Numerical investigation of convective heat and mass transfer in a trapezoidal cavity filled with ternary hybrid nanofluid and a central obstacle

Zehba Raizah; Samrat Hansda; Shuruq F. Alkhaldi

doi:10.1515/ntrev-2025-0246

Article Open Access

Numerical investigation of convective heat and mass transfer in a trapezoidal cavity filled with ternary hybrid nanofluid and a central obstacle

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Published/Copyright: December 4, 2025

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From the journal Nanotechnology Reviews Volume 14 Issue 1

Abstract

This study investigates the combined heat and mass transfer characteristics in a trapezoidal cavity saturated by ternary hybrid nanofluid with a circular obstacle, considering the effects of key dimensionless parameters, including the buoyancy ratio (N), obstacle radius (r ₀), Rayleigh number (Ra), Lewis number (Le), and nanoparticle volume fraction (ϕ). A numerical approach is employed to analyze the streamlines, isotherms, and concentration contours under varying conditions. The results indicate that increasing N enhances convective transport, while negative values lead to flow instability. Larger obstacle sizes significantly impact circulation patterns, affecting both heat and mass transfer rates. Higher Ra values intensify convection, improving thermal and solutal transport. Additionally, increasing Le suppresses mass diffusion, while higher nanoparticle concentrations enhance thermal conductivity but may hinder convective flow. These findings provide valuable insights into optimizing convective transport in enclosed systems, relevant to industrial and environmental applications.

Keywords: ternary hybrid nanofluid; enhanced heat transfer; cavity flow modeling; GFEM; trapezoidal enclosure; natural convection

1 Introduction

The study of convective heat transfer within enclosures containing bluff bodies is a field of significant academic and practical interest, driven by its relevance to applications such as electronic component cooling, nuclear reactor design, and heat exchanger optimization. The introduction of an internal body, or blockage, fundamentally alters the thermal and hydraulic fields by disrupting boundary layer development and modifying flow patterns. This intervention presents a dual effect: while it can promote fluid mixing and mitigate thermal stratification to enhance heat transfer, it may also induce stagnation zones that diminish the system’s overall thermal efficiency. The net performance is intricately dependent on the blockage’s geometry, thermophysical properties, and placement, as well as the enclosure’s boundary conditions. A substantial body of research has focused on optimizing these parameters to augment heat transfer. The geometric characteristics of the internal body have been identified as a critical factor. For example, Alsabery et al. [1] noted that the block size becomes particularly vital in convection-dominated regimes. Similarly, Boukendil et al. [2] demonstrated that the size and location of inner bodies significantly influence both convective and radiative heat transfer. Expanding on geometric complexity, Tayebi and Chamkha investigated the effects of wavy solid blocks [3] and wavy circular cylinders [4], revealing that non-standard shapes can markedly affect flow topology and energy transmission. A common strategy to improve thermal performance is the use of nanofluids. A consistent finding across numerous studies is that the average Nusselt number Nu_avg, a measure of convective heat transfer, increases with higher nanoparticle volume fractions ϕ and Rayleigh numbers Ra. This trend was independently confirmed by Mahmoodi and Sebdani [5] for Cu-water nanofluids, Rahmati and Tahery [6] for water-TiO₂ nanofluids, and Raisi [7] for copper-water nanofluids with an internal heat-generating body. Further supporting this, Sheremet et al. [8] observed that the presence of nanoparticles was directly responsible for upgrading heat transfer within their studied cavity.

The imposition of an external magnetic field (MHD) introduces another layer of control, typically acting to suppress fluid motion. Sivaraj and Sheremet [9] observed that a magnetic field could diminish the rate of energy transfer within a porous cavity. This suppressive effect of the Lorentz force was also highlighted by Ashouri et al. [10] and Tayebi and Chamkha [3], who found that both the magnetic field and the thermal conductivity of the solid block could profoundly influence the system’s flow structure and thermal performance.

Other contributing factors have also been explored. In the context of porous media, Alsabery et al. [11] revealed that the Nusselt number enhances with a rising Darcy number. The geometry of the main enclosure, not just the internal body, also plays a role, as Rahmati and Tahery [6] found that average Nusselt number improved by elongating the enclosure’s length. The effect of the cavity’s inclination has also been considered by researchers such as Das and Reddy [12]. Collectively, this research demonstrates that while optimized block arrangements can enhance heat transfer, the complex flow-structure interactions warrant continued investigation.

