The low thermal conductivity of conventional heat transfer fluids limits the thermal performance of shell-and-tube heat exchangers used in many industrial applications. To overcome this limitation, the present study numerically investigates three-dimensional mixed convective heat transfer and entropy generation in a shell-and-tube heat exchanger employing an Ag–Fe₃O₄–MWCNT/water tri-hybrid nanofluid. The governing continuity, momentum, and energy equations are solved using the finite element method (FEM) implemented in COMSOL Multiphysics. The effects of the Reynolds number (10–100), Richardson number (0.2–1.0), and nanoparticle volume fraction (2–4%) on the flow behavior, temperature distribution, average Nusselt number, heat exchanger effectiveness, and entropy generation are systematically analyzed. The results reveal that increasing both the Reynolds number and nanoparticle concentration significantly enhances the convective heat transfer performance owing to improved effective thermal conductivity and stronger fluid mixing. At Re = 100 and φ = 4%, the average Nusselt number increases by 24.7% compared with the reference case, while the heat exchanger effectiveness improves by 18.3%. However, the enhanced thermal performance is accompanied by an increase of 11.5% in entropy generation due to greater thermal and fluid friction irreversibilities. Furthermore, increasing the Richardson number strengthens buoyancy effects, leading to additional enhancement in heat transfer. The novelty of this work lies in providing a comprehensive three-dimensional FEM analysis of an Ag–Fe₃O₄–MWCNT/water tri-hybrid nanofluid in a shell-and-tube heat exchanger, together with a detailed evaluation of the combined effects of Reynolds number, Richardson number, and nanoparticle concentration on heat transfer enhancement and thermodynamic performance. The findings demonstrate the considerable potential of tri-hybrid nanofluids for improving the efficiency of compact thermal systems and provide useful guidelines for the design and optimization of advanced heat exchangers.

The paper focuses on thermal behaviours of a porous longitudinal rectangular fin under various nonlinear interactions, consisting of thermal conductivity that is dependent on temperature, nonlinear convection, thermal radiation, and magnetohydrodynamic (MHD) interactions. The novelty lies in the simultaneous integration of multiple nonlinear effects (MHD, radiation, nonlinear convection, porosity, and variable conductivity) under realistic boundary conditions, which has not been addressed collectively in previous studies. In this study it is assumed that a realistic boundary configuration will be used i.e. the base of the fin is convectively cooled, and the tip is thermally insulated. The current formulation is based on exponential change of thermal conductivity, power-law convection, radiative heat exchange, and magnetic damping in a porous material, as opposed to the traditional fin models that use constant material properties and linear convection. The nonlinear boundary-value problem thus obtained is numerically solved by MATLAB BVP4C solver with Lobatto IIIA collocation scheme to obtain smooth and physical consistent temperature distributions along the fin. Parametric analysis suggests that with an increase in convection conductivity parameter, base Biot number, porosity, radiation, and magnetic parameters, heat dissipation increases and temperature gradients grow steeper. Conversely, a higher exponential conductivity variation facilitates the axial transfer of heat and decreases the total heat transfer rate. Fin efficiency increases significantly from about 0.40 to 0.65, achieving nearly 60% enhancement due to the combined increase in magnetic parameter and temperature ratio parameter.

PurposeThis study aims to examine how vertical sinusoidal vibration influences heat transfer and entropy generation in Rayleigh–Bénard (RB) nanofluid convection. Design/methodology/approachThis study analyzes the coupling between RB instability and externally applied time-varying vertical forcing with adjustable frequencies and amplitudes. The governing equations for the nanofluid RB system are solved numerically using the finite element method to capture the transient and steady convective regimes. FindingsThe results show that increasing the vibration parameter φ elevates both the intrinsic and extrinsic thermal irreversibilities during the transient and stationary regimes, respectively. The onset of instability in the nanofluid lags behind that of a base fluid, with increasing delay as φ grows. Within the studied frequency range, the system’s thermal and entropic responses to sinusoidal excitation are nearly sinusoidal, and the flow can exhibit heat-transfer and entropy-production resonances at specific critical frequencies corresponding to natural modes of the system. Practical implicationsUnderstanding how vertical vibrations affect heat transfer and entropy generation in convective flows has broad relevance for thermal management in microgravity environments, advanced electronics cooling, heat exchanger design and process engineering where vibrational effects are significant. Originality/valueThe literature shows limited exploration of the interplay between vibration and RB flow instability in nanofluids and numerically investigates entropy production and heat-transfer resonances under variable-frequency and variable-amplitude forcing, contributing new insights into vibrational modulation of RB convection in nanofluids.

