Effects of staggered transverse zigzag baffles and Al2O3–Cu hybrid nanofluid flow in a channel on thermofluid flow characteristics

Hussein Togun; Ali Basem; Tuqa Abdulrazzaq; Sumanth Shashidhara; Hayder I. Mohammed; Azher M. Abed; Mohaimen Al-Thamir; Abdellatif M. Sadeq; Nirmalendu Biswas; Krishna Kumar Yadav

doi:10.1515/eng-2025-0130

Article Open Access

Effects of staggered transverse zigzag baffles and Al₂O₃–Cu hybrid nanofluid flow in a channel on thermofluid flow characteristics

Hussein Togun , Ali Basem , Tuqa Abdulrazzaq , Sumanth Shashidhara , Hayder I. Mohammed , Azher M. Abed , Mohaimen Al-Thamir , Abdellatif M. Sadeq , Nirmalendu Biswas and Krishna Kumar Yadav

Published/Copyright: August 2, 2025

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From the journal Open Engineering Volume 15 Issue 1

Abstract

This work examines the effects of staggered transverse zigzag baffles and hybrid nanofluid flow in a channel on the ferrofluid flow characteristics. The hybrid nanofluids Al₂O₃–Cu (2%) flow through the horizontal channel and are heated from the bottom. The W-shaped baffles, attached to the heated bottom wall, faced the right-hand side at an angle of 45° to the flow attack. Four different cases of baffle arrangements are also scrutinized. The mathematical models are analyzed numerically using the finite volume-based technique, adopting the k–w turbulence model. The key contribution of this study is the innovative combination of zigzag baffles with hybrid nanofluids, providing an effective passive method for improving heat transmission in industrial uses. The findings indicate substantial enhancements: a heat transfer improvement of up to 92.4% relative to smooth channel flow and a 48.5% increase in pressure drop. The research indicates that the orientation and positioning of the baffle substantially affect the density and intensity of created vortices, hence optimizing turbulence and flow redirection. Due to the reduction in the fluid velocity (initiated by the baffles) and increasing turbulence, the pressure in the flow passage increases with increasing Re, and the pressure reduces as the flow passes through the domain. The baffles’ direction has a considerable impact on the turbulence; the baffles’ top point and angle of direction also impact the flow direction and density of the swirls produced.

Keywords: channel flow; W-shaped baffle; hybrid nanofluid; turbulent flow; flow characteristics

Nomenclature

c _p: specific heat (J kg⁻¹ K⁻¹)
g: gravitational acceleration (m s⁻²)
H: height of the baffle (m)
k: thermal conductivity (W m⁻¹ K⁻¹)
L: channel length (m)
L _s: gap between the baffles
Nu: Nusselt number (average)
P: pressure (dimensionless)
Pr: Prandtl number
Re: Reynolds number
T: temperature (K)
u, v: velocities (m s⁻¹)
U, V: velocities (dimensionless)
x, y: Cartesian coordinates (m)
X, Y: dimensionless Cartesian coordinates

Greek symbols

α: thermal diffusivity (m² s⁻¹)
β: thermal expansion constant (K⁻¹)
θ: temperature (dimensionless)
θ: inclination of the baffle (°)
μ: dynamic viscosity (kg m⁻¹ s⁻¹)
ν: kinematic viscosity (m² s⁻¹)
ρ: density (kg m⁻³)
σ: electrical conductivity (S m⁻¹)
φ: nanoparticle volume fraction (dimensionless)
ψ: stream function (dimensionless)

Subscripts

a: ambient
c: cold
f: base fluid
h: hot
loc: local
max: maximum
s: solid nanoparticles

1 Introduction

Numerous strategies have been developed to improve heat transfer in various arrangements that require higher thermal performance, such as heat-exchanging devices, electronic cooling systems, solar collectors, and combustion chambers. In cooling channels and heat exchangers, one of the most important techniques is to create corrugated surfaces in the flow path in the form of transverse baffles, inclined baffles, V-baffles, and perforated baffles, etc., because of their significant potential for improving the heat transfer. Guo and Anand [1] investigated the heat transfer in a channel simply considering a baffle. Heat transfer is significantly higher on the front face of the baffle than on the back, and recirculation length around the baffles increases as the Reynolds number (Re) and baffle height increase. The computations of laminar flow and heat exchange in the entry region of a horizontal channel with transverse in-line baffles were performed by Bazdidi-Tehrani and Naderi-Abadi [2]. The results of the computations showed that the position of the occasionally fully developed zone is affected significantly by the Reynolds number. Mousavi and Hooman [3] numerically studied the heat transfer and flow in the entry section of a conduit with staggered baffles. They observed that Re and Prandtl numbers influence the position of the fully developed zone. The forced convective process over a heated baffle in a conduit is numerically studied by Saim et al. [4] for turbulence and heat transfer augmentation. According to the findings, the regions of lower and higher pressures are related to the circulation zones. The strong effect occurs in the downstream portion of the second baffle plate, which causes the higher flow speeds detected at the duct’s outlet segment due to the negative velocity profile.

