Numerical Thermo-Hydraulic Performance Evaluation of a Double-Pipe Heat Exchanger Using Various Nanofluids and Straight and Inclined Grooved Semi-Circular Baffles

2.1 Geometry description

Utilizing a concentric tube heat exchanger and a comprehensive design of the thermo-hydrodynamic phenomena research (as in Figures 1 and 2) are provided, and Table 1 summarizes all examined configurations (nanofluids, baffle types, orientations). Understanding and characterizing the mass and heat transfer between the two circulating fluids—hot water utilized as a supplementary fluid and cold water as the primary fluid—is the goal of this work. Since the heat exchanger is set up in a counter-current manner, the two fluids enter through both ends of the exchanger and flow in opposing directions. In precise terms, hot water enters the system at a temperature of 357 K, whereas cold water enters at an initial temperature of 300 K. The outer tube measures 54 mm in diameter and 3 mm in thickness, while the inner tube measures 26 mm in diameter and 2 mm in thickness.

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Figure 1. The semi-circular baffles with and without grooves

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Figure 2. The schematic diagram of double tube heat exchanger

Table 1. The configurations (nanofluids, baffle types, orientations)

Both tubes have a total length of 1000 mm, which guarantees a consistent flow pattern. Additionally, the external wall of the tube is made adiabatic, which ensures efficient thermal insulation and reduces energy losses from heat exchange with the outside environment. Semi-circular baffles are inserted into the partition wall of the inner tube. The first baffle is positioned L1 = 100 mm away from the tube entrance; this distance was carefully considered to prevent a depression from forming between the entering flow and the first obstacle that is met. Keeping a sufficient distance between baffles and the flow that enters reduces the likelihood of unwanted events like flow separation or elevated pressure losses, improves system performance, and lessens flow disruptions. The grooves have a radius of 3 mm with distances of r₁ = 5 mm and r₂ = 9 mm. Table 2 displays all the details of computational geometry.

Table 2. The computational model's geometrical requirements

Table 3 represents the thermophysical properties and provides references to the precise values we utilized in our tests. Understanding and characterizing the transfer of mass and heat between the two circulating fluids—hot water utilized as the secondary fluid and cold water as the primary fluid—the two fluids enter in opposing directions inside the tubes.

The following simple hypotheses were used in this investigation: (i) constant properties assessed at the inlet temperature; (ii) a single-phase nanofluid model with efficient thermo-physical properties, ignoring particle-base fluid slip; (iii) steady, incompressible turbulent flow; and (iv) no radiation or MHD effects, since the current work concentrates on baffle configuration and nanofluid kind, while such physics are recommended for future extensions; (v) Newtonian behavior without phase change; (vi) adiabatic exterior casing and no-slip at solid walls; and (vii) a suitable k–ε turbulence model for separated internal flows with improved wall treatment. Similar numerical heat transport studies frequently use these assumptions, and the conclusion acknowledges their limitations.

Table 3. Thermophysical properties of base fluid water (H₂O) and solid nanoparticles [16]

A pressure-based solver utilizing the SIMPLE method and second-order upwind discretization was employed to run the simulations in ANSYS Fluent. Convergence was reached when all residuals fell below 10⁻⁶, and the monitored Nusselt number (Nu) and pressure drop fluctuated by less than 0.1% using the realizable k–ε turbulence model with enhanced wall treatment.

Because of their exceptional chemical stability, low toxicity, cost-effectiveness, and relatively high thermal conductivity, oxide-based nanoparticles like AlO₃ and TiO₂ were selected for the current investigation. Furthermore, in water-based nanofluids, these nanoparticles show good dispersion stability, guaranteeing consistent and repeatable improvement of convective heat transfer in heat exchanger applications.

2.2 Boundary conditions

When this investigation was started, simplistic assumptions like turbulent and incompressible flow were used. At the inlet temperature, the fluid's physical characteristics remain unchanged by temperature. The pipe's outside wall is adiabatic, meaning that no heat is transferred across it. The outer wall of the heat exchanger was treated as adiabatic to prevent heat loss to the surroundings, while the interface between the inner and outer tubes allowed conjugate heat transfer between the hot and cold fluids. No constant wall temperature or heat flux condition was imposed, as heating was provided by the hot water stream in the annulus. At the outlet, a pressure outlet boundary condition with zero gauge pressure was applied, assuming fully developed flow; heat transport from radiation is disregarded. The inlet velocity profile shows a consistent flow distribution at the inlet. The conditions set at the boundary for the ongoing investigation are given in Table 4.