The manuscript considers the fractional-order Burger’s equation in two dimensions, which is a non-linear viscous fluid dynamical model. A systematic numerical technique involving a finite difference-based L1-scheme is implemented to approximate the solution of the proposed problem. The proposed technique involves the semi-discretisation of the fractional-order time derivative using the L1-scheme, followed by orthogonal collocation using Hermite splines. This technique fully discretises the 2D Burger’s equation for both the time and spatial domains into an algebraic system of equations. To ensure the accuracy and reliability of the method, numerical illustrations are presented for validation. The unconditional stability and optimal order of convergence of the technique signify its applicability to higher-order non-linear boundary value problems. The work is further supported by the comparison of the numerical values obtained from the proposed technique with those already reported in the literature.

ABSTRACTThe significance of this study is to understand the complex interplay between fluid flow and surface roughness. Modeling surface roughness adds a new dimension for examining fluid dynamics, which is essential for understanding phenomena like drag force, heat transfer, and mass transfer. In this context, the aim of the present work focuses on modeling the magnetohydrodynamic peristaltic slip flow of Casson nanofluid and analyzing the role of multiple slip effects over a non‐uniform rough channel. A novel rough non‐uniform model is effectively governed by a set of nonlinear coupled governing partial differential equations, which are simplified under long wavelength and creeping flow approximations. The resulting simplified equations are solved numerically using Mathematica's built‐in ND‐Solve tool. The study primarily examines the velocity, temperature, and concentration profiles graphically for various pertinent physiological parameters. Additionally, engineering interests like skin friction coefficients, Nusselt numbers, and Sherwood numbers are reported in tabular form, revealing intrinsic flow oscillations. The results are further explored by analyzing pressure drop, friction force, and bolus shapes created by the sinusoidal motion of the fluid. Such insights are vital for comprehending internal fluctuations during peristaltic transport. In summary, skin friction and Nusselt numbers are typically higher for rough versus smooth surfaces. Also, roughness induces stresses, conductive‐convective heat transfer, and viscous effects. Further, magnetically activated rough surfaces and nanoparticle interactions create flux balances. Magnetic effects reduce bolus size due to resistive forces. The findings of this study have important applications in biomedical engineering, aerospace engineering, heat transfer enhancement, and environmental remediation.

Understanding the complex interaction between heat and mass transfer in non-Newtonian microflows is essential for the development and optimization of efficient microfluidic and thermal management systems. This study investigates the magnetohydrodynamic (MHD) thermosolutal convection of a Casson fluid within an inclined, porous microchannel subjected to convective boundary conditions. The nonlinear, coupled equations governing momentum, energy, and species transport are solved numerically using the MATLAB bvp4c solver, ensuring high numerical accuracy and stability. To identify the dominant parameters influencing flow behavior and to optimize transport performance, a comprehensive hybrid optimization framework—combining a modified Taguchi design, Grey Relational Analysis (GRA), and Principal Component Analysis (PCA)—is proposed. This integrated strategy enables the simultaneous assessment of skin friction, Nusselt number, and Sherwood number, providing a rigorous multi-objective evaluation of system performance. Comparative validation with benchmark results from the literature confirms the accuracy and reliability of the present formulation and its numerical implementation. The results highlight the intricate coupling among flow slip, buoyancy effects, and convective transport mechanisms. Increased slip flow enhances axial velocity, while a higher solutal Biot number intensifies concentration gradients near the channel walls. Conversely, a lower thermal Biot number diminishes the temperature field, indicating weaker heat transfer across the boundaries. PCA results reveal that the first principal component (PC1) accounts for most of the system variance, demonstrating the dominant influence of coupled flow and transport parameters on overall system performance.