Moreover, a turbulent airflow through a conduit was studied numerically by Saim et al. [5] for the heat transfer features, adopting the k–w turbulence model. The axial velocity distribution reveals reasonably significant recirculating cells beyond the facets of each baffle. Boonloi and Jedsadaratanachai [6] presented turbulent forced convective phenomena in a heated channel with distinct V-shaped baffles. They discovered that the heat transfer and pressure fall augmentations were 2.5–5.75 and 4–22.5 times higher than in the smooth channel. For oily wastewater, a modified resistance model was used by Behroozi [7] to simulate the effects of baffle configuration on cross-flow microfiltration performance. The absolute relative error is reduced from 6.54 to 0.03% when the calculated values are compared to experimental data using the improved resistance model. The baffles placed near the membrane surface are more effective in separating oil from oil-in-water emulsions, but they may cause problems at longer processing times. Therefore, central baffles are suggested for industrial applications. Al-Juhaishi et al. [8] used a typical k–ε turbulence model and wall treatment to examine the enhanced heat transfer in a curved channel with baffles. The results reveal that NB = 13, angle = 90°, and Re = 5,000 are the optimal conditions for the greatest heat transfer compared to other situations.

Furthermore, under the same conditions, the extreme thermal performance factor (TEF) of the undulated conduit has baffles of 4.4. Also, Saha et al. [9], Sahel et al. [10], and Alhumoud and Almashan [11] used a standard k–ε turbulence model to analyze the turbulent fluid flow distributions in a rectangular conduit with several types of baffles (plane baffle, trapezoidal baffle, perforated baffles, and square baffle). The length of the recirculating region decreases as the baffle height lowers, and vice versa. On the other hand, Menni et al. [12] used the turbulence model k–ε to investigate flow characteristics and heat transmission in a rectangular-shaped channel with baffles positioned in a staggered manner (two transverse, staggered, S-shaped, solid-type baffles). They found that the region facing the second S-baffle had the highest axial variations in the Nusselt number and the skin friction coefficient, whereas the area near the first S-baffle had the lowest. The heat transmission, friction loss, and thermal augmentation factor were higher in the channel containing S-obstacles with a large Reynolds number than in the channel with a reduced Reynolds number.

Furthermore, various studies have been performed on the use of baffles on tube and shell-type heat exchangers. You et al. [13] investigated flow resistance and heat transfer in a tube-and-shell heat exchanger (on the shell side) adopting flower baffles. They found that using flower-type baffles increases the flow speed and the amount of heat transported through the convective process on the shell area. They also discovered that flower baffles may be used to create various flow patterns, which improve the heat exchanger’s overall hydraulic and thermal performance compared to standard baffle designs. The influences of using different baffle configurations in tube and shell heat exchangers on heat transmission and fluid flow processes were numerically investigated by Ambekar et al. [14]. A single-segmented baffle (straight) was used in the shell zone for a fixed flow rate and the rate of heat transfer, and it reached peak values. The effect of graded baffle size on channel heat exchanger performance was analytically examined by Sahel et al. [15]. The collected conclusions indicate that the new suggested design provides better thermohydraulic performance. Friction factors dropped by 4–8% in the channel with a downgraded baffle ratio of 0.08.

Moreover, multiple studies have recently combined nanofluids with various heat transfer improvement approaches. Ma et al. [16] employed LBM in a bent channel to investigate Al₂O₃/water nanofluid convection and heat transfer. They discovered that regardless of Re or vertical passage factor, the local and average Nu augmented as the nanoparticle concentration increased. The heat transfer through a facing step baffle channel was investigated by Heshmati et al. [17]. They used a backward-facing step with an angled slotted baffle and nanofluids. Various nanoparticle concentrations (0–4%), Re values ranging from 50 to 400, and diameters ranging from 20 to 50 were utilized. SiO₂ nanoparticles (20 nm size) and a 2% concentration were determined to have superior heat transfer. Mohammed et al. [18] investigated mixed convection of nanofluidic flow in a duct with a baffle and backward-facing step. Several factors were used in their research, including several sorts of nanopowders (CuO, SiO₂, ZnO, and Al₂O₃) with different concentrations (1–4%) and sizes (25–80 nm). The impacts of baffle positions (∞ ≤ D ≤ 4), width (0.01 ≤ wb ≤ 0.04), and height (0.005 ≤ hb ≤ 0.015) ranges were investigated. According to the findings, the heat transfer augmented with the nanoparticle concentrations and Re increased but dropped as the nanoparticle’s diameter increased.

Furthermore, the impact of height and position of the baffles on the thermal behavior is substantial, whereas the width and number of the baffles are negligible. Li and Gao [19] utilized delta-shaped baffles to enhance heat transfer in a cross-corrugate triangular duct. The heat transport and 3D turbulent flow in the channel were studied numerically. It was discovered that after the baffle height equals the corrugation height, the friction factor in the duct with apex angles of 90° and 60° is not strongly related to Re, resulting in an Nu increase of 2.1–4.3 times.