The following equations are used to calculate the values in Table 1 for each volume fraction that was investigated in this study. The same equation is observed in the study [10]. Density, viscosity, specific energy, and thermal conductivity are all represented by the corresponding equations. The section on nomenclature explains symbols and subscripts. For the fluid mixture's 300 K inlet temperature, fixed property values were chosen from tables. The thermo-physical characteristics of the base fluid and nanofluids were assessed at the inlet temperature and considered to be constant throughout this investigation. This assumption is supported by the heat exchanger's comparatively tiny temperature range (less than 50 K), which has been shown in prior research to have little effect on density, viscosity, and thermal conductivity [10, 11]. It is anticipated that temperature-dependent features will have little effect in the current arrangement, even if they can increase forecast accuracy in situations with greater temperature gradients. However, a sensitivity analysis or the implementation of temperature-dependent features is noted as a possible avenue for further research.

Table 4. The boundary conditions of the simulation

As the temperature changes during heat transfer, the numbers computed in Table 1 stay the same. Since the temperature differential is no more than 50 K and variations in the values of properties that correspond to a temperature differential may be disregarded, this is not an issue and can be ignored.

$\rho_{n f}=(1-\varphi) \rho_{b f}+\varphi \rho_p$             (1)

$\left(\rho C_p\right)_{n f}=(1-\varphi)\left(\rho C_p\right)_{p f}+\varphi\left(\rho C_p\right)_p$            (2)

$\mu_{n f}=\mu_{p f}(1+2.5 \varphi)$            (3)

$k_{n p}=\frac{k_p+2 k_{b f}+2\left(k_p-2 k_{b f}\right) \varphi}{k_p+2 k_p-2\left(k_p-2 k_{b f}\right) \varphi} k_{b f}$            (4)

2.3 Mathematical modeling

The problem's mathematical formulation makes the assumption that the velocity of flow is constant with time, turbulent, and incompressible. The equations for continuity, momentum transfer, and energy flow in three dimensions (3D):

Equation of continuity [22]:

$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$            (5)

Momentum equations for x, y and z directions [22]:

$u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y}+w \frac{\partial u}{\partial z}=-\frac{1}{\rho} \frac{\partial P}{\partial x}+\frac{\mu}{\rho}\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2}\right)$           (6)

$u \frac{\partial v}{\partial x}+v \frac{\partial v}{\partial y}+w \frac{\partial v}{\partial z}=-\frac{1}{\rho} \frac{\partial P}{\partial y}+\frac{\mu}{\rho}\left(\frac{\partial^2 v}{\partial x^2}+\frac{\partial^2 v}{\partial y^2}+\frac{\partial^2 v}{\partial z^2}\right)$            (7)

$u \frac{\partial w}{\partial x}+v \frac{\partial w}{\partial y}+w \frac{\partial w}{\partial z}=-\frac{1}{\rho} \frac{\partial P}{\partial z}+\frac{\mu}{\rho}\left(\frac{\partial^2 w}{\partial x^2}+\frac{\partial^2 w}{\partial y^2}+\frac{\partial^2 w}{\partial z^2}\right)$            (8)

Energy equation [23]:

$u \frac{\partial T}{\partial x}+v \frac{\partial T}{\partial y}=\alpha\left(\frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial y^2}\right)$            (9)

The single-phase effective- property formulation is used in this study to model nanofluids. The governing equations of Newtonian incompressible motion are maintained, and the impact of nanoparticles is included by altering the thermal and physical characteristics (ρ, μ, cp, k) in accordance with standard correlations. Particle–fluid slip mechanisms like Brownian motion and thermophoresis (as taken into account in the Buongiorno two-phase model) are not included, nor are any new transport equations for the particle phase solved. Numerical nanofluid studies with low particle densities and mild temperature gradients frequently employ this simplification. This approach's shortcomings are acknowledged, and future research is advised to compare it with two-phase models.

The mean heat transfer coefficient ($\underline{h}$) is calculated by the following expression [24]:

$\underline{h}=\frac{Q}{A_s\left(T_w-T_b\right)}$              (10)

where, the mean wall temperature is attained by [25]:

$T_w=\frac{1}{n} \sum T_{w n}$             (11)

The channel's bottom surface is T_wn.

The following is the mean bulk temperature (T_b) [26]:

$T_b=\frac{\int_0^L \int_0^H \int_0^W \rho c_p u T d x d y d z}{\int_0^L \int_0^H \int_0^W \rho u d x d y d z}$         (12)

The mean Nu is estimated as follows [27]:

$N u=\frac{\underline{h} \cdot D_h}{k}$            (13)

where, $D_h$ is the hydraulic diameter of the tube.

