Novel Fin-Integrated Baffle Design for a Shell-and-Tube Heat Exchanger: An Experimental Study

The design of fins fabricated through conventional routes using fiber and baffle assembly, topologically optimised layouts, and good mechanical properties. The fin position is considered for maintenance requirement which are the flow passages created by the fin baffle arrangement remain accessible for inspection, cleaning, and long-term operating reliability.

2.1 Thermal design

The total heat load of the STHX can be calculated using the heat balance equations for the hot and cold fluid streams, with the hot fluid flowing through the tube and the cold fluid through the shell, as given by Eqs. (1)–(3), assuming steady-state and adiabatic conditions:

$Q_{{cold}}=Q_{{hot}}$        (1)

$Q_{{cold}}=\left[\dot{m} . C c\left(T c_{{out}}-T c_{{in}}\right)\right]_{{shell}}$          (2)

$Q_{{hot}}=\left[\dot{m} . C h\left(T h_{{in}}-T h_{{out}}\right)\right]_{{tube}}$        (3)

The total heat load was calculated using the logarithmic mean temperature difference (LMTD) method, as shown in Eqs. (4)–(5):

$Q=$ U.A. $\Delta T_{{LMTD}}$       (4)

$\Delta T_{L M T D}=\frac{\left(T h_{{in}}-T c_{{out}}\right)-\left(T h_{{out}}-T c_{{in}}\right)}{\ln \frac{\left(T h_{{in}}-T c_{{out}}\right)}{\left(T h_{{out}}-T c_{{in }}\right)}}$        (5)

The total convective heat transfer coefficient (U), total heat transfer area (A), and $\Delta T_{L M T D}$ is the temperature difference between the two fluids at the two ends of the STHX. The temperature of the hot fluid inlet (Th_in), the cold fluid inlet (Tc_in), and the temperature of the hot fluid outlet (Th_out) and cold fluid outlet (Tc_out). The total heat transfer area (A) was calculated based on the tube diameter (d_tube), which is determined as the average of the inner (d_intube) and outer (d_outtube) diameters of the tube, tube length (L_tube), and number of tubes (N_tube), as shown in Eq. (6):

$A=\pi \cdot \frac{\left(d_{{intube}}+d_{{outtube}}\right)}{2} \cdot L_{{tube}} \cdot N_{{tube}}$        (6)

Based on theoretical calculations, the fouling resistance or thermal energy resistance (R_th) is assumed negligible, so the fouling resistance in Eq. (7) can be written for the cylindrical tube and both overall convective heat transfer coefficients of hot (h_h) and cold (h_c) fluids, respectively. The thermal conductivity of the tube (k) is described in Eq. (8) for the clean surface of the total convective heat transfer coefficient (U) for the tube and shell sides.

$R_{t h}=\frac{1}{h_h \cdot A_{{intube}}}+\frac{\ln \left(\frac{d_{{outtube}}}{d_{{intube}}}\right)}{2 \pi \cdot k \cdot L_{{tube}}}+\frac{1}{h_c \cdot A_{{outtube}}}$            (7)

$\frac{1}{U}=R_{t h}$         (8)

We use the Dittus-Boelter and Churchill-Bernstein approach to calculate the shell side of the convective heat transfer coefficient and the pressure drop. To solve the convective heat transfer coefficient of the tube side, the Nusselt number of the hot fluid (Nu_hot) is calculated using the internal-flow Dittus-Boelter approach, with n = 0.4 for heating of the fluid and n = 0.3 for cooling of the fluid [17]. This correlation is applicable only to the internal flow on the tube side and was therefore not applied to the shell side flow. The structural parameters such as baffle spacing, cut ratio, number of fins, and fin dimensions are adapted to laboratory equipment. The total number of tubes is 22. On the shell side (cold fluid), all the results are based on a constant baffle cut ratio of 20% with a spacing of 100 mm. The number of baffles is 8 baffles inserted in the shell. The Nusselt number of cold fluid (Nu_cold) is calculated using the Churchill and Bernstein approach for Reynolds number (Re) between 100 < Re < 10⁷. The tube's convective-heat-transfer-coefficient (hot fluid) was obtained using the appropriate method [18], as shown in Eqs. (9)–(12).