Ajeel et al. [20] presented a study on the thermal behavior and design constraints in an undulated duct having L-shaped baffles and nanofluidic flow. The κ–ε model was utilized to study the impact of corrugations, baffles, and geometric parameters such as corner angles (30–90°) and blockage ratio (0.25–0.4) on the thermal-hydraulic performance at various Reynolds numbers (8,000–32,000) and ZnO particle concentrations (0–0.04). The findings showed that due to the effects of undulations and baffles, the production of vortex flow and augmented turbulence can recover heat transfer augmentation. It is also seen that using water–ZnO nanofluids in energy storage can increase the thermal performance and reduce running time while conserving energy because of its increased thermal conductivity. Recently, Menni et al. [21] numerically studied the impact of obstacles (using a baffle) on a turbulent flow (using Al₂O₃–H₂O nanofluid) and heat transmission in a duct by the standard k–ε turbulence model. They discovered improvements of 45.071, 58.404, 82.413, and 92.433% in the heat transfer rate when associated with the smooth duct utilizing similar Al₂O₃ nanoparticle concentrations. The study of the thermal behavior in the presence of various complex baffles under the nanofluid flow has also been investigated by several researchers [20,22–25].

From the literature mentioned above, the impact of using arc baffles with normal nanofluids on increasing the thermal performance has been considered by numerous researchers, and few studies have adopted the effect of nanofluids and different types of baffles (except Arc-baffle) on the improvement in heat transfer. However, no former numerical and experimental studies have been conducted on the impact of staggered transverse zigzag baffles with hybrid nanofluids on flow characteristics. This study examines the combined impact of staggered transverse zigzag baffles and Al₂O₃–Cu hybrid nanofluids on heat transmission and flow dynamics within heat exchangers. The research will measure the substantial improvement in heat transfer rates through these integrated methods while simultaneously analyzing the corresponding increases in pressure drop. This research aims to optimize the design for real industrial applications by examining the effects of baffle shapes and orientations on turbulence formation, velocity profiles, and pressure distribution. This study seeks to determine the viability and efficacy of using zigzag baffles with nanofluid technology to enhance the thermal performance of heat exchangers.

2 Problem statement and mathematical formulation

2.1 Physical descriptions

Figure 1 shows the schematics of the physical model and four different baffle arrangements. The channel (length L) is horizontal and heated (with heat flux) from the bottom. The W-shaped baffles (of height H) are attached to the bottom wall, facing the right-hand side with an angle of θ = 45° of the flow attack. Four cases (Cases 1–4) of the baffle arrangements are scrutinized here. The left baffle is placed at a distance of L _in from the channel inlet, and the right baffle is placed at a distance of L _out from the channel outlet. The gap between the baffles is L _s. The hybrid nanofluids Al₂O₃–Cu (2%) are considered as a working fluid. Four different positional effects of the baffles on the thermal behavior are studied systematically: Case 1 (W-shaped baffles), Case 2 (oppositely placed W-shaped baffles), Case 3 (inversely placed W-shaped baffles), and Case 4 (oppositely and inversely placed W-shaped baffles).

Figure 1

Schematics of the physical model along with the different arrangements of the baffles: (a) Overall geometry, (b) Case 1 (W-shaped baffles), (c) Case 2 (oppositely placed W-shaped baffles), (d) Case 3 (inversely placed W-shaped baffles), and (e) Case 4 (oppositely and inversely placed W-shaped baffles).

This work has substantial implications for practical applications, especially in improving the performance and efficiency of heat management systems. Integrating staggered transverse zigzag baffles with Al₂O₃–Cu hybrid nanofluids is highly effective for application in heat exchangers, electronic cooling systems, and industrial energy systems, where optimal heat dissipation is essential. The enhanced heat transfer rates presented in this study may result in more compact and economical heat exchangers, improving performance in HVAC, power generation, and renewable energy systems. Moreover, these developments are pertinent to the automotive and aerospace sectors, where enhancing thermal management may diminish energy usage, bolster system dependability, and facilitate the creation of more sustainable and efficient technologies [26–29].

2.2 Governing equations

The computational models in this study are based on several key assumptions to ensure accurate and manageable simulations.

The fluid flow is assumed to be steady and incompressible, with the nanofluids treated as single-phase Newtonian fluids.
The thermal and physical properties of the hybrid nanofluids (Al₂O₃–Cu/water) are considered temperature-independent and uniformly distributed throughout the flow.
The baffle and channel walls are assumed to be rigid, smooth, and perfectly insulated, except for the heated bottom wall, where a constant heat flux is applied.
The turbulence model adopted is the k–ω SST model, which assumes isotropic turbulence and is suitable for capturing near-wall effects.

These assumptions help streamline the analysis while maintaining a reasonable level of accuracy in capturing the thermofluid behavior. The conservation of mass, momentum, and energy equations (single-phase models) are stated as follows [23,30]:

(1) ρ ∂ ∂ x i ( u i ) = 0 ,

(2) ρ ∂ ∂ x j ( u i u j ) = − ∂ P ∂ x i + ∂ ∂ x i μ ∂ u i ∂ x j + ∂ u j ∂ x i + ∂ ∂ x j ( − ρ u i ′ u j ′ ¯ ) ,

(3) ∂ ∂ x i [ u i ( ρ E ) + P ] = ∂ ∂ x j λ + c p μ t Pr t ∂ T ∂ x j + u i ( τ ij ) eff .