The average friction factor (f) can be obtained by the following expression [28]:

$f=\frac{\Delta P}{\frac{1}{2} \rho u_{a v g .}^2} \cdot \frac{D_h}{L}$            (14)

Performance index [29] is computed for each example in order to compare the combined effects of increased pressure drop and improved heat transfer resulting from the introduction of a baffle at the same time.

$\eta=\frac{\left(N u_w / N u_o\right)}{\left(f_w / f_o\right)^{1 / 3}}$             (15)

Although Eqs. (6)-(9) are stated in a general conservation form, it should be emphasized that the nanofluid influences are integrated through their efficient thermophysical characteristics.

Eqs. (1)-(4) define them. These characteristics, which adhere to the common single-phase nanofluid model found in the study, take the place of the traditional fluid parameters in the governing equations.

The Realizable k–ε turbulent conditions model with improved wall treatment was utilized in every simulation. Because of its shown capacity to precisely forecast fully developed turbulent flows in interior channels, this model was selected. It is a good fit for the current setup because it has been thoroughly proven in the study for heat exchanger systems involving intricate flow separation and recirculating zones. It is a semi-empirical model with two equations: one for turbulent kinetic energy dissipation (ε) and another for turbulent kinetic energy transit (k).

For turbulent kinetic energy (k) [30]:

$\begin{gathered}\rho\left(\frac{\partial}{\partial x}(k u)+\frac{\partial}{\partial y}(k v)+\right. \\ \left.\frac{\partial}{\partial z}(k w)\right)=\frac{\partial}{\partial x}\left(\frac{\mu_t}{\sigma_k} \frac{\partial k}{\partial x}\right)+\frac{\partial}{\partial y}\left(\frac{\mu_t}{\sigma_k} \frac{\partial k}{\partial y}\right)+\frac{\partial}{\partial z}\left(\frac{\mu_t}{\sigma_k} \frac{\partial k}{\partial z}\right)+G-\rho \varepsilon\end{gathered}$             (16)

For energy dissipation rate (ε) [30]:

$\begin{gathered}\rho\left(\frac{\partial}{\partial x}(\varepsilon u)+\frac{\partial}{\partial y}(\varepsilon v)+\right. \left.\frac{\partial}{\partial z}(\varepsilon w)\right)\\=\frac{\partial}{\partial x}\left(\frac{\mu_t}{\sigma_{\varepsilon}} \frac{\partial \varepsilon}{\partial x}\right)+\frac{\partial}{\partial y}\left(\frac{\mu_t}{\sigma_{\varepsilon}} \frac{\partial \varepsilon}{\partial y}\right)+\frac{\partial}{\partial z}\left(\frac{\mu_t}{\sigma_{\varepsilon}} \frac{\partial \varepsilon}{\partial z}\right)+\rho \frac{\varepsilon}{k} G- C_{1 \varepsilon} \rho \frac{\varepsilon}{k}\end{gathered}$              (17)

where, G is referred to as the generation term and is given [30]:

$\begin{gathered}G=\mu_t\left[2\left(\frac{\partial u}{\partial x}\right)^2+2\left(\frac{\partial v}{\partial y}\right)^2+2\left(\frac{\partial w}{\partial z}\right)^2+\right. \\ \left.\left(\frac{\partial v}{\partial y} \frac{\partial u}{\partial x}\right)^2+\left(\frac{\partial v}{\partial z} \frac{\partial w}{\partial x}\right)^2+\left(\frac{\partial v}{\partial z} \frac{\partial w}{\partial y}\right)^2\right]\end{gathered}$            (18)

2.4 Mesh description

Governing equations stated in the previous section are solved by employing ANSYS FLUENT. The system of equations for the entire domain is solved iteratively employing the provided boundary. It is possible to create structured or unstructured grids and control volumes of various shapes, such as hexahedral and tetrahedral control volumes. Since the tetrahedral mesh is beneficial for the separation flow, it is used as illustrated in Figure 3. It is evident that the mesh is extremely tiny in order to capture the flow movements in the areas close to the surfaces and around the baffles.