This study examined the influence of geometric parameters on free convective heat transfer in a zigzag-walled cavity filled with a hybrid nano-fluid composed of magnesium oxide (MgO) and single-walled carbon nanotubes (SWCNT) suspended in water. Utilizing validated multi-physics software grounded in the Galerkin finite element method (GFEM), we systematically analyzed how variations in Rayleigh number (Ra) from 10 4 to 10 6 , nanofluid volume fraction ([Formula: see text]) ranging from 0.01 to 0.04, and the number of wall undulations (from 1 to 8) affect thermal performance. The findings revealed that both the Rayleigh number and the number of wall undulations had a significant positive impact on the average Nusselt number (Nu), indicating enhanced heat transfer rates. Among the various obstacle shapes investigated, the diamond-shaped configuration emerged as the most effective in promoting thermal performance due to its ability to create favorable flow patterns. This research provides valuable insights for optimizing heat transfer processes in complex geometrical configurations employing hybrid nanofluids, contributing to advancements in thermal system design.

Thermal reflection through nonlinear porous surface associated to nanofluid with inertial impact has been featured in this analysis. The flow is governed by a viscous, incompressible nanofluid, with resistance effects modeled through the Darcy–Forchheimer relation. Thermophoretic and diffusion of Brownian are incorporated to account for coupled heat and mass transfer mechanisms. Furthermore, the influence of a magnetic field is considered, introducing non-uniform Lorentz force effects into the flow dynamics. Additional phenomena including a space-dependent heat source/sink and a first-order chemical reaction are also examined to address realistic industrial and environmental applications. To model the system in simple form, appropriate transportations are accounted. A sufficient numerical technique for solving the problem is subject to implementation of Keller box method. The study provides a comprehensive parametric analysis with physical observations with help of several graphs. The physical interpretations of the results offer valuable insights into optimizing heat and mass transport in nanofluid systems, relevant to engineering processes such as polymer extrusion, thermal management in porous structures, and nanomaterial processing.

Maximizing the efficiency of thermal engineering equipment involves minimizing entropy generation, which arises from irreversible processes. This study examines thermal transport and entropy generation in viscous flow over a radially stretching disk, incorporating the effects of magnetohydrodynamics (MHD), viscous dissipation, Joule heating, and radiation. Similarity transformations are used to obtain dimensionless nonlinear ordinary differential equations (ODEs) from the governing coupled partial differential equations (PDEs). The converted equations are then solved by using the BVP4C solver in MATLAB. To validate the findings, the results are compared with previously published studies under fixed parameter conditions, demonstrating strong agreement. Various key parameters are analyzed graphically to assess their impact on velocity and temperature distributions. Additionally, Bejan number and entropy generation variations are presented for different physical parameters. The injection parameter (S < 0) increases the heat transfer rate, while the suction parameter (S > 0) reduces it, exhibiting similar effects on fluid velocity. The magnetic parameter (M) effectively decreases entropy generation within the range of approximately 0 <= eta <= 0.6. Beyond this interval, its influence diminishes as entropy generation values converge, with similar trends observed for the Bejan number. Furthermore, increased thermal radiation intensity is identified as a critical factor in enhancing entropy generation and the Bejan number.