Further research has continued to explore the nuanced effects of internal obstacles on convective heat transfer. Studies have moved beyond simple geometries to consider complex shapes and properties, such as corrugated blocks, which play a vital role in regulating flow and energy transfer characteristics. The orientation of elliptic blockages has been analyzed by Billah et al. [13], while Roy [14], 15] investigated geometries involving wavy walls and various internal cylinder shapes (square, circular, elliptic), noting that the Rayleigh number and wall undulation significantly amplify the flow strength. The physical properties of the obstacle, such as permeability, have also been a focus. Vijaybabu and Vijaybabu [16] and Dhinakaran Shruti and [17] found that while permeability enhances fluid momentum, an applied magnetic field diminishes its kinetic energy, a conclusion supported by Hamid et al. [18], who observed reduced heat transfer with a rising Hartmann number. The size and position of the obstacle remain critical parameters, with Hamid et al. [19] reporting a 400 % upgrade in central energy distribution as an obstacle’s radius grew from 0.1 to 0.3. This finding is corroborated by numerous researchers who confirm that the location of the heated body profoundly influences the resulting thermal fields and flow topology [20], [21], [22]. While single-phase thermal convection is extensively documented, a significant research gap persists concerning double-diffusive natural convection (DDNC) in enclosures with internal bodies. Arising from coupled thermal and solutal buoyancy forces, DDNC introduces a higher degree of complexity to the transport mechanisms. The limited literature in this specific area shows that the obstacle’s presence significantly alters the coupled heat and mass transfer. For instance, Ismael and Ghalib [23] found that a solid body’s position dictates its effectiveness in heat transfer. The influence of governing parameters is also crucial; several studies report that the Nusselt (Nu) and Sherwood (Sh) numbers are typically enhanced by an increasing Rayleigh number (Ra) and buoyancy ratio (N) but suppressed by a rising Lewis number (Le) and Hartmann number (Ha) [24], [25], [26]. Interestingly, Al-Farhany et al. [24] noted that increasing the size of an internal triangular blockage could counterintuitively decrease the average heat and mass transfer rates. Research by Vijaybabu [27] on magneto-thermosolutal convection highlights the importance of the magnetic field’s direction and reveals that irreversibilities from mass transfer can dominate the system’s total entropy generation. To further augment performance, recent efforts have focused on advanced working fluids. Ternary hybrid nanofluids (THNFs) colloidal suspensions of three distinct nanoparticle types-have emerged as a superior alternative to mono- and binary nanofluids due to their enhanced thermal conductivity and stability. A multitude of studies have consistently demonstrated significant improvements in heat transfer when employing THNFs in various configurations, including trapezoidal, porous, and triangular enclosures [28], [29], [30], [31], [32], [33], [34]. The integration of these advanced fluids into DDNC systems represents a promising frontier. Initial investigations have confirmed their potential, with Alzahrani et al. [35] reporting improved thermosolutal performance under MHD conditions. Recent work has also explored magneto-radiative DDC in annuli [36] and the impact of chemical reactions [37]. Chattopadhyay [38] found that for non-Newtonian ternary ferrofluids, increasing the Casson parameter and Lewis number significantly boosts mass transfer, even if heat transfer remains relatively stable.

1.1 Research objective

To address the mentioned gaps, the primary objectives of this study are:

To numerically simulate convective heat and mass transfer of ternary hybrid nanofluids (THNFs) inside a trapezoidal cavity with a central obstacle.
To develop a comprehensive understanding of how geometric configurations and nanofluid properties influence flow topology, species distribution, and heat transfer.
To analyze the effects of key governing parameters on fluid flow, heat transfer, and species transport within the system.
The simulated findings aim to inform the design and optimization of efficient thermal systems, ultimately contributing to enhanced energy utilization and system performance across multiple industries.

1.2 Novelty of the present study

This study introduces several novel aspects that distinguish it from existing research:

First numerical investigation of double-diffusive convection of ternary hybrid nanofluids (THNFs) in a trapezoidal cavity with a central obstacle, a configuration not widely explored in existing literature.
Incorporation of a central obstacle to examine its role in modifying flow circulation, heat transport, and solutal distribution within trapezoidal enclosures.
Comprehensive analysis of the combined effects of cavity geometry, obstacle presence, and nanoparticle composition, providing new insights into multiparametric influences on convective transport.
Detailed evaluation of heat and mass transfer enhancement through the computation of Nusselt and Sherwood numbers under varying thermal and solutal conditions.