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Figure 3. The considered mesh generation of the tube and the cross-section

Figures 5–7 refer to the outcomes of the three simulated cases of nanofluids: (TiO₂, Al₂O_3, and Ag) with H₂O. Each figure explains a comparison of the results that gained from the presence of straight and inclined baffles, with and without grooves. The Nu was utilized to calculate the heat transfer rate for each heat exchanger in each of the evaluated cases. The relation between Nu and fluid flow velocity is depicted in the figures. In general, they exhibit a direct proportionality for each of the three nanofluid cases. The rise in Nu for the grooved baffles case was evident for all nanofluid cases. The presence of grooves clearly provided a benefit in terms of enhancing heat transfer. The explanation for this occurrence seems to be as follows: in a heat exchanger, impediments are encountered one after another by the flow pattern, and separation of streams at the edge of baffles results in a rapid shift in momentum and turbulent flow. At Re = 14000, the inclined semi-circular baffles increased the average Nu by approximately 31% compared with the straight tube for the Al₂O₃–H₂O nanofluid. Furthermore, compared with the smooth tube, the use of semi-circular inclined grooved baffles increased the average Nu by approximately 40–65%, depending on the Re (4000–14000), nanofluid type, and baffle configuration. The maximum enhancement was obtained for the inclined grooved baffles with Al₂O₃–H₂O at Re = 14000.

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Figure 5. Nusselt number (Nu) results for TiO₂-H₂O

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Figure 6. Nusselt number (Nu) results for Al₂O₃-H₂O

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Figure 7. Nusselt number (Nu) results for Ag-H₂O

Greater turbulence and weakening of the thermal boundary layer cause Nu to rise with Re for all nanofluids; inclined-grooved baffles provide the strongest enhancement through enhanced secondary flows and vortex generation. Ag–H₂O's higher density and viscosity limit its relative benefits despite its intrinsic conductivity, whereas Al₂O₃–H₂O exhibits the best performance because of its highly efficient thermal conductivity and stability. Because of the additional form drag and cross-flow swirls caused by baffle insertion, the friction factor increases with baffle insertion but reduces with Re. The effects are especially noticeable in systems with inclined grooves.

Even though Ag nanoparticles have the highest intrinsic thermal conductivity, the proposed single-phase effective-property model predicts thermo-hydraulic performance based on the combined influence of all effective thermo-physical properties rather than just thermal conductivity. The flow field and convective heat-transfer coefficient (h) are altered by concurrent variations in effective viscosity, density, and specific heat. As a result, Al₂O₃–H₂O offers a better balance between flow characteristics and thermal enhancement, leading to a better overall (h).

As regards the friction factor (f) outcomes, Figures 8–10 represent the comparison of the nanofluids (TiO₂, Al₂O_3, and Ag) with H₂O. The values of Al₂O₃-H₂O give the greatest values of friction factor (f), followed by TiO₂-H₂O, then Ag-H₂O. The outcomes report that a gradual decrease occurs for friction factor (f) as the Re rises. Also, there is a notable increase specially the grooved configuration, in the values of the friction factor (f) for inclined cases of baffles, especially the grooved, due to the inclination of baffles without grooves, causing the inserts' grooves to minimize pressure losses and air recirculation zones. This optimizes hydrodynamics. This interaction is responsible for higher pressure drop. The addition of grooves reduces the pressure-drop penalty in comparison to the corresponding ungrooved baffles, even though all baffled designs have greater friction factors (f) than the smooth tube because of the extra flow blockage. This phenomenon is explained by the creation of localized recirculation zones within the grooves, which partially minimize the wall-shear stress and create drag without sacrificing the improved fluid mixing, diminish the upstream stagnation region, and promote downstream flow reattachment.

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Figure 8. Friction factor (f) results for TiO₂-H₂O

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Figure 9. Friction factor (f) results for Al₂O₃-H₂O

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Figure 10. Friction factor (f) results for Ag-H₂O

Thus, the friction factor (f) index becomes lower as Re increases up to Eq. (14). The improvement of the effective thermo-physical characteristics included in the single-phase model, specifically the enhanced effective thermal conductivity and the altered effective viscosity and density of the suspension, is the main cause of the rise in the Nu seen with nanofluids. Furthermore, the semi-circular baffles enhance fluid mixing and continually disturb the thermal boundary layer by encouraging flow separation, recirculation, and secondary vortex generation. Higher convective heat-transfer rates are produced by the inclined and grooved baffle arrangements, which also lessen the thickness of the thermal barrier layer and reinforce these secondary motions. Brownian motion and thermophoretic particle migration are not mentioned as direct mechanisms for the anticipated increase because the current work uses a single-phase effective-property formulation.

