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Computational modelling of plate-fin and tube heat exchanger for heat transfer and pressure drop analysis

The heat transfer and pressure drop characteristics of plate-fin and tube heat exchanger is analyzed by using computational modeling. The parameters which are considered in this analysis are space between the two fins, length of the fin and tube ellipticity. The governing equations of continuity, momentum and energy are solved using the commercially available FLUENT software. Seven different cases are considered for heat transfer and pressure drop analysis. The main findings are related to the spacing between the fins, which is critical in terms of pressure drop. The tube ellipticity provides an increase in heat transfer coefficient and reduces in pressure drop.


Introduction
The plate-fin and tube heat exchanger are a cross-flow type heat exchanger, which uses plates as fins as indicated in ( Figure  1); therefore, the flow external to the tubes is unmixed. Often, it is categorized as a compact heat exchanger to emphasize its relatively high heat transfer surface area to volume ratio. The plate fin and tube heat exchanger is widely used in many industries, including the aerospace industry, for its compactness and low weight.
Different types of fin patterns, in addition to the plate, exist, such as louver, convex-louver, and wavy; however, in general, the plate fin tends to be the best in terms of performance and of constructional effectiveness. The tube geometry used in plate fin and tube heat exchangers is either circular or elliptical. The majority of the studies dealing with plate fin and tube heat exchangers have been conducted resorting to experiments.
Shepherd [1] analyzed early experimental data for heat transfer of plate fin and circular tube heat exchanger. Later on, Schulemberg [2] extended the analysis to plate fin and elliptical tubes. Kayansayan [3] investigated experimentally the effects of the outer surface geometry on the performance of flat plain fin and circular tube heat exchangers with four-row coils. Jang et al. [4] studied fluid flow and heat transfer over a multi row (1-6 rows) plate-fin and tube heat exchanger both numerically and experimentally. They considered effects of different geometrical parameters such as tube arrangement, tube row numbers and fin pitch (8-12 fins per inch) for the Reynolds number (based on the fin spacing and the frontal velocity) ranging from 60 to 900 and observed an average heat transfer coefficient of staggered arrangement is 15%-27% higher than that of in-lined arrangement, while the pressure drop of staggered configuration is 20%-25% higher than that of in-lined configuration. Wang et al. [5] investigated experimentally heat transfer and pressure drop for plate fin and tube heat exchanger. Beecher et al. [6] reported heat transfer data for twenty wavy geometries. Kays et al. [7] analyzed heat transfer and pressure drop of heat exchanger with louvered fins. Achaichia et al. [8] experimentally studied the heat transfer and pressure drop of tube and louvered fin surfaces; later [11] developed an analytical model for predicting air-side heat exchanger performance of louvered fin geometry. Rocha et al. [12] experimentally estimated the overall heat transfer coefficient of plate fin heat exchangers by considering circular and elliptical tubes. Kundu et al. [13] conducted a dimensional optimization for plate fin and tube heat exchangers with equilateral staggered triangular and rectangular pitch. Romero-Mendez et al. [14] used numerical techniques to estimate the effect of spacing between fins on heat transfer and pressure drop for single row fin and tube heat exchanger. Wang et al. [15] experimentally analyzed the effect of tube rows, fin pitch, and tube diameter on heat transfer and pressure drop for plate fin and tube heat exchanger. Wang et al. [16] presented correlations of the Colburn and friction factors for plate fin and tube heat exchangers. Saboya et al. [17] determined the average heat transfer coefficient for plate fin and elliptic tube heat exchangers using the naphthalene sublimation technique.
Torikoshi et al. [18] numerically investigated a plain fin and tube heat exchanger. Erek et al. [19] numerically investigated the effect of fin geometry on heat transfer and pressure drop for plate fin and tube heat exchangers, but they used one particular mass flow rate of the flue gas. Abu Madi et al. [20] determined the effect of geometrical parameters of flat and corrugated fins and the results are presented in terms of Colburn and friction factors.
The present work is focused on the numerical investigation estimation of heat flow, pressure drop, and temperature and velocity fields for the plate fin and tube heat exchanger with one row tube configuration; the analysis will be focused on the effect of fin spacing, ellipticity and fin height on the numerically predicted parameters.

Description of the problem
The plat fin and tube heat exchanger, which is the object of the present study, is schematically depicted in (Figure 2a circulating in the tube is water and it is considered to be fully developed turbulent flow. The convective heat transfer between the tube and fin is calculated using Gnielinski equation [21], which is given as:   The no-slip boundary condition is applied to the tube and the plate fins. The remaining computational boundaries take a symmetry condition. The material of the tube and plate fins is assumed to be copper.

Governing equations
The process is assumed to steady state and the governing equations describing conservation of mass, momentum and energy are expressed in vector form as follows [22]: Where, σ_k and σ_ε are the turbulent Prandtl numbers for the turbulent kinetic energy and its dissipation. Turbulent kinetic energy (k) and its dissipation rate (ε) are coupled to the governing equations via the turbulent viscosity relation (μ_t=ρC_μ k^2/ε). C_μ is not a constant value as in the standard k-ε model. The empirical constants, C_2, σ_k and σ_ε are equal to 1.9, 1.0 and 1.3, respectively [24].

Results and discussion
Static temperature contours  (Figure 4) (g-i). Therefore, it can be said that an increase in grid spacing will lead to a decrease of the difference between the inlet and outlet temperature. The influence of the length L2 (Figure 3a) on the temperature field is also analyzed. The change in L2 is equivalent to alter the distance between tube passes. The temperature field for the length L2 equal to 15.1 mm and fin spacing of 0.5 mm is shown in Figure   4 (a-c). The temperature field for the length L2 equal to 18.1 is reported in Figure 6 (Table 2). Total pressure contours  Figure 7 (d-f), Figure 7 (g-i) respectively. The effect of total pressure on ellipticity is also studied. (Figure 8) (a-i) represents the total pressure contours at fin spacing s = 0.5 mm with effect of ellipticity at various velocities.

Q=kA(∆T)/L (7)
( Figure 9) (a-c) represents the total pressure contours when the space between the fins s = 0.5 with effect of L2. The total pressure drop across the flow area for all the cases are summarized in (Table   3).

Conclusion
The present work focus on the heat flow and total pressure distribution across the plate fin and tube heat exchanger has been analyzed by using FLUENT software. The prototype of the plate fin and tube heat exchanger is designed in GAMBIT software and exported to FLUENT software for solving purpose. The study consists of several cases of fin geometry such as fin tube center, fin height; fin spacing and tube ellipticity are investigated, numerically.