The units of single parameters for the continuity, momentum, and energy equations are kg/m³, N/m³, and J/(m³ s), respectively.

Here, E = T + ( u 2 / 2 ) , and ( τ ij ) eff defines the stress tensor (deviatoric) expressed by

(4) ( τ ij ) eff = μ eff ∂ u j ∂ x i + ∂ u i ∂ x j ,

Menter’s [31] SST k–w turbulence model [32–34] can be expressed as

(5) ρ ( ∂ ∂ x i ( ku i ) ) = ∂ ∂ x j µ + μ t σ k ∂ k ∂ x j + G k − Y k ,

(6) ρ ∂ ∂ x i ( ω u i ) = ∂ ∂ x j µ + μ t σ ω ∂ ω ∂ x j + G ω − Y ω + D ω ,

where μ t is given by

(7) μ t = ∝ * ρ k ω ,

and ∝ * is calculated as

(8) ∝ * = ∝ ∞ * ( ∝ 0 * + Re t / R k ) ( 1 + Re t / R k ) .

Here, Re t = ρ k / μ ω , ∝ 0 * = β i / 3 , and

(9) β i = F 1 β i , 1 + ( 1 − F 1 ) β i , 2 .

The constants of the k and ω equations are obtained from [35]

(10) σ k = 1 F 1 / σ k , 1 + ( 1 − F 1 ) σ k , 2 ,

(11) σ ω = 1 F 1 / σ ω , 1 + ( 1 − F 1 ) σ ω , 2 .

The blending function (F ₁) is given as

(12) F 1 = tanh ( Φ 1 4 ) ,

where

(13) Φ 1 = min max k 0.09 ω y 500 μ ρ y 2 ω , 4 ρ k σ ω , 2 D ω + y 2

and

(14) D ω + = max 2 ρ 1 σ ω , 2 1 ω ∂ k ∂ x i ∂ ω ∂ x j , 10 − 10 ,

where D ω + is the positive cross-diffusion part.

According to Equation (5), G _k means the turbulent kinetic energy production due to the gradients of mean velocity, while G _ω denotes the production of ω, and D ω denotes the cross-diffusional relationships:

(15) D ω = 2 ( 1 − F 1 ) ρ σ ω , 2 1 ω ∂ k ∂ x j ∂ ω ∂ x i ,

where Y _k and Y ω show the dissipation of k and ω , and are set as

(16) Y k = ρ β * k ω ,

(17) Y ω = ρ β i ω 2 .

G _k can be found by

(18) G k = τ t , ij ( ∂ u i / ∂ u j ) ,

where

(19) τ t , ij = μ t ∂ u i ∂ x j + ∂ u j ∂ x i − 2 3 ρ k δ ij .

G ω is also a function of G k :

(20) G ω = ρ α μ t G k .

Here, ∝ is given as

(21) ∝ = α ∞ α * ( ∝ 0 * + Re t / R k ) ( 1 + Re t / R k ) ,

where ∝ ∞ is determined as

(22) ∝ ∞ = F 1 ∝ ∞ , 1 + ( 1 − F 1 ) ∝ ∞ , 2 ,

where

(23) ∝ ∞ , 1 = β i , 1 β ∞ * − ĸ 2 σ ω , 1 β ∞ * ,

(24) ∝ ∞ , 2 = β i , 2 β ∞ * − ĸ 2 σ ω , 2 β ∞ * .

3 Thermophysical properties of hybrid nanofluids

The hybrid nanofluids consisting of Al₂O₃–Cu nanoparticles suspended in base fluid water were utilized here. In this study, a single-phase, incompressible Newtonian fluid model is employed. Table 1 displays the thermophysical properties of water, Al₂O₃, and Cu. Table 2 displays the relationship between the thermal conductivity and dynamic viscosity of hybrid nanofluids and the volume percentage of solids. The mixing model determines the density and specific heat capacity of Al₂O₃–Cu/water [31,39,40]. That is,

(25) ρ nf = φ cu ρ cu + φ Al 2 O 3 ρ Al 2 O 3 + ( 1 − φ ) ρ f .