Figures 11–13 refer to the overall performance of the three simulated cases of nanofluids. According to the statistics, at Re = 4000, the thermo-hydraulic performance criterion (PEC) of Al₂O₃–H₂O was approximately 23% higher than that of TiO₂–H₂O and approximately 41% higher than that of Ag–H₂O for the inclined grooved baffle configuration. Furthermore, the findings demonstrated that by raising the turbulence of the fluid in motion and generating bigger recirculation zones, inclining the baffles improves the heat exchanger's overall performance. By inserting grooves into these baffles, this was enhanced and made more active since the grooves increased mixing, which in turn accelerated the rate of heat transfer. As a result, in the case of the inclined grooved baffles, the heat exchanger's total performance peaked. The highest overall performance rating was recorded for the case of inclined grooved baffles at Re = 4000. It amounted to 1.67 for Al₂O₃-H₂O, 1.6 for TiO₂-H₂O and 1.51 for Ag-H₂O. This interaction is responsible for a greater pressure drop friction factor (f) than the rise of heat transfer. Thus, the overall-performance index becomes lower at this configuration in comparison with the other cases. Because the improvements in nanofluid conductivity and baffle-induced turbulence balance the pressure penalty, PEC is highest at low Re. Because of its excellent conductivity and stability, Al₂O₃–H₂O performs best in inclined-grooved baffles, which maximize PEC by producing vigorous secondary flows and minimizing stagnation. PEC decreases in all circumstances when Re rises because increasing pressure drop diminishes the relative benefit.

Table 6 summarizes the main percentage improvements covered in the preceding sections to increase the traceability of the quantitative results. The provided percentages can be clearly read and consistently compared thanks to this summary, which establishes a direct connection between the graphical results and the numerical discussion.

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Figure 11. Overall performance results for TiO₂-H₂O

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Figure 12. Overall performance results for Al₂O₃-H₂O

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Figure 13. Overall performance results for Ag-H₂O

Figures 14 and 15 illustrate the contour and streamline plots of the anticipated velocity for the Al₂O₃-H₂O working fluid in the straight baffles (with and without grooves) case and the inclined baffles (with and without grooves) case. The vortices are created close to the baffles in the core flow area, as seen in Figures 14 and 15. The disruption of the boundary layer and the uniformity of temperature in the center of the flow are largely due to longitudinal vortices.

The figures clearly show the variation that occurs in the form of flow between the four cases tested. The inclined baffle cases give more turbulence over a larger extent, a ripple shape, and a larger recirculation area than the straight cases. This indicates a positive effect of inclining the baffles on the mixing process and thus rising heat transfer. Not to mention the effect of the presence of grooves, which helped create greater turbulence and contributed to the improvement in vortex generation.

Table 6. A summary of the typical thermo-hydraulic performance

Statement in Discussion	Variable	Re	Nanofluid	Configuration	Baseline	Percentage Increase
Inclined baffles Improve heat transfer	Nu	14000	Al₂O₃–H₂O	Inclined Semi-circular Baffles	Straight Semi-circular Baffles	=31%
Inclined groove baffles improve heat transfer	Nu	14000	Al₂O₃–H₂O	Inclined Groove Semi-circular Baffles	Inclined Semi-circular Baffles	=28%
Semi-circular baffles enhance heat transfer	Nu	4000–14000	All nanofluids	All baffled configurations	Smooth Tube	=0–65%
Best thermal enhancement	Nu	14000	Al₂O₃–H₂O	Inclined Grooved Baffles	Smooth Tube	=65%
Friction factor	f	14000	Al₂O₃–H₂O	Inclined Semi-circular Baffles	Straight Semi-circular Baffles	=26%
Friction factor	f	14000	Al₂O₃–H₂O	Inclined Groove Semi-circular Baffles	Inclined Semi-circular Baffles	25%
Superior thermo-hydraulic performance	PEC	4000	Al₂O₃–H₂O	Inclined Grooved Baffles	TiO₂–H₂O (same geometry)	=23%
Superior thermo-hydraulic performance	PEC	4000	Al₂O₃–H₂O	Inclined Grooved Baffles	Ag–H₂O (same geometry)	=41%

Note: Nu = Nusselt number; Re = Reynolds number; f = Friction Factor; PEC = Performance Evaluation Criterion.

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Figure 14. Streamline velocity of the four cases when Al₂O₃-H₂O nanofluid as working fluid at Reynolds number (Re) = 4000

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Figure 15. Velocity contour of the four cases when Al₂O₃-H₂O nanofluid as working fluid at Reynolds number (Re) = 4000

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Figure 16. Temperature contour of the four cases when Al₂O₃-H₂O nanofluid as working fluid at Reynolds number (Re) = 4000

Figure 16 illustrates how adding baffles impacts the temperature distribution in several cases. The presence of the baffles reorganizes the temperature distribution. The flow mixing has been raised results from turbulators with baffles inserted. The boundary layer of heat tends to be thicker in regions that are farther away from the ribs. The distribution of boundary layers (where the variety of temperature rises at(inclined grooved)) illustrates the effect of each instance. In general, employing baffles improves the temperature dispersion compared to the smooth tube.