$R e=\frac{\rho \cdot V \cdot d_{{intube}}}{\mu}$     (9)

$N u_{h o t}=0,023 R e_{h o t}{ }^{4 / 5} P r^n$    (10)

$h_{{hot}}=\frac{N_u \cdot k}{d_{{intube}}}$                (11)

The convective heat transfer coefficient of the cold fluid (shell) and pressure drop were calculated using the Sieder and Tate correlation with parameters: the equivalent shell diameter for triangular pitch (d_e), tube pitch (P_T), cold fluid volumetric flow rate (Q_s), as shown in Eq. (12) and Eq. (13):

$N u_{{cold}}=0.36 .\left(\frac{d_e . Q_S}{\mu}\right)^{0.55}\left(\frac{c . \mu}{k}\right)^{0.33}\left(\frac{\mu}{\mu_w}\right)^{0.14}$            (12)

$d_e=\frac{\left(4 P_T \cdot 6.88 P_T-\pi d_{{outtube}}{ }^2\right)}{\pi d_{{outtube}}}$       (13)

The cold fluid volumetric flow rate (Q_s) was converted to the mass flow rate using $Q_s=\dot{m} / \rho$, where ρ is the fluid density evaluated at the mean fluid temperature. The Q_s was then obtained by substituting this mass flow rate, together with tube pitch, distance between tubes (C), inner diameter of shell (d_shell), and the distance between baffle (B), as shown in Eq. (14):

$Q_s=\frac{\dot{m} \cdot P_T}{d_s \cdot C \cdot B}$        (14)

Kern method is used to solve the problem of pressure drop in the shell side (cold fluid) using Eq. (15). N is the number of baffles, µ is the dynamic viscosity of the fluid, µ_w is the dynamic viscosity of the tube-wall, and the friction factor (f) can be calculated considering the value of Re as shown in Eq. (16):

$\Delta P_{{cold}}=\frac{f \cdot Q_s \cdot d_{{shell}}(N+1)}{2 \cdot \rho \cdot d_e \cdot\left(\frac{\mu}{\mu_w}\right)^{0.14}}$            (15)

$f=\exp \left(0.576-0.19 \ln \left(R e_{{cold}}\right)\right), 400<R e_{{cold}}<10^6$            (16)

In the tube side (hot fluid), the hot fluid volumetric flow rate (Q_t) is used to calculate the pressure drop. s is the specific gravity, V_hot is hot fluid velocity, and g is the acceleration of gravity, as shown in Eq. (17):

$\Delta P_{h o t}=\frac{f \cdot Q_t \cdot L_{t u b e} \cdot N}{5 \cdot 22 \cdot 10^{10} \cdot d_e \cdot s \cdot \phi_t}+\frac{4 \cdot N \cdot V_{h o t}{ }^2}{s \cdot 2 \cdot g}$                (17)

The shell is a cylindrical vessel in which the tube bundle is placed inside them. The thermal design of the STHX consists of the heat transfer area, number of tubes, tube length and diameter, tube pitch, number and type of baffles, and the pressure drops on both the shell and tube sides. The calculation of the heat transfer coefficient for the hot and cold fluids is assumed to be a single-phase flow without phase change occurring during the heat transfer process. This assumption simplifies the analysis and makes it easier to use conventional convective heat transfer coefficient correlations based on Re and Nu. The heat balance equation assumes steady-state conditions and adiabatic operation at the shell, consistent with classical STHX design assumptions for one shell pass and one tube pass [19]. This assumption is valid when heat losses to the environment are negligible due to the low thermal conductivity of the shell material and the large ratio of heat transfer surface area to external shell surface area.

The LMTD approach applied in Eq. (5) provides the actual mean driving force between the hot and cold fluids in counter-current flow [19]. Compared to the ε–NTU method, this approach is simpler and more intuitive when inlet and outlet fluid temperatures are known a priori from experimental data [6]. However, for multipass configurations, the LMTD must be corrected using a correction factor F, since the actual flow in multipass STHXs is never purely counter-current. Perry's Chemical Engineers' Handbook stipulates that an F value below 0.8 indicates thermodynamically inefficient design, and the HX Design Handbook sets a minimum threshold of F = 0.75 for economic feasibility [20]. With F values of 0.883–0.955 achieved in the present work, the fin-modified design demonstrates good thermohydraulic feasibility.

