/viscous forces

$\mathbf{{R e}=\rho U_{i n} D_h / \mu}$          (7)

where, D_h is the hydraulic diameter which is One of the important parameters which characterizing the flow in ducts or tubes is the hydraulic diameter. This is used with fluid properties and Reynolds number to calculate inlet velocity [21].

$D_h=\frac{4 A_c}{P_{e r}}=\frac{4 A_c L}{A}$          (8)

where, L is the total length of the plate-fin channel, A is the total heat transfer area, and Ac is the free flow area in the cross section.

The Nusselt number on the heated tube is defined as [12]:

$\mathrm{Nu}=\frac{1}{A_{(x, z)}} \int_0^l \int_0^w N u d z d x$          (9)

$N u=\frac{h D_h}{k}$          (10)

where, h is the actual average gas-side heat transfer coefficient.

The definition of the friction coefficient in terms of shear stress at the channel surface as:

$\mathrm{C}_{\mathrm{f}}=\tau_{\mathrm{w}} / \frac{1}{2} \rho \mathrm{U}^2$           (11)

where, τ_w is the wall is shear stress and defined as [22]:

$\tau_{\mathrm{w}}=\mu \sqrt{\left(\frac{\partial \mathrm{u}}{\partial \mathrm{y}}\right)^2+\left(\frac{\partial \mathrm{w}}{\partial \mathrm{y}}\right)^2}$           (12)

Additionally, the friction factor (Fanning fraction factor) is provided by [12]:

$c_f=\frac{f}{4}$           (13)

A dimensionless term, the Colburn (j) factor is a function of the Pr number and the Re number. It is crucial for figuring out the fluid's heat transfer coefficient. The source of the J-factor is [12]:

$\mathrm{j}=\mathbf{S t} \operatorname{Pr}^{2 / 3}=\frac{\mathrm{h}}{\rho \mathrm{uC}_p} \operatorname{Pr}^{2 / 3}$           (14)

Additionally, this component aids in the different correlations which are researchers have built to assess the fluid flow parameters, where St is the Stanton number.

3.5 Grid independency

In order to select the optimal grid and obtain a better solution, a grid independence study is prepared. The investigation of grid independence is taken into account in the current results seven different values. Table 2 provides a summary of the specified grid for all shapes. At Re=600, the f-factor is calculated for each arrangement. It is discovered that the value of the f-factor has barely changed. The grid resolution examination exposes that at the cells 249670, 171214, 151214, 182214 and 186213 cells respectively, the PR, PT, OR, OT and ORT become independent of the grid.

Table 2. Different studied cases and them different grids with their f-factor results

3.6 Solving by FLUENT

The commercial (CFD) code can be used to solve the numerical method of the discredited governing equations. Ansys Fluent 2021 R1 is the program uses to calculate the current numerical investigation. Fluent is frequently used in this field and it is regarded as some of the best code currently in use [23]. The governing equations are approximated using a laminar model and finite volume discretization. The numerical computation employs a pressure-based solver with double precision. On the PFHE surface, a non-slip boundary condition is used. For pressure velocity coupling, the SIMPLE method is employed. The discretization of all terms was done using a second order upwind approach.

3.7 Validations

Through this work the f-factor values for the OSF fin in the PFHE is established numerically, for the experimental works of [13]. The validations include the f-factor is displayed in Figure 6.

6.png

Figure 6. Comparison of the numerical values and the experimental data of f-factor f air tests for [13]

The average deviation for f-factor between the experimental works [13] and the numerical work is 3% which shows a good agreement.