Table 1

Physical properties of water and nanoparticles [36,37]

Physical properties	Water	Cu	Al₂O₃
c _p (J kg⁻¹ K⁻¹)	4,179	385	765
ρ (kg m⁻³)	997.1	8,933	3,970
k (W m⁻¹ K⁻¹)	0.613	400	40
β (K⁻¹)	21 × 10⁻⁵	1.67 × 10⁻⁵	0.85 × 10⁻⁵
δ ( Ω m⁻¹)	0.05	5.96 × 10⁷	1 × 10⁻¹⁰

Table 2

Thermophysical properties of hybrid nanofluids [38]

φ %	k _nf (W m⁻¹ K⁻¹)	μ nf (kg m⁻¹ s⁻¹)
2.0	0.6849921	0.001935

The combined solid volume fraction of the Al₂O₃ and Cu nanopowders is given as

(26) φ = φ Cu + φ Al 2 O 3 ,

(27a) ( ρ c p ) nf = ( 1 − φ ) ( ρ c p ) f + φ cu ( ρ c p ) Cu + φ Al 2 O 3 ( ρ c p ) Al 2 O 3 ,

(27b) k nf = k f ( k s + 2 k f ) − 2 φ ( k f − k s ) ( k s + 2 k f ) + φ ( k f − k s ) ; where k s = k Cu + k Al 2 O 3 ,

(27c) μ nf = μ f ( 1 − φ ) − 2.5 ,

(27d) σ nf = σ f 1 + 3 ( σ s / σ f − 1 ) φ ( σ s / σ f + 2 ) − ( σ s / σ f − 1 ) φ ; where σ s = σ Cu + σ Al 2 O 3 .

The working fluid enters horizontally through the left inlet opening at a uniform velocity U _in and a constant temperature T _in = 25°C and exits through the right opening. A constant temperature is applied to the heated baffle faces. All other faces are thermally insulated, and no-slip conditions (u = 0, v = 0) at the walls are assumed. At the outlet of the channel, zero-gauge pressure (atmospheric pressure) and temperature gradient are imposed. Baffle surfaces are modeled as rigid, smooth, and thermally insulated, which means that no heat transfer occurs through the baffles.

4 Numerical techniques, validation, and grid-independent study

The transport partial differential equations (Equations (1)–(3)) are solved numerically using ANSYS Fluent, a finite volume-based solver, while adhering to the appropriate boundary conditions. The computational domain is carefully constructed and discretized in ANSYS Workbench, employing a structured mesh made up of quadrilateral elements. This mesh configuration provides the necessary precision to address the geometrical intricacies of the problem. To accurately capture boundary layer effects, a non-uniform meshing approach is adopted, focusing on generating finer grids in critical regions, particularly near the cylinder walls and the obstructing block, where sharp gradients are expected. ANSYS Fluent pressure-based solver is utilized to perform the simulations. The SIMPLE algorithm (semi-implicit method for pressure-linked equations) is used to couple pressure and velocity fields, ensuring effective and stable convergence for incompressible flow conditions. The governing equations, including pressure, momentum, and energy equations, are discretized using the second-order upwind scheme. This method significantly enhances solution accuracy by reducing numerical diffusion and ensuring reliable results, particularly in regions dominated by convection effects [41,42]. The iterative process is managed with a stringent convergence criterion, ensuring that residuals for all governing equations are reduced to below 10⁻⁸. This rigorous threshold is essential to achieving numerical stability and ensuring that the results accurately represent the underlying physical phenomena. By incorporating these advanced computational strategies, ANSYS Fluent enables a high-fidelity simulation of complex flows, ensuring that the generated results are both accurate and robust while meeting the highest numerical standards.

In this section, an attempt is made to check whether the process adopted in the current study is in the right direction. For this, 2-v/w-shaped ribs are used by Menni et al. [43]. The process conditions are similar to those maintained by Menter [31]. Figure 2 shows the graph, representing the fluid temperature on the X-axis and channel height on the Y-axis. The trend of the graph remains the same, but the value is a bit deviated. A less than 10% deviation is observed from the referred work.

Figure 2

Validation work concerning the published work of Menni et al. [43].

Since the validation of the work agreed with the referred work, the next step is to perform the grid-independent study using the same conditions as above. The Quad-dominated element is used for the current study, and the grid size is varied between 0.0009 and 0.007 m. The grid size vs. pressure drop is drawn, as shown in Figure 3 for Case 1, Re = 12,000, and φ = 2%. It is observed that from 0.007 to 0.002, the error is more than 2%, but as the grid size reduced below the range 0.001–0.0009 m, this error decreased to less than 1%. Therefore, for the current numerical analysis, we have taken a grid size of 0.001 m rather than 0.0009 m to reduce the computational size and time.

Figure 3

Grid-independent analysis.

5 Results and discussion

This work numerically analyses the effects of staggered transverse zigzag baffles with hybrid nanofluids on flow characteristics in a horizontal channel at different Reynolds numbers (Re = 12,000, 17,000, 22,000, 27,000, and 32,000). Four different arrangements of the baffles are also analyzed. The flow and hydraulic properties of the studied cases are explained using the velocity, streamlined contours, and corresponding pressure drop, which are also analyzed. The Al₂O₃–Cu volumetric concentration of hybrid nanofluids is fixed at φ = 2% for the entire study.