The series-resistance thermal model in Eq. (7) is a cylindrical geometry model that neglects fouling resistance, assuming clean tube surfaces during short-duration laboratory tests. Although this simplification is appropriate for the experimental conditions considered, fouling resistance must be included for industrial applications, as it significantly degrades the overall heat transfer coefficient (U) over operating time [21]. The selection of stainless steel 304 for the tubes [k = 16.2 W/(m·K)] and PMMA (plexiglass) for the shell [k = 0.24 W/(m·K)] represents an interesting trade-off [6]. The high tube conductivity minimizes conductive wall resistance, while the low PMMA conductivity on the shell side acts as a natural insulator, approaching the assumed adiabatic shell condition. The choice of PMMA also enables visualization of flow patterns and bubble behavior during experimentation, providing additional diagnostic value. The Dittus-Boelter correlation in Eq. (10), with n = 0.3 for cooling and n = 0.4 for heating, applies within the fully turbulent regime (Re > 10,000, Pr between 0.7–16,700) [18]. However, this correlation has limitations in the transitional and laminar regimes, which are likely encountered at low flow rates (1.8 L/min) in the present work. These limitations must be addressed with regime-specific correlations in subsequent analyses.

The Kern method adopted for the shell side provides a simple, reliable, and widely applied STHX design approach. This method estimates the shell-side heat transfer coefficient using the shell diameter for triangular pitch (d_e) and the cold fluid velocity, accounting for tube pitch, clearance, and baffle spacing. However, the Kern correlation has well-known conservative limitations. It tends to underestimate the actual heat transfer coefficient because it neglects bypass-stream and leakage-stream effects, which are accounted for by the more accurate Bell–Delaware method [22, 23]. Comparative studies have shown that the discrepancy between the two methods grows with increasing number of baffles and variations in normalized baffle spacing [22]. The Sieder–Tate correlation in Eq. (12) introduces a viscosity-ratio correction (μ/μw)^0.14 to account for the effect of near-wall fluid viscosity variations with temperature, significantly improving predictive accuracy, particularly at low flow rates and large temperature differences.

For crossflow over the tube bundle, the Hilpert [24] and Zhukauskas [25] correlations were selected with C = 0.9 and n = 0.4 for staggered arrangements. This choice aligns with the Re range of 10–100 and Prandtl number (Pr) range of 0.7–500 from which the underlying experimental data were generated, matching the crossflow regime expected across small-diameter tube bundles [25].

This experimental study used an STHX type with the structure of one shell pass and one tube pass. The total number of tubes inside the shell was 20 tubes with a 12.7 mm outside diameter (BWG 20) and a length of 700 mm. The tube bundle was arranged in a 30° triangular pitch layout with a tube pitch of 17.8 mm. This model configuration was selected to provide a better heat transfer coefficient compared to a square pitch configuration due to increased turbulence and compact tube spacing. The shell had a total length of 700 mm, with an inner diameter of the shell is 110 mm. This experimental study used eight baffles with a baffle spacing of 100 mm, single segmental, and a cut-off of 20%. We determined that the baffle spacing was carefully selected to avoid excessive pressure drop. To increase the heat transfer performance, the baffles were modified by attaching fins to each baffle. Each fin had dimensions of 105 mm in length, 25 mm in width, and 1.5 mm in thickness, as illustrated and shown in Figure 1(a-c). The materials of the shell and tubes are polymethyl methacrylate (PMMA, plexiglass) and stainless steel 304, respectively. The thermal conductivity of plexiglass (PMMA) and stainless steel 304 are 0.24 W/(m·K) and 16.2 W/(m·K), respectively [6]. The selection of stainless steel 304 for the tube material ensures good corrosion resistance and adequate thermal conductivity. Figure 2(a-c) shows the placement of fins inside the shell. The fins are placed between tubes, with a total of 7 fins as shown in Figure 2(c). The addition of fins will influence the effective heat transfer area and promote flow disturbance, which is expected to improve the thermal performance.

tu_pian_1.png

Figure 1. Design of finned baffle modified, (a) design of fin, (b) finished fin, and (c) fin on baffle

tu_pian_2.png

Figure 2. Placement of finned, (a) bundle of the tube, (b) fin on baffle, and (c) scheme of fin

tu_pian_3.png

Figure 3. Experimental installation, (a) schematic diagram of shell-and-tube heat exchangers (STHX), and (b) equipment

STHX laboratory that are used in this study, as shown in Figure 3, had two tanks to store hot and cold fluids at two different temperatures. A controlled test facility using laboratory equipment with calibrated flow and differential-pressure instrumentation was constructed for this purpose, enabling repeatable comparison between the fin-integrated baffle configuration and the conventional baffle baseline under identical operating conditions. The equipment has two pumps, two flowmeters, and two valves to circulate and set the flow rate for each hot and cold fluid, as shown in Figure 3. The electric heater was installed as source heat generation set to 1.7 kW, and the radiator as a cooling system for the hot fluid. Pressure transducers were installed at the inlet and outlet of the shell and tube using a differential pressure transmitter ST3000 model STD910. These apparatuses were used to investigate the fluid pressure distribution in the shell and tube sides. The measuring range of the pressure transmitter was -1000 to 1000 Pa, with accurate measurement of linear output based on the equipment of ± ((0.15 + 0.15 × (1.0/(greatest range value/lower range value))) %. The fluid temperatures were measured using a thermocouple (K type) [6, 7]. The fluid temperature and pressure data were collected using NI 9213 and NI 9203, respectively. Each operating condition was repeated 2 times on different days, and the maximum deviation of the measurements between repeated runs was below 1%.

