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This article presents a numerical study of the heat transfer properties of a nanofluid created using engine oil as the common fluid and Fe3O4 nanoparticles within a square cavity embedded with porous media using the LTNE model in the presence of a Cattaneo–Christov heat flux. To obtain the governing boundary layer equations, the Boussinesq approximation and Darcy model are employed.

By applying the Finite Element method, the modeling equations for dimensionless vorticity, stream function and temperature contours with conforming boundary and initial conditions are scrutinized.

One important finding is that streamlines create a core vortex that is oriented centrally and has longer thermal relaxation times. In contrast, solid state isotherms are hardly affected by growth in thermal relaxation parameter values when compared to fluid state isotherms.

The research work carried out in this work is original and no part is copied from others.

The purpose of this study is to derive a physics based complete-flux approximation scheme by solving suitable nonlinear boundary value problems (BVP) for finite volume method for mixed convection problems, to study the mixed convection phenomenon inside partially and differentially heated cavity for various sets of flow parameters. And, to study the impact of source terms on the cell-face fluxes for various sets of flow parameters for mixed convection problems.

The governing equations have been discretized by finite volume method on a staggered grid, and the cell-face fluxes have been approximated by local nonlinear BVP. The cell-face flux is represented as a sum of homogeneous and an inhomogeneous flux term. The proposed flux approximation is fully physics based as it considers the pressure gradient term, thermal buoyancy term and the other source terms in the cell-face flux calculation. The scheme comes out to be second order accurate in space tested with known solution. Also, the scheme has been implemented to study the mixed convection problems in a partially and differentially heated cavity.

The numerical order of convergence study shows that the proposed scheme is of second order in space. The scheme is first validated with existing benchmark literature for the mixed convection problem. As the proposed cell-face flux approximation scheme is a homogeneous part and an inhomogeneous part, this study quantifies the influence of the several source terms on the cell-face flux with the help of the inhomogeneous flux term. Then, the mixed convection problems in a partially and differentially heated cavity has been studied. Also, the effect of heat transfer rate at the hot wall is studied for different height of the heat source with different directions of wall movement. The numerical findings show that the local Nusselt number at the left wall is higher when the top and bottom walls move in opposite directions compared to when they move in the same direction, regardless of the Richardson number. In addition, the heat transfer rate at the hot portion of the left wall increases uniformly as the Richardson number decreases when the walls move in opposite directions. However, when the top and bottom walls move in the same direction, the increase in heat transfer rate is not uniform due to the formation of secondary re-circulation of the fluid near the bottom wall.

In this work, the flux approximation is conducted through local nonlinear BVPs, an approach that, to the authors’ knowledge, has not been previously applied to mixed convection problems. One of the strong advantages of the proposed scheme is that it can quantify the influence of source terms, namely, pressure gradient, cross-flux and the thermal buoyancy force, on the cell face fluxes required in the finite volume methods. Furthermore, the study explores mixed convection in a partially and differentially heated cavity, which is also novel within the current literature. These factors contribute to the originality and scientific value of the research.

This study aims to provide an in-depth analysis of entropy generation (EG) during natural convection within the annular space between confocal elliptic cylinders, with a specific focus on the influence of Brownian motion on nanofluid behavior.

A finite volume control method was used to conduct a detailed numerical analysis, examining the behavior of various nanofluids across a range of volume concentrations (2%–6%) and Rayleigh numbers. The study explores heat transfer (HT) and fluid flow mechanisms, particularly highlighting the role of nanoparticle Brownian motion in enhancing thermal conductivity.

The findings reveal that increased Rayleigh numbers significantly improve HT rates, while at lower Rayleigh values, EG is primarily governed by thermodynamic irreversibility. At higher Rayleigh numbers, this irreversibility plays a less dominant role in overall entropy production.

This study offers a novel perspective on the interplay between Rayleigh numbers, Brownian motion and EG, providing valuable insights for optimizing HT processes in engineering applications involving nanofluids.

Using passive techniques like twisted tapes and corrugated surface is an efficient method of heat transfer improvement, since the referred manners break the boundary layer and improve the heat exchange. This paper aims to present an improved dual-flow parabolic trough collector (PTC). For this purpose, the effect of an absorber roof, a type of turbulator and a grooved absorber tube in the presence of nanofluid is investigated separately and simultaneously.

The FLUENT was used for solution of governing equation using control volume scheme. The control volume scheme has been used for solving the governing equations using the finite volume method. The standard k–e turbulence model has been chosen.

Fluid flow and heat transfer features, as friction factor, performance evaluation criteria (PEC) and Nusselt number have been calculated and analyzed. It is showed that absorber roof intensifies the heat transfer ratio in PTCs. Also, the combination of inserting the turbulator, outer corrugated and inner grooved absorber tube surface can enhance the PEC of PTCs considerably.