Figures 4 and 5 show the axial velocity and the streamlines for Case 1 at various Re numbers (12,000, 17,000, 22,000, 27,000, and 32,000). Streamlines provide a clear visual representation of the fluid flow within the channel, helping to identify critical flow behaviors influenced by the geometry and boundary conditions. The W-shaped baffles faced the right-hand side at a 45° angle of the flow attack. After the entry to the channel, fluid flow interacts with the heated bottom wall and is then obstructed by the baffles, which leads to the fluid flow through the narrow gaps between the baffle tip and the upper wall. The velocity contours show that the inlet fluid flow velocity reduces behind the baffles, especially in the areas close to the rear side of the baffles. The blue spots behind the baffles indicate the formation of a vortex, which is clearly shown in the streamline contours. In the areas confined between the top edge of the baffles and the top wall, the flow velocity is maximum since the baffles work as a nozzle by reducing the cross-sectional area. Reducing the cross-sectional area and the existence of the vortex region cause a dramatic change in the flow direction. The high velocity from the upper region of the channel remains in that range and direction until the outlet cross-section due to the short length of the channel. For all the cases of Re, the behavior of the flow is almost the same, but with a different flow velocity. In general, vortices develop behind the baffles due to sudden changes in the flow direction. These recirculation zones enhance turbulence and disrupt the flow stability, promoting greater thermal mixing. The size and strength of these vortices are directly influenced by baffle orientation, spacing, and Reynolds number (Re), with higher Re intensifying turbulence.

Figure 4

Axial velocity counter for Case 1 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

Figure 5

Streamlines for Case 1 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

The maximum velocity of the flow appears in the areas between the two baffles, and the maximum velocity drops gradually after passing the second baffle, unlike Case 1 (Figures 4 and 5), which presents the maximum generated fluid along the channel since the barriers are softer. The axial velocity registered a minimum value in the areas beside the walls and behind the baffles due to the generation of the vortices. The general behavior is identical for all Re values, except the velocity values, which are higher in the case of higher Re. The flow characteristic for the last studied case (the left baffle is in the opposite direction of the flow, and the right baffle faces the flow direction). Because of the soft top edge of the left baffle, the flow slips over the top edge, generating a high velocity. The faster flow is caused by the reduction of the cross-sectional area of the channel. In this case, the main observation is that the maximum velocity remains at the top of the channel until the outlet section. The axial velocity registered a minimum value between the two baffles; however, the angular velocity appears behind the baffles and at the angle of each baffle. Zigzag baffles act as deflectors, redirecting the flow into narrow gaps. This leads to secondary flows and swirl patterns, which are crucial for breaking thermal boundary layers and improving convective heat transfer.

The flow hits the upper wall and is directed downward, creating more giant swirls behind the baffles. The figures clearly show that the baffles work as an explant barrier when its front side faces the direction of the flow. The general conduct of the flow properties is similar for all Re values, but the velocity range is different. Changing both baffles’ orientations to face the flow direction is illustrated in Figures 6 and 7. These figures show axial velocity and the streamlines for various values of Re. As mentioned, the baffles present an excellent barrier for the flow in this case, and at the top region, the flow hits the top point edge of the baffle and scatters upward, then is directed downward after hitting the upper channel wall. The appearance of vortexes is denser due to the barrier’s strength.

Figure 6

Axial velocity counter for Case 3 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

Figure 7

Streamlines for Case 3 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

Figures 8 and 9 show the velocities and the stream flow contours of Case 2 for different values of Re. The flow is also mixed with a hybrid nanoparticle. The W-shaped baffles are placed in opposite directions, whereas the right baffle faces the right direction and the left one faces the left. The general behavior in these cases is similar to that of previous cases, with different patterns. The top point of the left baffle faces the left side, attacks the flow, and scatters it upward (Figure 10).

Figure 8

Axial velocity counter for Case 2 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

Figure 9

Streamlines for Case 2 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

Figure 10

Streamlines for Case 4 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

Figure 11 shows the axial velocity contours for all the studied cases with Re = 32,000 and the supplied power of 4,000 W/m². The velocity data of Cases 1 and 4 are almost similar regarding the maximum and minimum velocity distribution. Because of the soft angle of the top part of the left baffle facing the flow, the stream moves in a horizontal line to the outlet section. The minimum axial velocity appears behind the baffles (places of generating vortexes), and is also clearly illustrated in Figure 12, which shows the streamlines for the cases under the same conditions. When the left baffles face the flow (Cases 2 and 3), it blocks most of the flow, and the escaping stream is directed upward, hitting the upper wall channel and then flows downward behind the baffles and swirls. The maximum flow scatters in the areas between the two baffles. Maximum velocities are observed in gaps between baffles, enhancing convective heat transfer in these regions. Recirculation zones behind baffles exhibit reduced velocities, corresponding to regions of intense mixing.

Figure 11

Comparison of axial velocity fields for Cases 1–4 for Re = 32,000 and q = 4,000 W/m².

Figure 12

Comparison streamlines for Cases 1–4 for Re = 32,000 and q = 4,000 W/m².

Furthermore, Case 1 shows relatively organized flow patterns, with limited turbulence and well-contained vortices. This makes it effective for applications requiring moderate heat transfer without excessive pressure penalties. The staggered arrangement (Case 2) creates denser and overlapping vortices, increasing turbulence and enhancing flow mixing. This setup is ideal for uniform heat dissipation needs. Reversed orientations (Case 3) of the baffles result in chaotic turbulence, larger vortex zones, and greater flow disruption. While maximizing heat transfer, this case sacrifices energy efficiency. Case 4 combines characteristics of Cases 1 and 3, striking a balance between turbulence and flow stability. It offers a compromise between performance and energy requirements. Staggered baffle configurations (Case 2) produce asymmetrical flow, resulting in alternating vortices. This disrupts flow uniformity more effectively than symmetric setups (Case 1). Cases with opposing orientations (Case 3) cause abrupt changes in the flow direction, creating highly chaotic patterns and intensifying turbulence.