The inlet and outlet temperatures of the shell and tube were measured using calibrated thermocouples with an accuracy of ± 0.1 ℃, flow rate with 10L/min (± 1% of reading), and differential pressure with a smart differential-pressure transmitter of the resonant-sensor class. Data were recorded only after temperature variations remained within ±0.1 ℃ and flow/pressure variations within ± 1% for at least 30 minutes.

The experimental study was conducted under the ambient temperature of 25 to 27 ℃. Countercurrent flow was used in this experiment. We use 3 kinds of variations in mass flow rate, first using same mass flow rate between tube/hot fluid and shell/cold fluid. Second, using increasing the tube/hot fluid mass flow rate and fixed mass flow rate in shell/cold fluid. Third, using a fixed mass flow rate in tube/hot fluid and increasing the shell/cold fluid. The mass flow rate used in the experiment is set to 1.8, 3, 5, 7, and 9 L/min, for both shell and tube-side. To simplify the variation of mass flow rate name of shell and tube-sides, the first words are set to hot fluid mass flow rate, and the second words are set to cold fluid mass flow rate as $\dot{m}_{{hot}}-\dot{m}_{{cold}}: 1.8-1.8 ; 3-3 ; 5-5 ; 7-7 ; 9-9$ (the first variation of mass flow rate, $\dot{m}_{{hot}}-\dot{m}_{{cold}}$ with both hot and cold fluid in the same flow rate). $\dot{m}_{{hot}}-\dot{m}_{{cold}}$ : 1.8-7; 3-7; 5-7 (the second variation of mass flow rate, $\dot{m}_{{hot}}-\dot{m}_{{cold}}$ with increasing the hot fluid and constant the cold fluid). $\dot{m}_{{hot}}-\dot{m}_{{cold}}: 7-1.8 ; 7-3 ; 7-$5 (the third variation of mass flow rate, $\dot{m}_{{hot}}-\dot{m}_{{cold}}$ with constant hot fluid and increasing the cold fluid). Using Eq. (6), the total heat transfer area is $0.558 \mathrm{~m}^2$. Thermophysical properties of saturated water are used in the experiment. Dimensions of the properties of saturated water: Temperature (T); $\mu(\mathrm{Pa} \cdot \mathrm{s})$; $k[\mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})] ; \rho\left(\mathrm{kg} / \mathrm{m}^3\right) ; \operatorname{Cp}[\mathrm{kJ} /(\mathrm{kg} \cdot \mathrm{K})]$.

This study investigates the effect and characteristics of the finned baffle modification on the small STHX. As a result, the pressure drop increased with increasing volumetric flow rates. The results about the baffle-modified fin can be considered for industrial applications. The model of the baffle-modified fin can also be recommended with some modifications to decrease the pressure drop significantly, so the parameters and variations should be manufactured for the best results of the pressure drop limit of the STHX. Numerical design can be used to predict the next. The highest and lowest heat (DQ) differences are investigated at flow rate variations of 7-1.8 L/min of 268.5 W and 3-7 L/min of 15.1 W, respectively. The coefficients of convective heat transfer in the tube-side and shell-side are shown to be between 279.44 and 330.85 W/(m²·K) and 24.02 and 45.58 W/(m²·K), respectively. The difference in maximum temperature between hot and cold fluids for the flow rates 1.8, 3, 5, 7, and 9 L/min was indicated at 1.8 L/min as 14 ℃ (hot fluid) and 6.2 ℃ (cold fluid). The lowest and highest ΔP experimentally occurred at both flow rates of 1.8 and 9 L/min of 7.8 Pa and 87.3 Pa for hot fluid, and 351.7 Pa and 4908.6 Pa for cold fluid, respectively. The highest effectiveness occurred at the flow rate with variation 1.8-7 L/min of 87.33%. The effectiveness for both at the same flow rates averaged 58.59%.