Purpose The purpose of this study is to explore numerically the conjugate natural convection of a nanofluid (Al2O3/water) within a non-Darcy’s porous square cavity containing two opposing solid blocks influenced by a horizontal external magnetic field. Design/methodology/approach The configuration studied involves a square cavity filled with a porous medium saturated by Al2O3/water nanofluid. The vertical walls are isothermal with hot and cold wall temperatures, while the horizontal walls are adiabatic. Two baffles, with high thermal conductivity relative to the fluid, are positioned midway on the vertical hot and cold walls. A constant horizontal magnetic field is applied, influencing natural convection, heat transfer and fluid motion within the cavity. The Koo–Kleinstreuer–Li (KKL) model, which provides a more accurate representation of the viscosity and thermal conductivity at the nanoscale, was used to include the effect of Brownian motion on the nanofluid’s properties. Conservation equations are modelled via the Darcy–Brinkman–Forchheimer formulation and solved numerically with the finite volume method implemented in a FORTRAN program. Velocity-pressure coupling is achieved using the SIMPLER algorithm. The study investigates the influence of various parameters such as Rayleigh and Darcy numbers, nanoparticle volume fraction and magnetic field strength. Findings The results indicate that increasing Rayleigh number (Ra), Darcy number (Da) and nanofluid volume fraction (f) enhances flow dynamics, promoting convection and significantly improving heat transfer, particularly nanoparticle-facilitated. Conversely, Hartman number Ha diminishes heat transfer by restraining fluid motion through the Lorentz force. Later, a novel correlation of the average Nusselt number (Nu) ¯ versus Ra, Da, f and Ha has been established to simplify future predictions of the heat transfer rate for similar configurations. Research limitations/implications This study has several limitations. It relies on steady-state conditions, potentially overlooking transient behaviours that could arise in real applications. The assumption of a uniform magnetic field and homogeneity in nanofluid properties may not accurately represent actual conditions. Additionally, while the Darcy–Brinkman–Forchheimer model is effective, it may not fully capture scenarios where inertial effects are significant. The investigation covers a range of Rayleigh and Darcy numbers as well as nanoparticle volume fractions but does not consider factors such as temperature-dependent fluid properties and non-Newtonian behaviour, which could further influence heat transfer and fluid dynamics. Practical implications The implications of this research are considerable for the design of thermal systems using nanofluids in porous media, especially in applications involving magnetic fields. The derived correlation for the average Nusselt number serves as a valuable predictive tool for engineering applications. Future work should address these limitations by incorporating transient analyses and exploring a wider array of operational parameters to deepen the understanding of nanofluid behaviour in magnetically influenced settings. Social implications The findings of this study have significant social implications, particularly in enhancing energy efficiency in thermal management systems. Improved heat transfer in applications such as HVAC, refrigeration and renewable energy systems can lead to reduced energy consumption and lower utility costs for consumers. Furthermore, the application of nanofluids in environmentally friendly technologies aligns with global sustainability goals, potentially reducing carbon footprints and promoting cleaner energy solutions. By advancing the understanding of nanofluid behaviour in porous media, this research contributes to the development of innovative, sustainable technologies that can improve energy accessibility and environmental quality for communities. Originality/value This study presents a novel numerical analysis of the natural convection of Al2O3/water nanofluid in a non-Darcy porous cavity influenced by a horizontal magnetic field, with the consideration of conjugated opposing baffles on hot and cold walls. It investigates the effects of Ra, Da and Ha numbers and nanoparticle volume fraction on flow and heat transfer using the Darcy–Brinkman–Forchheimer model. A new correlation between the average Nusselt number and key parameters is introduced, providing an advanced predictive tool for engineering applications. The findings have direct relevance to advanced thermal management systems, including electronic cooling, energy storage and industrial heat exchangers, where optimizing heat transfer efficiency is critical.

Magneto-free convective of hybrid nanofluid with an inner adiabatically rotating cylinder and a hot side wall was analyzed in a non-Darcy-permeable cavity. The Darcy-Forchheimer model has been used for the permeable domain. The solutions of employing equations are obtained by the Finite Element Method. The role of different Rayleigh (103 <= Ra <= 106) for various angular velocity (0 <=$$\Omega $$Omega <= 6000), Darcy (10-5 <= Da <= 10-2), and Hartmann number (0 <= Ha <= 100) are illustrated. The obtained data were compared with already cited researches, and a great degree of accuracy and compatibility were found symmetric. The implications of relevant parameters on velocity, stream functions, isotherms and mean Nusselt number are graphically examined. Estimations demonstrate that the mean improvement in heat transfer is more pronounced with the enhancement in Darcy number, the angular velocity, Rayleigh number, and decays through the rise of Hartmann number. It is also observed that an increment in Ra leads to an apparent incremental increase in the stream function outcome. A significant enhancement was also noticed in Nu number with augmentation in the Da and Ra numbers, but certain decline occurred for augmented values of Ha number and rotation speed.