Results of the current study show that the PTC with two heat transfer fluids, outer and inner surface corrugated absorber tube, inserting the twisted tape and absorber roof have the maximum Nusselt number ratio equal to 5, and PEC higher than 2.5 between all proposed arrangements for investigated Reynolds numbers (from 10,000 to 20,000) and nanoparticles [Boehmite alumina (“λ-AlOOH)”] volume fractions (from 0.005 to 0.03). Maximum Nusselt number and PEC correspond to nanoparticle volume fraction and Reynolds number equal to 0.03 and 20,000, respectively. Besides, it was found that the performance evaluation criteria index values continuously grow by an intensification of nanoparticle volume concentrations.

Thermal energy storage systems use thermal energy to elevate the temperature of a storage substance, enabling the release of energy during a discharge cycle. The storage or retrieval of energy occurs through the heating or cooling of either a liquid or a solid, without undergoing a phase change, within a sensible heat storage system. In a sensible packed bed thermal energy storage system, the structure comprises porous media that form the packed solid material, while fluid occupies the voids. Thus, a cavity, partially filled with a fluid layer and partially with a saturated porous layer, has become important in the investigation of natural convection heat transfer, carrying significant relevance within thermal energy storage systems. Motivated by these insights, the current investigation delves into the convection heat transfer driven by buoyancy and entropy generation within a partially porous cavity that is differentially heated, vertically layered and filled with a hybrid nanofluid.

The investigation encompasses two distinct scenarios. In the first instance, the porous layer is positioned next to the heated wall, while the opposite region consists of a fluid layer. In the second case, the layers switch places, with the fluid layer adjacent to the heated wall. The system of equations for fluid and porous media, along with appropriate initial and boundary conditions, is addressed using the finite difference method. The Tiwari–Das model is used in this investigation, and the viscosity and thermal conductivity are determined using correlations specific to spherical nanoparticles.

Comprehensive numerical simulations have been performed, considering controlling factors such as the Darcy number, nanoparticle volume fraction, Rayleigh number, bottom slit position and Hartmann number. The visual representation of the numerical findings includes streamlines, isotherms and entropy lines, as well as plots illustrating average entropy generation and the average Nusselt number. These representations aim to provide insight into the influence of these parameters across a spectrum of scenarios.

The computational outcomes indicate that with an increase in the Darcy number, the addition of 2.5% magnetite nanoparticles to the GO nanofluid results in an enhanced heat transfer rate, showing increases of 0.567% in Case 1 and 3.894% in Case 2. Compared with Case 2, Case 1 exhibits a 59.90% enhancement in heat transfer within the enclosure. Positioning the porous layer next to the partially cooled wall significantly boosts the average total entropy production, showing a substantial increase of 11.36% at an elevated Rayleigh number value. Positioning the hot slit near the bottom wall leads to a reduction in total entropy generation by 33.20% compared to its placement at the center and by 33.32% in comparison to its proximity to the top wall.

Hybrid nanofluids are more effective in the enhancement of heat transfer than mono nanofluids. The mono nanofluid’s thermophysical properties are limited, so it is not enough to succeed in the required thermal performance. The Darcy–Forchheimer hybrid nanofluid flow based on Ag and TiO2 has been used for the applications of drug delivery. In photoelectrochemical (PEC) biosensing applications, the detection of targets has been greatly enhanced by the use of various TiO2 nanostructures. Biosensors, drug delivery systems and medical devices can benefit greatly from the combination of Ag and TiO2.

The Ag and TiO2 hybrid nanofluid flow in an inclined squeezing channel is considered for the applications of drug delivery. The channel walls are permeable and allow fluid in the form of suction and injection, while the flow medium inside the channel is also nonlinearly porous. A set of nonlinear differential equations is created from the main governing equations. The model problem is solved by using the artificial neural network (ANN), and the results are plotted and discussed. Recent and past results have been observed to have a strong correlation.

It can be concluded that the contracted and expanding parameter nature is the main factor in controlling hybrid nanofluid flow in the inclined squeezing flow. The values of the other parameters vary the profile’s growth. The central zone has the lowest absolute value of normal pressure drop for the pair of cases with positive or negative Reynolds. The lower heated wall becomes more efficient when the increase is used with a 5% volume fraction. The lower wall has an increasing percentage of 6.9% and 9.75% when using nanofluid and hybrid nanofluid, respectively.