This study addresses these gaps by investigating thermosolutal convection of a ternary hybrid nanofluid within a trapezoidal enclosure containing a circular baffle. A two-dimensional, steady-state incompressible model governed by continuity, momentum, energy, and species equations is developed. Ternary hybrid nanofluid properties are estimated using mixture-based correlations, and the equations are solved via the finite element method with a Galerkin scheme. Dimensionless parameters (Ra, N, Le, ϕ, r ₀) are varied to assess their effects on flow, heat, and mass transfer, with streamlines, isotherms, and concentration fields analyzed for physical insight and design relevance. The results enhance the fundamental understanding of heat and mass transfer in hybrid nanofluids, providing practical guidance for developing energy-efficient thermal management systems in advanced engineering applications.

2 Mathematical analysis

2.1 Problem definition and geometry

The geometric configuration of the present study, as depicted in Figure 1, comprises a two-dimensional trapezoidal cavity that encloses a centrally positioned heated circular obstacle. The cavity is saturated with a ternary hybrid nanofluid consisting of Al₂O₃/Ag/CuO nanoparticles dispersed in water. All the cavity boundaries are assumed to be adiabatic, while the circular obstacle maintains a uniform elevated temperature and a constant nanoparticle concentration in its vicinity.

Figure 1:

Physical model.

The following physical assumptions are applied in the current investigation:

the flow is steady, laminar, two-dimensional, incompressible, and viscous,
the working fluid is treated as a Newtonian liquid,
all thermophysical properties are considered constant, except the density, which varies with temperature according to the Boussinesq approximation,
no-slip velocity boundary conditions are applied on all solid walls,
the inner obstacle is heated, while the cavity walls are thermally insulated,
the thermophysical properties of the base fluid (water) and nanoparticles (Al₂O₃, CuO, and Ag) are summarized in Table 1.

Table 1:

Physical attributes of Al₂O₃, CuO, Ag and water [28], 39], 40].

Physical properties	Water	Al₂O₃ (s1)	CuO (s2)	Ag (s3)
ρ	997.1	3,970	6,320	10,500
K	0.613	40	76.5	429
C _P	4,179	765	531.8	235
β × 10⁻⁵	21	0.580	1.8	1.89
α	1.47 × 10⁻⁷	1.32 × 10⁻⁵	2.28 × 10⁻⁵	1.74 × 10⁻⁴
μ	8.9 × 10⁻⁴	⋯	⋯	⋯
Pr	6.2	⋯	⋯	⋯

2.2 Governing equations and thermophysical properties

Depending on the assumptions mentioned, the two-dimensional flow can be described mathematically by Navier–Stokes equations, as follows [41], 42]:

(1) ∂ u ∂ x + ∂ v ∂ y = 0

(2) u ∂ u ∂ x + v ∂ u ∂ y = − 1 ρ thnf ∂ p ∂ x + μ thnf ρ thnf ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2

(3) u ∂ v ∂ x + v ∂ v ∂ y = − 1 ρ thnf ∂ p ∂ y + μ thnf ρ thnf ∂ 2 v ∂ x 2 + ∂ 2 v ∂ y 2 + g ρ thnf ρ β θ thnf θ − θ c − ρ β c thnf c − c c

(4) u ∂ θ ∂ x + v ∂ θ ∂ y = α thnf ∂ 2 θ ∂ x 2 + ∂ 2 θ ∂ y 2 + Q 0 ρ C p thnf θ − θ c

(5) u ∂ c ∂ x + v ∂ c ∂ y = D thnf ∂ 2 c ∂ x 2 + ∂ 2 c ∂ y 2

Under the dimensional boundary conditions:

On all walls of the cavity: u = v = θ = c = 0

On the inner circular: u = v = 0, θ = θ _h and c = c _h

To transfer the dimensional equations into a non-dimensional form, the following transformations are used:

X = x L , Y = y L , U = u L α f , V = v L α f , T = θ − θ c θ h − θ c , P = p L 2 ρ thnf α f 2 , Φ = c − c c c h − c c ,

The dimensionless governing equations are:

(6) ∂ U ∂ X + ∂ V ∂ Y = 0

(7) U ∂ U ∂ X + V ∂ U ∂ Y = − ∂ P ∂ X + μ thn ρ thn ∂ 2 U ∂ X 2 + ∂ 2 U ∂ Y 2

(8) U ∂ V ∂ X + V ∂ V ∂ Y = − ∂ P ∂ Y + μ thn f ρ thn f ∂ 2 V ∂ X 2 + ∂ 2 V ∂ Y 2 + ( ρ β θ thnf ρ thnf β f RaPr T + N Φ