The behavior of buoyancy-driven magnetohydrodynamic (MHD) nanofluid flows with temperaturesensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling, nuclear reactors, and metallurgical processes. This study focuses on the boundary layer flow of a Casson-based sodium alginate Fe3O4 nanofluid influenced by magnetic field-dependent viscosity and thermal radiation, as it interacts with a vertically stretching sheet under dissipative conditions. To manage the inherent nonlinearities, Lie group transformations are applied to reformulate the governing boundary layer equations into similarity forms. These reduced equations are then solved via the Spectral Quasi-Linearization Method (SQLM), ensuring high accuracy and computational efficiency. The analysis comprehensively explores the impact of key parameters-including mixed convection intensity, magnetic field number)-on flow characteristics and heat transfer rates. Findings reveal that increasing magnetic field-dependent viscosity diminishes both skin friction and thermal transport, while buoyancy effects enhance heat transfer but lower shear stress on the surface. This work provides critical insights into controlling heat and momentum transfer in Casson nanofluids, advancing the design of thermal management systems involving complex fluids under magnetic and buoyant forces.

This study presents a finite propagation speed model for stagnation point flow of hybrid nanofluid with applications of nonlinear radiated effects. A synthesized hybrid nanofluid is subject to the utilization of Al2O3 and gamma-Al2O3 nanoparticles dispersed in ethylene glycol (EG) and engine oil. Heat transfer impact is further assessed with an external heat source and quadratic thermal constraints. This combination is strategically chosen due to its enhanced thermal conductivity and industrial relevance in lubrication, heat exchangers, and automotive cooling systems. The governing equations, formulated based on boundary layer approximations, are transformed into a system of nonlinear ordinary expressions. For the solution approach, the shooting technique is implemented. It is claimed that the hybrid nanofluid exhibits superior heat transfer performance compared to conventional nanofluids, making it a promising candidate for energy-efficient thermal management applications. The findings of this study contribute to the optimization of nanofluid-based thermal systems in engineering applications such as aerospace, manufacturing, and electronic cooling technologies.

The investigation of heat transfer due to hybrid nanofluid near the oblique stagnation point flow has novel industrial and thermal applications. Such a configuration arises in the aerodynamic surfaces, like aircraft and turbine blades. The improvement in transport processes due to hybrid nanomaterials is important for thermal management in high-performance systems. The current investigation seeks to explore heat transfer management in oblique stagnation point flow of hybrid nanomaterial impacted with nonlinear radiated effects. The suspension of hybrid nanofluid is assumed to be the decomposition of aluminum oxide (Al2O3) and silicon oxide (SiO2) nanoparticles with human blood and ethylene glycol (C2H6O2). A non-Fourier model, namely, the Cattaneo-Christov approach, is implemented to modify the energy equation. The flow problem is truncated into dimensionless form by entertaining appropriate variables. The numerical simulations for such a system are accomplished with the shooting method. The comparative thermal simulations are detected for mono nanofluid (MNF) and hybrid nanofluid (HNF). The analysis for the Nusselt number and wall shear force is observed graphically. It has been examined the obliquely velocity declined for free stream stagnation flow coefficients. Boosted variation in heat transfer is noticed against the surface heating parameter and the radiated phenomenon. The claimed results present significance in automotive industries, solar processes, heat exchangers, thermal management systems, cooling phenomenon, and so forth.

This research paper examines the melting process of a nano enhanced phase change material (nePCM) based on paraffin wax and alumina nanoparticles in an insulated heat exchanger consisting of heated double inner tubes, surrounded by the nePCM that stores the acquired latent thermal energy and melts. The article investigates factors that directly influence the efficiency of this system, for instance, fins emplacement, along with the volume fraction 2% ≤ φ ≤ 6% of the nanoparticles and their impact on the melting process, temperature distribution, as well as the energy stored. Through a program based on the Finite Element Method, four different structures are considered to assess their thermal performance. The results demonstrate the importance of fin location, especially in the central region of the heat exchanger. As heat distribution predominantly shifts toward the system’s surface and around the heating tubes, strategically arranging fins between these tubes becomes critical for optimal performance. Notably, the utilization of a continuously connected heating system (configuration c) has shown to be highly efficient in improving heat transfer, yielding rapid melting and optimized thermal storage, followed by the performance of configuration (d) with inclined discontinuous inclined fins, particularly at φ = 4%, considering it the optimal concentration of the nanoparticles.