The authors believe that no one has ever investigated the Darci–Forchheimer flow in a squeezing inclined channel for medical applications. The physical properties of the Ag and TiO2 hybrid nanofluid make it suitable for use as a medication in the biomedical field. The ANN is also a novel approach to solving the current problem. This research is focused on stabilizing hybrid nanofluid flow in the squeezing and porous channels by optimizing normal pressure under the influence of embedded parameters. This main part of the research is not usually mentioned in the existing literature.

Hybrid nanofluids can effectively utilize the antimicrobial properties of TiO2 and Ag nanomaterials for drug delivery applications due to their unique properties. Ag and TiO2 nanomaterials have the ability to control temperature distribution during the flow in an inclined channel, which is crucial for uniform drug delivery. Controlling the release rate of drugs and maintaining the flow stability is largely dependent upon the increase in temperature. The Ag and TiO2 nanoparticles are effective in localized hyperthermia treatments, and this procedure necessitates a temperature higher than the body’s temperature. Therefore, increasing the temperature profile is essential for drug delivery.

Hybrid nanofluids can effectively utilize the antimicrobial properties of TiO2 and Ag nanomaterials for drug delivery applications due to their unique properties. Ag and TiO2 nanomaterials have the ability to control temperature distribution during the flow in an inclined channel, which is crucial for uniform drug delivery. Controlling the release rate of drugs and maintaining the flow stability is largely dependent upon the increase in temperature. The Ag and TiO2 nanoparticles are effective in localized hyperthermia treatments, and this procedure necessitates a temperature higher than the body’s temperature. Therefore, increasing the temperature profile is essential for drug delivery.

The authors believe that no one has ever investigated the Darci–Forchheimer flow in a squeezing channel for medical applications. Moreover, the walls of the channel and the flow medium are both porous. The physical properties of the Ag and TiO2 hybrid nanofluid make it suitable for use as a medication in the biomedical field. The idea of a hybrid nanofluid flow in a squeeze channel using blood-based Ag and TiO2 is also new and important for drug delivery applications. The ANN is also a novel approach to solving the current problem.

This paper aims to explore, through a numerical study, buoyant convective phenomena in a porous cavity containing a hybrid nanofluid, taking into account the local thermal nonequilibrium (LTNE) approach. The cavity contains a solid block in the shape of a cross (+). It will be helpful to develop and optimize the thermal systems with intricate geometries under LTNE conditions for a variety of applications.

To attain the objective, the system governing partial differential equations (PDEs), expressed as functions of the current function and temperature, and are solved numerically by the finite difference approach. The authors carefully examine the heat transfer rates and dynamics of the micropolar hybrid nanofluid by presenting fluid flow contours, isotherms of the liquid and solid phases, as well as contours of streamlines, isotherms and concentration of the fluid. Key parameters analyzed include heated length (B = 0.1–0.5), porosity (ε = 0.1–0.9), heat absorption/generation (Q = 0–8), length wave (λ = 1–3) and the interphase heat transfer coefficient (H* = 0.05–10). The equations specific to the flow of a micropolar fluid are converted into classical Navier–Stokes equations by increasing the porosity and pore size.

The results showed that the shape, strength and position of the fluid circulation are dictated by the size of the inner obstacle (B) as well as the effective length of the heating wall. The lower value of obstruction size, as well as heating wall length, leads to a higher rate of heat transfer. Heat transfer is much higher for the higher amount of heat absorption instead of heat generation (Q). The higher porosity values lead to lesser fluid resistance, which leads to a superior heat transfer from the hot source to the cold walls. The surface waviness of 4 leads to superior heat transfer related to any other waviness.

This work can be further investigated by looking at thermal performance in the existence of various-shaped obstructions, curvature effects, orientations, boundary conditions and other variables. Numerical simulations or experimental studies in different multiphysical contexts can be used to achieve this.

Many technical fields, including heat exchanging unit, crystallization processes, microelectronic units, energy storage processes, mixing devices, food processing, air conditioning systems and many more, can benefit from the geometric configurations investigated in this study.

This work numerically explores the behavior of micropolar nanofluids (a mixture of copper, aluminum oxide and water) within a porous inclined enclosure with corrugated walls, containing a solid insert in the shape of a cross in the center, under the oriented magnetic field, by applying the nonlocal thermal equilibrium model. It analyzes in detail the heat transfer rates and dynamics of the micropolar nanoliquid by presenting the flow patterns, the temperature of liquid and solid phases, as well as the variations in the flow, thermal and concentration fields of the fluid.