(9) U ∂ T ∂ X + V ∂ T ∂ Y = α thnf α f ∂ 2 T ∂ X 2 + ∂ 2 T ∂ Y 2 + q α thnf α f T

(10) U ∂ Φ ∂ X + V ∂ Φ ∂ Y = D thnf D f 1 Le ∂ 2 Φ ∂ X 2 + ∂ 2 Φ ∂ Y 2

The dimensionless boundary conditions are:

On all walls of the cavity: U = V = T = Φ = 0

On the inner circular: U = V = 0, T = 1 and Φ = 1

The effective properties of the ternary hybrid nanofluid are calculated using classical mixture models adapted for multi-nanoparticle suspensions.

The choice of Al₂O₃/Ag/CuO as the ternary nanoparticle combination is based on their complementary thermal characteristics. Al₂O₃ provides chemical stability and baseline thermal performance, Ag offers exceptionally high thermal conductivity, and CuO contributes moderate thermal enhancement with good dispersion stability. When combined, these nanoparticles can produce a synergistic effect that enhances overall thermal conductivity and convective heat transfer performance beyond that of any individual or binary mixture. This combination is also expected to impact the fluid’s viscosity and diffusion characteristics in a balanced manner.

The effective models for the ternary hybrid nanofluid are:

Density:

ρ thnf = 1 − ϕ 3 1 − ϕ 2 1 − ϕ 1 ρ f + ϕ 1 ρ s 1 + ϕ 2 ρ s 2 + ϕ 3 ρ s 3

Viscosity:

μ thnf = μ f 1 − ϕ 1 2.5 1 − ϕ 2 2.5 1 − ϕ 3 2.5

Specific heat capacity:

ρ c P thnf = 1 − ϕ 3 1 − ϕ 2 1 − ϕ 1 ρ c P f + ϕ 1 ρ c P s 1 + ϕ 2 ρ c P s 2 + ϕ 3 ρ c P s 3

Thermal expansion coefficient:

ρ β thnf = 1 − ϕ 3 1 − ϕ 2 1 − ϕ 1 ρ β f + ϕ 1 ρ β s 1 + ϕ 2 ρ β s 2 + ϕ 3 ρ β s 3

Thermal conductivity:

K thnf = K hnf K s 3 + 2 K hnf − 2 ϕ 3 K hnf − K s 3 K s 3 + 2 K hnf + ϕ 3 K hnf − K s 3

where:

K hnf = K nf K s 2 + 2 K nf − 2 ϕ 2 K nf − K s 2 K s 2 + 2 K nf + ϕ 2 K nf − K s 2 , and K nf = K f K s 1 + 2 K f − 2 ϕ 1 K f − K s 1 K s 1 + 2 K f + ϕ 1 K f − K s 1

Thermal diffusivity:

α thnf = K thnf ρ C P thnf

Solutal diffusivity:

D thnf = 1 − ϕ 1 1 − ϕ 2 1 − ϕ 3 D f

2.3 Quantities of interest

The average Nusselt and average Sherwood parameters on the hot inner cylinders are defined as:

(11) N u avg = − 1 2 π ∫ 0 2 π k thnf k f ∂ T ∂ n d ξ

(12) S h avg = − 1 2 π ∫ 0 2 π D thnf D f ∂ C ∂ n d ξ

where n refers to the normal direction of the inner shape.

3 Numerical method

The numerical solution of the governing equations (6)–(10), subject to the boundary conditions, is carried out using the Galerkin weighted finite element method. In this approach, the system of partial differential equations is transformed into a set of integral equations through the application of the Galerkin weighted residual technique, as described in ref. [43].

3.1 Nonlinear residual equations in FEM

Let Ω denote the computational and let ψ _i be the shape (test) functions associated with the nodes of the finite elements.

The field variables (U, V, P, T, Φ) are approximated within each element using shape functions:

(13) U ≈ ∑ i = 1 N U i ψ i X , Y , V ≈ ∑ i = 1 N V i ψ i X , Y , T ≈ ∑ i = 1 N T i ψ i X , Y , Φ ≈ ∑ i = 1 N Φ i ψ i X , Y , P ≈ ∑ i = 1 N P i ψ i X , Y

where ψ _i(X, Y) is the shape function.

For each node i, the residual equations are derived by substituting the approximations into the weak form and setting the residuals to zero.