Figure 13 shows the pressure in the channel at various cross-sections for Case 1 for different Re values. The general state of the pressure profile is that the pressure increases with the increase in Re. The bend in the line appears due to the gap between the baffles and the upper wall, where the pressure changes compared to the lower regions. At a distance of 0.179 m from the entrance (Figure 13a), the pressure at the top part of the channel is slightly less than the lower part. The bend of the pressure line increases with increasing Re due to the generation of a wider and faster swirl in the cases of the higher Re. The average pressures at the vertical line at a location of 0.179 m are 900 and 3,100 Pa for Re = 17,000 and 32,000, respectively. At a deeper location of the channel (x = 0.255 m), the pressure shows different behaviors, whereas the pressure increases at the top part of the channel, and this change increases with increasing Re, as shown in Figure 13b. When Re = −32,000, the pressure at the base of the channel is 338 Pa and increases to 422 Pa at the top part. The pressure for each Re in the current location is much less than that at the previous location (x = 0.179 m) since the second location is behind the baffles. Figure 13c shows the pressure value at a distance of 0.335 m from the entrance, which is also located between the baffles, for various values of Re. At this position, the pressure drops to a quarter at the middle of the channel for each value of Re since the velocities at those areas are too low compared to the channel’s lower and upper parts. The average pressures for Re = 12,000 and 32,000 are 50 and 275 Pa, respectively. It is worth mentioning that the drop in the pressure at the middle of the channel increases with increasing Re. The pressure line crosses the channel at 0.525 m of the entrance section, located behind the baffles for the mentioned Re, as illustrated in Figure 13d. The central point in this section is that the pressure registered negative values for all values of Re. The lowest value appears for the case of the highest Re, whereas the average pressure is equal to −500 Pa. The pressure also shows a lower value at the middle of the channel, and the lowest value for Re = 32,000 is −620 Pa. Generally, the pressure for higher Re fluctuates (between lower and higher values) more than those with a lower Re. The highest and the lowest values of the average Re registered are 3,200 and −500 Pa at the location of 0.179 and 0.525 m when Re = 32,000; however, they are 850 and −60 Pa at the location of 0.179 and 0.525 m when Re = 12,000. This behavior is caused by the pressure dropping and fluctuating more with increasing the flow rate in the domain. Figure 14 shows the pressure profile at the vertical line of the channel for various locations when Re = 32,000. The figure illustrates that the pressure value drops deeper from the entrance (pressure is maximum at the inlet section and minimum at the outlet section). In front of the baffles, the pressure is 3,200 Pa (maximum); however, behind the baffles, the pressure takes a negative value of −500 Pa (minimum). The pressures fluctuate in a narrow domain (between 200 and 600 Pa) in the area between the two baffles. Overall, the obstructions from the baffles create regions of high pressure upstream, followed by sharp drops in the recirculation zones behind the baffles. This pattern reflects energy losses due to turbulence and flow resistance. The overall pressure drop increases with Re due to higher inertial forces and turbulence.

Figure 13

Pressure drop profiles for Case 1 at Vol. 2% and different Reynolds numbers at (a) x = 0.179 m, (b) 0.255 m, (c) x = 0.335 m, and (d) x = 0.525 m.

Figure 14

Pressure drop profiles for Case 1 at different locations with Re = 32,000.

In Case 2, when the left baffle is oriented in the opposite direction, the flow on the x line is equal to 0.255 m and flows backward in general due to the generated swirls between the baffles (Figure 14). The local pressures have a negative value for all Re values in the areas between the baffles. The pressure reduces with increasing Re since the pressure fluctuates in the broader range between the negative and positive values. Further, the pressure drops at the center of the channel registered a larger value for the higher Re than those at the upper and lower parts. The average pressures are −120 and −1,350 Pa for Re = 12,000 and 32,000, respectively. Figure 6b shows the pressure across the channel at Re = 27,000 Pa and for various regions (x1–x4). The pressure in position 1 has the highest value since it is not affected by the baffles; however, the pressures sharply drop to the negative values due to the high turbulence for the regions between and behind the baffles. Increasing the turbulence in the channel increases the drop in pressure. The average pressures for the locations x2 and x3 (between the baffles) are −1,000 and −1,100, respectively; however, the pressure increases to −200 at x4 (behind the baffles) (Figure 15).

Figure 15

Pressure drop profiles for Case 2 for different (a) Reynolds numbers at x = 0.255 m and (b) locations at Re = 27,000.

