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This work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al₂O₃), silicon dioxide (SiO₂) and titanium dioxide (TiO₂) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.

Through the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.

Numerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.

The fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

The purpose of this study is to numerically investigate the geometric influence of different corrugation profiles (rectangular, trapezoidal and triangular) of varying heights on the flow and the natural convection heat transfer process over isothermal plates.

This work is an extension and finalization of previous studies of the leading author. The numerical methodology was proposed and experimentally validated in previous studies. Using OpenFOAM® and other free and open-source numerical-computational tools, three-dimensional numerical models were built to simulate the flow and the natural convection heat transfer process over isothermal corrugation plates with variable and constant heights.

The influence of different geometric arrangements of corrugated plates on the flow and natural convection heat transfer over isothermal plates is investigated. The influence of the height ratio parameter, as well as the resulting concave and convex profiles, on the parameters average Nusselt number, corrected average Nusselt number and convective thermal efficiency gain, is analyzed. It is shown that the total convective heat transfer and the convective thermal efficiency gain increase with the increase of the height ratio. The numerical results confirm previous findings about the predominant effects on the predominant impact of increasing the heat transfer area on the thermal efficiency gain in corrugated surfaces, in contrast to the adverse effects caused on the flow. In corrugations with heights resulting in concave profiles, the geometry with triangular corrugations presented the highest total convection heat transfer, followed by trapezoidal and rectangular. For arrangements with the same area, it was demonstrated that corrugations of constant and variable height are approximately equivalent in terms of natural convection heat transfer.

The results allowed a better understanding of the flow characteristics and the natural convection heat transfer process over isothermal plates with corrugations of variable height. The advantages of the surfaces studied in terms of increasing convective thermal efficiency were demonstrated, with the potential to be used in cooling systems exclusively by natural convection (or with reduced dependence on forced convection cooling systems), including in technological applications of microelectronics, robotics, internet of things (IoT), artificial intelligence, information technology, industry 4.0, etc.

To the best of the authors’ knowledge, the results presented are new in the scientific literature. Unlike previous studies conducted by the leading author, this analysis specifically analyzed the natural convection phenomenon over plates with variable-height corrugations. The obtained results will contribute to projects to improve and optimize natural convection cooling systems.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

A few earlier studies presented infeasible heatline trajectories for natural convection within annular domains involving an inner circular cylinder and outer square/circular enclosure. The purpose of this paper is to revisit and illustrate the correct heatline trajectories for various test cases.

Galerkin finite element based methodology and space adaptive grid have been used to simulate natural convective flows within the annular domains. The prediction of heatlines involves derivatives at the nodes, which are evaluated based on finite element basis functions and contributions from neighboring elements.

The heatlines in the earlier work indicate infeasible heat flow paths such as heat flow from one portion to the other of isothermal hot walls and heat flow across the adiabatic walls. Current results illustrate physically consistent heat flow paths involving perpendicularly emerging heatlines from hot to cold walls for conductive transport, long heat flow paths around the closed-loop heatline cells for convective transport and parallel layout of heatlines to the adiabatic walls. Results also demonstrate complex heatlines involving multiple flow vortices and complex flow structures.

Current work translates heatfunctions from energy flux vectors, which are determined by using basis sets. This work demonstrates the expected heatline trajectories for various scenarios involving conductive and convective heat transport within enclosures with an inner hot object as a first attempt, and the results are precursors for the understanding of energy flow estimates.

The entropy and thermal behavior analyses of non-Newtonian nanofluid double-diffusive natural convection inside complex domains may captivate a bunch of scholars’ attention because of the potential utilizations that they possess in modern industries, for example, heat exchangers, solar energy collectors and cooling of electronic apparatuses. This study aims to investigate the second law and thermal behavior of non-Newtonian double-diffusive natural convection (DDNC) of Al₂O₃-H₂O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by a magnetic field.

For the governing equations of the complicated and practical system with all considered parameters to be solved via a formidable numerical approach, the finite element method acts as an approach to achieving the desired solution. This method allows us to gain a detailed solution to the studied geometry.

This investigation has been executed for the considered parameters of range, such as power-law index, baffle length, Lewis number, buoyancy ratio, Hartmann number and Rayleigh number. The main results reveal that isothermal and concentration lines are significantly more distorted, indicating intensified concentration and temperature distributions because of the growth of baffle length (L). Nu_ave decreases by 8.4% and 0.8% while it enhances by 49.86% and 33.87%, respectively, because of growth in the L from 0.1 to 0.2 and 0.2 to 0.3.

Such a comprehensive study on the second law and thermal behavior of DDNC of Al₂O₃-H₂O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by magnetic field has not yet been carried out.

Thermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.

The mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.

The graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.

Such complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.

To the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.

This paper deals with numerical studies into combined conduction, convection and radiation from a heated vertical electronic board are provided here.