Continuity equation residual:

(14) R n C ≈ ∑ i = 1 N U i ∫ ∂ ψ i ∂ X ψ n d X d Y + ∑ j = 1 N V i ∫ ∂ ψ i ∂ Y ψ n d X d Y

Momentum equations residual:

(15) R n U ≈ ∑ i = 1 N U i ∫ ∑ i = 1 N U i ψ i ∂ ψ i ∂ X + ∑ i = 1 N V i ψ i ∂ ψ i ∂ Y ψ n d X d Y + ∑ i = 1 N ∫ − ∑ i = 1 N P i ψ i ∂ ψ i ∂ X ψ n d X d Y + ∑ i = 1 N U i ∫ μ thnf ρ thnf ∂ ψ i ∂ X ∂ ψ n ∂ X d X d Y + ∑ i = 1 N U i ∫ μ thnf ρ thnf ∂ ψ i ∂ Y ∂ ψ n ∂ Y d X d Y

(16) R n V ≈ ∑ i = 1 N V i ∫ ∑ i = 1 N U i ψ i ∂ ψ i ∂ X + ∑ i = 1 N V i ψ i ∂ ψ i ∂ Y ψ n d X d Y + ∑ i = 1 N ∫ − ∑ i = 1 N P i ψ i ∂ ψ i ∂ Y ψ n d X d Y + ∑ i = 1 N V i ∫ μ thnf ρ thnf ∂ ψ i ∂ X ∂ ψ n ∂ X d X d Y + ∑ i = 1 N V i ∫ μ thnf ρ thnf ∂ ψ i ∂ Y ∂ ψ n ∂ Y d X d Y + RaPr ρ β θ thnf ρ thnf β f × ∫ ∑ j = 1 N T i ψ i ψ n d X d Y + N ∫ ∑ j = 1 N Φ i ψ i ψ n d X d Y

Energy equation:

(17) R n T ≈ ∑ i = 1 N T i ∫ ∑ i = 1 N U i ψ i ∂ ψ i ∂ X + ∑ i = 1 N V i ψ i ∂ ψ i ∂ Y ψ n d X d Y + ∑ i = 1 N T i ∫ α thnf α f ∂ ψ i ∂ X ∂ ψ n ∂ X + ∂ ψ i ∂ Y ∂ ψ n ∂ Y d X d Y + ∫ q α thnf α f ∑ j = 1 N T i ψ i ψ n d X d Y

Concentration equation:

(18) R n Φ ≈ ∑ i = 1 N Φ i ∫ ∑ i = 1 N U i ψ i ∂ ψ i ∂ X + ∑ i = 1 N V i ψ i ∂ ψ i ∂ Y ψ n d X d Y + ∑ i = 1 N Φ i ∫ D thn D f 1 Le ∂ ψ i ∂ X ∂ ψ n ∂ X + ∂ ψ i ∂ Y ∂ ψ n ∂ Y d X d Y

The full residual system is thus a set of nonlinear algebraic equations of the form:

Res U , V , P , T = 0

A Newton-Raphson method is employed to solve the system of nonlinear algebraic equations expressed in a matrix. The iteration of the current work is assumed to be a convergence solution when the corresponding error of each variable is equal to or less than 10⁶.

3.2 Mesh generation

Accurate mesh generation is essential to capture the complex behavior of flow, heat, and mass transfer within the computational domain. In this study, the mesh was generated using COMSOL Multiphysics, adopting a triangular unstructured grid with a finer element size to ensure accurate results.

The final mesh used in the simulations consists of 17,371 domain elements and 657 boundary elements, as illustrated in Figure 2. To verify mesh independence, a mesh convergence test was conducted by comparing the average Nusselt number (Nu_avg) and Sherwood number (Sh_avg) for different mesh densities. Table 2 presents the results.

Figure 2:

Grid for the system.

Table 2:

Mesh independence test for different mesh densities.

Mesh level	Elements	Nu_avg	Sh_avg	Deviation from finer mesh (%)
Coarse	6,284	4.251	3.839	5.6 %
Normal	10,145	4.396	3.907	2.2 %
Finer (used)	17,371	4.493	3.995	–

The results indicate that beyond the finer mesh, further refinement produces negligible changes in the solution. Therefore, the finer mesh was selected for all simulations to ensure an optimal balance between accuracy and computational efficiency.

3.3 Validation of results

The results of the current study were validated against the experimental and numerical findings reported by Paroncini and Corvaro [44], as shown in Figure 3. Furthermore, Table 3 provides a summarized comparison between the present results and those reported by Mun et al. [45] and Kim et al. [46]. The strong agreement observed between our findings and those of previous studies confirms the reliability and accuracy of the numerical approach adopted.