In Case 3 (both baffles have the opposite direction), the pressure in location x (located between the baffles) is equal to 0.335 m and has negative values for all Re values, as shown in Figure 16. Due to the increasing turbulence with an increase in Re, the pressure drops more with a higher flow rate. The average pressure values of −300 and −2,700 Pa for Re = 12,000 and 32,000. Furthermore, the figure shows that the pressure drop in the middle of the channel increases with increasing Re compared with the upper and the lower parts of the line. Figure 7b shows the pressure profile for the mentioned location when Re = 22,000. The average pressure value is equal to 2,000 Pa at x1; then, due to the increasing turbulence of the flow, which is caused by the baffles, the pressure drops to negative values in the region between and behind the baffles. The minimum average pressure registered was 1,200 Pa at x3.

Figure 16

Pressure drop profiles for Case 3 for different (a) Reynolds numbers at x = 0.355 m and (b) locations at Re = 22,000.

Figure 17 shows the pressure for Case 4 (the second baffle is directed opposite to Case 1) for various values of Re at x2 (between the baffles). The pressure values are negative, indicating high turbulence in the region between the two baffles. The pressure in the top region of the channel is much higher than that in the middle and lower parts. The pressure at the top part of the channel is −15 Pa; however, the pressure in the middle and the bottom parts is −105 Pa for Re = 32,000. The variation between the pressure at the top and the bottom parts increases with increasing Re. Figure 18b shows the pressure in the different cross-sectional lines for Case 4 at Re = 12,000. At x1 (before passing the baffles), the average pressure is 370 Pa; however, between and behind the baffles, the average pressure is about zero and negative values due to the higher turbulence caused by the baffles compared to the entrance region.

Figure 17

Pressure drop profiles for Case 4 for different (a) Reynolds numbers at x = 0.255 m and (b) locations at Re = 12,000.

Figure 18

Axial velocity counter for Case 4 for (a) Re = 12,000, (b) Re = 17,000, (c) Re = 22,000, (d) Re = 27,000, and (e) Re = 32,000.

Overall, for Case 1, the moderate pressure drops with smooth transitions, reflecting controlled turbulence suitable for systems prioritizing energy efficiency. For Case 2, higher pressure gradients due to increased turbulence from staggered baffles. This enhances heat transfer at higher flow resistance. In Case 3, significant pressure drops occur because of severe turbulence and chaotic flow patterns, prioritizing performance over efficiency. Case 4 displays intermediate pressure behavior, balancing thermal performance and energy requirements.

6 Conclusion

The present work numerically explores the effects of staggered transverse zigzag baffles and hybrid nanofluid flow in a channel on the thermofluid flow characteristics. It is anticipated that the novel combination of staggered transverse zigzag baffles with hybrid nanofluids proposed in this study will be a promising passive technique for achieving good thermal performance in most industrial applications. Al₂O₃–Cu hybrid nanofluids (2%) with Reynolds numbers of 12,000, 17,000, 22,000, 27,000, and 32,000 were examined. The main conclusion in this work can be summarized as follows:

The baffles present an excellent barrier to the fluid flow when their front side faces the direction of the flow.
Generally, the pressure magnitude increases with an increase in Re.
The pressure magnitude reduces as the flow passes through the domain due to a decrease in velocity (caused by the baffles) and an increase in turbulence.
The greatest pressure drop occurs in the middle of the channel, particularly at the X3 position in Case 1, due to the combined effects of flow obstruction and increased turbulence created by the baffles.
Generally, the pressure is in the positive range at the entrance section before hitting the baffles, and mainly changes to the negative range between and behind the baffles.
The direction of the baffles significantly influences the generated turbulence; the direction of the angles and the top point of the baffles affect the flow direction and the density of the generated swirls.

This analysis quantifies the trade-offs between energy efficiency and heat transfer performance, underscoring the need for design optimization tailored to specific applications. The findings highlight the crucial role of baffles in redirecting flow and generating turbulence. This turbulence enhances thermal mixing but leads to higher pressure losses.

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Acknowledgments

The authors extend their appreciation to Dr. Shijo Thomas, Associate Professor, and the SMSE family at NIT Calicut for their constant support. They also thank Mr. Manjunatha S. J. and Mr. Lakshmi Narshima Prasad, Directors at Thermovac Aerospace Pvt. Ltd.

Funding information: The authors thank the Qatar National Library for providing open-access funding.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript, consented to its submission to the journal, reviewed all the results, and approved the final version of the manuscript. Hussien contributed to the conceptualization, supervision, project administration, and writing the original manuscript. Ali was involved in the formal analysis, investigation, and writing of the original manuscript. Tuqa handled the original manuscript’s software development, validation, and writing. Samantha participated in the investigation and visualization aspects of the study. Hayder provided resources and supervision. Azher contributed to formal analysis and validation. Mohaimen was involved in the investigation and visualization. Abdellatif was responsible for formal analysis and funding acquisition. Nirmalendu and Krishna contributed to reviewing and editing the original manuscript.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Received: 2024-09-09

Revised: 2025-06-20

Accepted: 2025-07-05

Published Online: 2025-08-02

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2025-0130

Keywords for this article

channel flow; W-shaped baffle; hybrid nanofluid; turbulent flow; flow characteristics

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