This study aims to investigate experimentally and numerically the thermal analysis of a wavy diverging-converging corrugated enclosure, partitioned into two parts under the effect of magnetohydrodynamic (MHD) natural convection. The left part was filled with Al₂O₃/C₂H₆O₂ nanofluid, while the right part was Al₂O₃/C₂H₆O₂ saturated by a porous medium, featuring a corrugated cylinder at the center. This system is relevant to many engineering applications. Key factors affecting thermal performance, such as nanofluid volume fraction, Darcy number, Hartmann number, inclination angle of MHD and Rayleigh number, were analyzed. This study evaluated the impact of these parameters on stream function, average Nusselt number and isothermal lines under three heat source scenarios: heating the corrugated cylinder, heating the magnetic source and heating the nanofluid, porous media and corrugated walls.

The main governing equations for the nanofluid flow are mass, momentum and heat transfer, while the porous media are modeled using the Darcy–Brinkmann model. These governing equations are transformed into a dimensionless form and solved numerically using COMSOL 6.0 based on the finite-element method. Dynamic viscosity, density and thermal conductivity equations are used to calculate the properties of the nanofluid at different volume concentrations.

The results showed that increasing the Rayleigh number (Ra) and Darcy number (Da) increased the Nusselt number by 55%, indicating enhanced heat transfer. A vertical magnetic source (γ = 90°) further improved thermal performance. Conversely, thermal performance decreased with increasing Hartmann number (Ha). The highest Nusselt number was observed when the heat source was applied to the corrugated cylinder, followed by the right side with nanofluid–porous contact and was lowest for the left side with nanofluid contact. Experimental data demonstrated that the presence of a magnetic field can significantly increase the temperature, thereby enhancing heat transfer by natural convection, particularly when the heat source is applied in the region of nanofluid–porous contact.

The primary originality of this work lies in the use of a novel design featuring a diverging-converging structure with a wavy wall. In addition, it uses two types of fluids simultaneously, dividing the enclosure into two sections: the right side contains nanofluid mixed with a porous medium, while the left side is filled with nanofluid only. The system also includes a corrugated cylinder at its center with four undulations. The position of the heat source significantly influences heat dissipation. Therefore, three different positions were examined: heating the cylinder at a constant temperature, heating the left side of the enclosure and heating the right side.

This study aims to explore entropy evaluation in the bi-directional flow of Casson hybrid nanofluids within a stagnated domain, a topic of significant importance for optimizing thermal systems. The aim is to investigate the behavior of unsteady, magnetized and laminar flow using a parametric model based on the thermo-physical properties of alumina and copper nanoparticles.

The research uses boundary layer approximations and the Keller-box method to solve the derived ordinary differential equations, ensuring numerical accuracy through convergence and stability analysis. A comparison benchmark has been used to authenticate the accuracy of the numerical outcomes.

Results indicate that increasing the Casson fluid parameter (ranging from 0.1 to 1.0) reduces velocity, the Bejan number decreases with higher bidirectional flow parameter (ranging from 0.1 to 0.9) and the Nusselt number increases with higher nanoparticle concentrations (ranging from 1% to 4%).

This study has limitations, including the assumption of laminar flow and the neglect of possible turbulent effects, which could be significant in practical applications.

The findings offer insights for optimizing thermal management systems, particularly in industries where precise control of heat transfer is crucial. The Keller-box simulation method proves to be effective in accurately predicting the behavior of such complex systems, and the entropy evaluation aids in assessing thermodynamic irreversibilities, which can enhance the efficiency of engineering designs.

These findings provide valuable insights into the thermal management of hybrid nanofluid systems, marking a novel contribution to the field.

This paper aims to investigate the thermal performance of equivalent square and circular thermal systems and compare the heat transport and irreversibility of magnetohydrodynamic (MHD) nanofluid flow within these systems.

The research uses a constraint-based approach to analyze the impact of geometric shapes on heat transfer and irreversibility. Two equivalent systems, a square cavity and a circular cavity, are examined, considering identical heating/cooling lengths and fluid flow volume. The analysis includes parameters such as magnetic field strength, nanoparticle concentration and accompanying irreversibility.

This study reveals that circular geometry outperforms square geometry in terms of heat flow, fluid flow and heat transfer. The equivalent circular thermal system is more efficient, with heat transfer enhancements of approximately 17.7%. The corresponding irreversibility production rate is also higher, which is up to 17.6%. The total irreversibility production increases with Ra and decreases with a rise in Ha. However, the effect of magnetic field orientation (γ) on total EG is minor.

Further research can explore additional geometric shapes, orientations and boundary conditions to expand the understanding of thermal performance in different configurations. Experimental validation can also complement the numerical analysis presented in this study.

This research introduces a constraint-based approach for evaluating heat transport and irreversibility in MHD nanofluid flow within square and circular thermal systems. The comparison of equivalent geometries and the consideration of constraint-based analysis contribute to the originality and value of this work. The findings provide insights for designing optimal thermal systems and advancing MHD nanofluid flow control mechanisms, offering potential for improved efficiency in various applications.