Figure 3:

Comparison between experimental and numerical study by Paroncini and Corvaro [44] and the present study different cases of the height of heat source.

Table 3:

Comparison between present results of Nu_avg at Pr = 6.82 and [45], 46].

Ra	10³	10⁴	10⁵	10⁶
Nu_avg present study	5.071	5.065	7.755	14.053
Nu_avg [45]	5.012	5.105	7.768	14.073
Nu_avg [46]	5.093	5.108	7.767	14.052

4 Results and discussion

This section presents the computational analysis of thermosolutal convection of ternary hybrid nanolfluid in a trapezoidal enclosure with centered heated circular obstacle. The simulations are carried out for several key factors including the Lewis number 1 ≤ Le ≤ 50, solid particle concentration of the ternary hybrid nanofluid 0 ≤ ϕ ≤ 3, buoyancy ratio −5 ≤ N ≤ 10, radius of the circular block 0.05 ≤ r ₀ ≤ 0.32, and Rayleigh number 10 ≤ Ra ≤ 10⁵. During the graphically presentation and simulation process, the Prandtl number is fixed at Pr = 6.2, and variation in one parameter is analyzed while others parameters are considered to be fixed. Figure 4 presents the streamlines, isotherms, and concentration contours for varying values of the Lewis number (Le), at fixed parameters Ra = 10⁵, ϕ = 0.21, N = 5. The Lewis number, which represents the ratio of thermal diffusivity to mass diffusivity, significantly influences the flow and transport characteristics. At low Le = 1, mass diffusion dominates, resulting in weaker convection cells, smoother isotherms, and more uniform concentration gradients. As Le increases to 50, thermal diffusivity becomes dominant, leading to more vigorous flow patterns and sharper convection cells. The streamlines become denser and more structured, while the isotherms compress around the heat source, indicating enhanced convective heat transfer. Similarly, the concentration contours become steeper and more localized near the boundaries, reflecting the increasing role of convection in mass transport. Overall, higher Lewis numbers shift the system behavior from a diffusion-dominated regime to a convection-driven regime, with significant impacts on heat and mass transfer performance. Figure 5 illustrates the streamlines, isotherms, and concentration contours for varying volume fractions ϕ of the ternary hybrid nanofluid. The nanoparticle concentration directly influences the nanofluid’s thermophysical properties, particularly its thermal conductivity and viscosity. For ϕ = 0, the flow exhibits symmetric, moderately intense convection cells with well-defined counter-rotating vortices. As ϕ increases to 2.1 and 3 %, the streamlines become more compact and concentrated, indicating enhanced buoyancy-driven convection and stronger fluid motion. This intensification results from the improved thermal conductivity of the nanofluid, which promotes more vigorous convective heat and mass transport.

Figure 4:

Streamlines, isotherms and concentrations under different values of Le at Ra = 10⁵, ϕ = 0.21, N = 5.

Figure 5:

Streamlines, isotherms and concentrations under different values of ϕ at Ra = 10⁵, N = 5, Le = 20.

Correspondingly, the isotherms at ϕ = 0 are evenly spaced and less distorted, characteristic of diffusion-dominated heat transfer. With increasing ϕ, the isotherms near the heated inner obstacle become increasingly compressed and distorted, reflecting the transition to a convection-dominated regime. At ϕ = 3 %, the isotherms exhibit strong distortion and tight packing, indicating efficient thermal distribution enhanced by the nanoparticle mixture. Similarly, the concentration profiles evolve with increasing ϕ. At ϕ = 0, the contours are smooth and uniform, suggesting weak convective mass transfer. For ϕ = 2.1 and 3 %, the contours become sharper and more localized near the heated region, with steeper gradients that indicate stronger convective influence on mass transport. This behavior results from increased effective diffusivity and enhanced mixing capacity of the nanofluid at higher nanoparticle loadings.

Generally, increasing the volume fraction of ternary hybrid nanoparticles enhances both heat and mass transfer by strengthening convective flow and improving thermal and solutal diffusivities.