Here three inbuilt heaters with decrease in their heights were placed in the vertical electronic board. With respect to the non-heat portions, two configurations were studied. The first considers the non-heat portions to be adiabatic, while in the second, they are non-adiabatic. The heat that is produced in three heaters is conducted along the board and is dissipated either from the heater portions alone or from the whole board by convection and radiation. Air is considered as working medium, while the equations of heat transfer and flow of fluid are handled without boundary layer approximations. These equations were further solved using finite volume method with Gauss–Seidel iteration method.

Results of various comparative studies were discussed to bring out the relevance of thermal conductivity, modified Richardson number and surface emissivity on different heat transfer and flow results concerning this problem.

The optimum values of surface emissivity, thermal conductivity and modified Richardson number have also been notionally explored.

In recent times, there has been a growing interest in buoyancy-induced heat transfer within confined enclosures due to its frequent occurrence in heat transfer processes across diverse engineering disciplines, including electronic cooling, solar technologies, nuclear reactor systems, heat exchangers and energy storage systems. Moreover, the reduction of entropy generation holds significant importance in engineering applications, as it contributes to enhancing thermal system performance. This study, a numerical investigation, aims to analyze entropy generation and natural convection flow in an inclined square enclosure filled with Ag–MgO/water and Ag–TiO2/water hybrid nanofluids under the influence of a magnetic field. The enclosure features heated slits along its bottom and left walls. Following the Boussinesq approximation, the convective flow arises from a horizontal temperature difference between the partially heated walls and the cold right wall.

The governing equations for laminar unsteady natural convection flow in a Newtonian, incompressible mixture is solved using a Marker-and-Cell-based finite difference method within a customized MATLAB code. The hybrid nanofluid’s effective thermal conductivity and viscosity are determined using spherical nanoparticle correlations.

The numerical investigations cover various parameters, including nanoparticle volume concentration, Hartmann number, Rayleigh number, heat source/sink effects and inclination angle. As the Hartmann and Rayleigh numbers increase, there is a significant enhancement in entropy generation. The average Nusselt number experiences a substantial increase at extremely high values of the Rayleigh number and inclination.

This numerical investigation explores advanced applications involving various combinations of influential parameters, different nanoparticles, enclosure inclinations and improved designs. The goal is to control fluid flow and enhance heat transfer rates to meet the demands of the Fourth Industrial Revolution.

In a 90° tilted enclosure, the addition of 5% hybrid nanoparticles to the base fluid resulted in a 17.139% increase in the heat transfer rate for Ag–MgO nanoparticles and a 16.4185% increase for Ag–TiO2 nanoparticles compared to the base fluid. It is observed that a 5% nanoparticle volume fraction results in an increased heat transfer rate, influenced by variations in both the Darcy and Rayleigh numbers. The study demonstrates that the Ag–MgO hybrid nanofluid exhibits superior heat transfer and fluid transport performance compared to the Ag–TiO2 hybrid nanofluid. The simulations pertain to the use of hybrid magnetic nanofluids in fuel cells, solar cavity receivers and the processing of electromagnetic nanomaterials in enclosed environments.

The purpose of this study is the hydrothermal analysis of the natural convection phenomenon within the heat exchanger containing nanofluids using the lattice Boltzmann method (LBM).

The thermal conductivity as well as dynamic viscosity of the CuO–water nanofluid is estimated using the Koo-Kleinstreuer-Li model. The LBM has been used with unique modifications to make it flexible with the curved boundaries. The local as well as total entropy generation assessment, local Nusselt variation, as well as heatline visualization are used.

The solid volume percentage of the CuO–water nanofluid, a range of Rayleigh numbers (Ra) and thermal settings of internal operational fins and bodies are all factors that have been thoroughly researched to determine their effects on entropy production, heat transfer efficiency and nanofluid flow.

The originality of this work is using a novel numerical method (i.e. curved boundary LBM) as well as the local/volumetric second law analysis for the application of heat exchanger hydrothermal analysis.

This study comprehensively examines entropy generation and thermosolutal performance of a ternary hybrid nanofluid in a partially active porous cabinet. The purpose of this study is to comprehend the intricate phenomena of double diffusion by investigating the dispersion behavior of Al₂O₃, CuO, and Ag nanoparticles in water.

The cabinet design consists of two horizontal walls and two curved walls with the lower border divided into a heated and concentrated region of length b and the remaining sections are adiabatic. The vertical borders are cold and low concentration, while the upper border is adiabatic. Two cavity configurations such as convex and concave are considered. A uniform porous medium is taken within the ternary hybrid nanofluid. This has been characterized by the Brinkman-extended Darcy model. Thermosolutal phenomena are governed by the Navier-Stokes equations and are solved by adopting a higher-order compact scheme.

The present study focuses on exploring the influence of several well-defined parameters, including Rayleigh number, Darcy number, Lewis number, Buoyancy ratio number, nanoparticle volume concentration and heater size. The results indicate that the ternary hybrid nanofluid outperforms both the mono and hybrid nanofluids in all considered aspects.

This study brings forth a significant contribution by uncovering novel flow features that have previously remained unexplored. By addressing a well-defined problem, the work provides valuable insights into the enhancement of thermal transport, with direct implications for diverse engineering devices such as solar collectors, heat exchangers and microelectronics.