Owing to superior thermal performances, the suspension of tri hybrid nanoparticles presents valuable applications across advanced heat transfer systems, heat exchangers, energy-efficient systems, aerospace engineering, automobile industries and biomedical applications. Current investigation seeks thermal insight to nonlinear radiated flow of tri hybrid nanofluid by using the non-Fourier heat flux model. A uniform suspension of three distinct category of nanoparticles including titanium oxide (TiO2), silicon dioxide (SiO2) and copper oxide (CuO) are utilized. The engine oil (SAE10W−30) is treated as a base material. The thermal performances of engine oil are important in automobile industry to enhance thermal fuel efficiency, protecting against corrosion and balancing the optimal operating temperature. The heat generation and convective thermal constraints are followed to study current model. The flow is subject to elastic stretching sheet. The governing equations are developed under certain thermal constraints. For solution methodology, the shooting scheme is implemented. The computational thermal simulations are for mono nanofluid (MNF), hybrid nanofluid (HNF) and tri hybrid nanomaterial (THNF). The results for skin friction and Nusselt number are also graphically compiled.

This study investigates the flow dynamics of magnetohydrodynamic Burgers' fluid induced by a stretching cylinder, emphasizing the effects of internal heat generation and absorption. A temperature-dependent heat source is integrated to examine the characteristics of thermal energy transfer within the system. By applying boundary layer theory, we transform the governing partial differential equations into a standard system of ordinary differential equations through similarity transformations. The BVP4C method is utilized to accurately solve the resulting equations for velocity and temperature profiles. Graphical representations illustrate the influence of various physical parameters on both thermal and flow profiles, supported by comprehensive analytical interpretations. To validate our findings, a comparison with existing literature is performed, confirming the consistency and significance of our results. This research offers valuable insights into the thermal and fluid behaviors of Burgers' fluids, with promising applications in the development of advanced biomedical devices.

The joint influences of variable heat source patterns and temperature-reliant viscosity on the onset of convective motion in porous beds in the presence of gravity variance have been investigated. The linear analysis is performed using normal mode analysis and the Galerkin technique is applied to analyze the impact of variable heating and changeable gravity field on the behavior of system stability. The exponential temperature-dependent viscosity is considered. We examined three different types of heat source and gravity variance function combinations: Convection is accelerated by increases in viscosity and the gravity variance parameter, but decelerated by increases in the heat source strength. Tt has been shown that the configuration is more stable when the gravity variance and heat source functions are combined in instance case (ii), but less stable when they are combined in case (i) and case (iii). (c) 2024 Sharif University of Technology. All rights reserved.

In this article, we have investigated the two-dimensional MHD steady boundary layer flow of a viscous magneto-micropolar liquid via an extending area. The impact of heat source /sink, and chemical reaction are considered. The governing equations are modeled in Cartesian coordinate system. Using the suitable similarity transformations, the partial differential equations system is changed into the nonlinear ordinary differential equations system. The resulting system of equations is solved through mathematical renowned software Mathematica. The impact of diverse parameters on microrotation, concentration, temperature and velocity are examined via graphs. The present study reveals that, the velocity is arising function of Soret number, Richardson number and Grashof number. It is mentioned that the greater velocity is located in the case of Newtonian liquid as in contrast to the micropolar liquid. In the absence of chemical reaction parameter the velocity is more. It is physically justified that, when the chemical reaction increases in the fluid medium, the velocity of the liquid reduces. It is also found that radiation parameter, chemical reaction parameter and Hartmann number augment the temperature. The current study leads many applications in poro and magneto mechanics.