Figure 6 illustrates the influence of the buoyancy ratio N on the streamlines, isotherms, and concentration contours. The buoyancy ratio N characterizes the relative contribution of thermal and solutes buoyancy forces. When N, only thermal buoyancy drives the flow. Positive N corresponds to assisting solutal and thermal forces, while negative N indicates opposing (competing) buoyancy effects. For N = −5 and N = −1, the flow exhibits weak, disorganized streamlines and poorly defined convection cells due to the opposing buoyancy forces. As N increases to 0, the flow stabilizes, and symmetric convection cells emerge, driven solely by thermal buoyancy. At N = 1, 5, and 10, the streamlines become more intense and organized, indicating stronger convective motion facilitated by aligned buoyancy effects. That shows that increasing N enhances convective circulation, while negative values suppress it. The isotherms follow a similar trend. At N = −5, they remain nearly horizontal, reflecting a diffusion dominated regime. Slight distortion appears at N = −1, and at N = 0, isotherms begin to bend and compress near the heat source. Positive N values cause significant distortion and compactness of the isotherms, indicating stronger convective heat transfer. Likewise, the concentration profiles are uniform and smooth for N = −5, signifying limited convective mass transport. As N increases, concentration gradients steepen and become more localized near the boundaries, indicating enhanced solutal convection. In summary, negative buoyancy ratios hinder convective transport by introducing opposing forces, whereas positive values intensify both heat and mass transfer through cooperative buoyancy effects. This dynamic plays a critical role in determining the thermal and solutal behavior of the nanofluid-filled cavity.

Figure 6:

Streamlines, isotherms and concentration under different values of N at Ra = 10⁵, ϕ = 0.21, Le = 20.

Figure 7 illustrates the effect of the circular obstacle’s radius r ₀ on flow, heat, and mass transfer. As r ₀ increases, the available flow domain is reduced, which significantly alters convective structures and transport efficiency. For smaller obstacles (e.g., r ₀ = 0.1, the streamlines form strong, symmetric convection cells around the obstacle, with vigorous fluid motion enhancing both heat and mass transfer. The isotherms are moderately distorted, indicating efficient convective heat transport, while the concentration contours display steep gradients and localized variation, reflecting active solutal convection. As the radius increases to r ₀ = 0.2, the obstacle disrupts the core of the flow, dividing it into smaller, localized cells. The streamlines become more confined, and both the isotherms and concentration contours begin to align horizontally and smooth out, suggesting a transition toward diffusion-dominated transport. At r ₀ = 0.32, the large obstacle severely restricts fluid motion, pushing streamlines to the cavity boundaries. The flow weakens considerably, and the isotherms appear nearly parallel to the walls, confirming that conduction dominates.

Figure 7:

Streamlines, isotherms and concentrations under different values of r ₀ at Ra = 10⁵, ϕ = 0.21, N = 5, Le = 20.

Similarly, the concentration field becomes uniform, with minimal convective influence. That indicates that increasing the obstacle size hinders convective circulation, reducing both thermal and solutal transport. This demonstrates the critical role of geometric obstructions in modulating flow behavior and transport mechanisms within enclosures.

Figure 8 represents the effect of the Rayleigh number Ra on flow structure, temperature distribution, and solutal transport. The Rayleigh number characterizes the ratio of buoyancy-driven convection to thermal diffusion and governs the onset and intensity of natural convection. At low Ra = 10, the flow is weak and diffusion-dominated. Streamlines show small, symmetric convection cells with minimal intensity. Isotherms remain nearly vertical, indicating that conduction is the primary heat transfer mechanism, and the concentration field is smooth and symmetric. As Ra increases to 100 and 10³, buoyancy effects become more pronounced. Larger, stronger vortices develop, and the isotherms begin to distort near the heat source, signaling enhanced convective heat transfer. Concentration contours also begin to steepen and localize, indicating growing influence of convection on solute transport. At high Ra = 10⁵, vigorous convection dominates. The flow becomes asymmetric, with dynamic vortex structures. Isotherms cluster tightly near the heat source, and concentration contours exhibit strong gradients and localization near boundaries, reflecting intense convective mixing. So, increasing Ra transitions the system from conduction- to convection dominated regimes. This significantly enhances heat and mass transfer performance, driven by the growing dominance of buoyancy-induced fluid motion.

Figure 8:

Streamlines, isotherms and concentration under different values of Ra at N = 5, ϕ = 0.21, Le = 20.

Figures 9–13 illustrate the effects of key dimensionless parameters on the average Nusselt number Nu_avg and average Sherwood number Sh_avg, which represent heat and mass transfer efficiency, respectively. Figure 9: Increasing the Lewis number Le leads to a decline in both Nu_avg and Sh_avg, with a steeper reduction observed in mass transfer. This trend indicates that higher Le suppresses solutal convection more than thermal convection, as thermal diffusivity becomes dominant and mass diffusion weakens.

Figure 9:

Influence of Le on Nu_avg and Sh_avg at Ra = 10⁵, ϕ = 0.21, N = 5.

Figure 10:

Influence of ϕ on Nu_avg and Sh_avg at a = 10⁵, N = 5, Le = 20.

Figure 11:

Influence of N on Nu_avg and Sh_avg at Ra = 10⁵, ϕ = 0.21, Le = 20.

Figure 12:

Influence of r ₀ on Nu_avg and Sh_avg at Ra = 10⁵, ϕ = 0.21, N = 5, Le = 20.

Figure 13:

Influence of Ra on Nu_avg and Sh_avg at ϕ = 0.21, N = 5, Le = 20.

Figure 10. The effect of nanoparticle volume fraction ϕ shows that increasing ϕ reduces Nu_avg more significantly than Sh_avg. This reduction is attributed to increased fluid viscosity caused by nanoparticle addition, which impedes convective flow, particularly affecting heat transport due to stronger coupling with temperature gradients.

Figure 11. The influence of buoyancy ratio N reveals non-monotonic behavior. For negative N, opposing buoyancy forces weaken convection, resulting in minimal change in Nu_avg and an initial decrease in Sh_avg. As N becomes positive, both metrics increase gradually due to reinforcing buoyancy forces, which enhance convective heat and mass transfer.

Figure 12. Increasing the obstacle radius r ₀ leads to a pronounced rise in Nu_avg, while Sh_avg increases only slightly. The larger obstacle promotes thermal mixing by redirecting flow paths, thereby intensifying heat transfer. However, its effect on mass transfer is less pronounced, likely due to limited enhancement of concentration gradients near the obstacle.

Figure 13. The Rayleigh number Ra positively affects both Nu_avg and Sh_avg, with Nu_avg increasing almost linearly. As Ra grows, stronger buoyancy-driven convection enhances both thermal and solutal transport, resulting in improved overall heat and mass transfer rates.

5 Conclusions

This numerical study investigates thermosolutal convection of a ternary hybrid nanofluid in a trapezoidal enclosure with a centrally heated circular obstacle. The analysis captures flow structure (streamlines), thermal distribution (isotherms), and solutal behavior (concentration contours), while heat transfer performance is assessed via the average Nusselt number across a wide range of dimensionless parameters.

Key findings include:

Positive values of the buoyancy ratio N enhance convection and mass transfer, while negative values weaken it, leading to a diffusion-dominated regime and potential instability.
Increasing the obstacle’s radius r ₀ generates larger vortices, which strengthens overall heat and mass transport.
High Ra values intensify convective flow, whereas at low values, thermal conduction becomes the dominant mechanism.
An increase in Le reduces mass transfer with a negligible impact on heat transfer.
Higher concentrations of ϕ improve heat transfer, but excessive loading increases fluid viscosity, which can impede circulation and limit the net benefit.

These findings underscore the complex interactions between cavity geometry, thermophysical properties, and buoyancy forces in determining heat and mass transfer performance. This study contributes to the current body of literature by integrating multiple controlling parameters within a unified modeling framework, thus offering a more holistic understanding of ternary hybrid nanofluid behavior in asymmetric enclosures.

Despite these insights, several limitations remain. The study assumes Newtonian behavior, steady-state conditions, and neglects possible nanoparticle agglomeration or thermophoretic effects. Future research could address these gaps by investigating non-Newtonian nanofluids, transient thermal responses, 3D geometries, or the influence of magnetic and electric fields, thereby extending the applicability of the model to real-world engineering systems.

Corresponding author: Zehba Raizah, Central Labs, King Khalid University, AlQura’a, Abha, P.O. Box 960, Saudi Arabia, E-mail: zaalrazh@kku.edu.sa

Acknowledgments

The authors extend their appreciation to University Higher Education Fund for funding this research work under Research Support Program for Central labs at King Khalid University through the project number CL/PRI/D/6.

Funding information: The authors extend their appreciation to University Higher Education Fund for funding this research work under Research Support Program for Central labs at King Khalid University through the project number CL/PRI/D/6.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: All data generated or analysed during this study are included in this published article.

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Received: 2025-04-12

Accepted: 2025-10-21

Published Online: 2025-12-04

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

Articles in the same Issue

https://doi.org/10.1515/ntrev-2025-0246

Keywords for this article

ternary hybrid nanofluid; enhanced heat transfer; cavity flow modeling; GFEM; trapezoidal enclosure; natural convection

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