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This study aims to examine magnetohydrodynamic mixed convective phenomena and entropy generation within a semicircular porous channel, incorporating impinging jet cooling and the effects of thermal radiation. The present study analyzes the complex flow dynamics and heat transfer characteristics of a highly diluted 0.1% (volume) concentration Cu–Al₂O₃/water hybrid nanofluid, based on findings from previous studies. The investigation is intended to support the development of effective thermal management systems across diverse industries, such as cooling of electronic devices and enhanced energy system applications.

This study incorporates a heated curved bottom wall and a cooling jet of Cu–Al₂O₃/water hybrid nanofluid impinging from the central top inlet, with two horizontal exit ports along the rectangular duct. Finite element-based simulations are conducted using COMSOL Multiphysics, using a single-phase homogeneous model justified by earlier works. This method uses experimental data of effective thermal conductivity and viscosity, emphasizing the evaluation of thermal performance in scenarios involving intricate geometries and multiphysical conditions. The study analyzes nondimensional variables such as Reynolds number (Re), modified Rayleigh number (Ra_m), Hartmann number (Ha), Darcy number (Da) and radiation parameter while maintaining a constant nanofluid volume fraction. A grid independence study and code validation were performed to ensure numerical accuracy.

The analysis indicates that elevated Re contribute to a lessening in the thermal boundary layer thickness, prompting flow separation and significantly amplifying the average Nusselt number. The mixed convective heat transfer enhancement, coupled with an overall reduction in total entropy generation, diminishes with a rising Ha. However, optimized combinations of higher values for modified Ra_m and Da yield improved heat transfer performance, particularly pronounced with increasing Ha. Radiative heat transfer exerts a detrimental impact on both heat transfer and entropy production.

While the single-phase model captures key macroscopic effects differentiating nanofluids from base fluids, it does not provide insights at the nanoparticle level. Future studies could incorporate two-phase models to capture particle-level dispersion effects. In addition, experimental validation of the findings would strengthen the study’s conclusions.

This work represents innovative perspectives on the development of efficient hydrothermal systems, accounting for the influences of thermal radiation, porous media and hybrid nanofluids within a complex geometry. The results offer critical insights for enhancing heat transfer efficiency in real-world applications, especially in sectors demanding advanced cooling solutions.

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.

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.

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 the numerical simulation of MHD flow of Williamson hybrid nanofluid over a porous stretched sheet. Cattaneo–Christov thermal and specie fluxes were used in the model. Partial differential equations are exploit to model the underlying physics of the situation (PDEs).

Using an acceptable similarity functions, these equations were changed into total differential equations (ODEs). The spectral relaxation method (SRM) was used to solve the linked and nonlinear altered ODEs. The Gauss–Seidel procedure is used to figure out how to use Chebyshev pseudospectral techniques in SRM. This is an iterative process.

Increasing the heat relaxation flow increases temperature distributions; increasing the mass relaxation flux increases concentration distributions. A higher value of thermal radiation heat generation and Eckert number was noticed to improve temperature and velocity distributions. Due to the imposed electromagnetic force, a higher magnetic field is detected to cause an elevation in the velocity distribution. Also, a higher thermal radiation is observed to upsurge the velocity in company with temperature distributions.

This research benefits from biomedical engineering, biological sciences, astrophysics and geophysics. The rheological applications of Williamson fluid finds usefulness in biological sciences. The nanoparticles as considered in this study finds applications in the field of biomedical engineering. Also, the application of the imposed electromagnetic field and magnetic field strength is very useful in the area of astrophysics. A good agreement may be found in the literature on this study’s findings.

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.

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.

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.

This study aims to develop a neurocomputational approach using the Levenberg–Marquardt artificial neural network (LM-ANN) to analyze flow and heat transfer characteristics in mixed convection involving radiative magnetohydrodynamic hybrid nanofluids. The focus is on the influence of morphological nanolayers at the fluid–nanoparticle interface, which significantly impacts coupled heat and mass transfer processes.

This research simplifies a complex system of higher-order nonlinear coupled partial differential equations governing the flow between orthogonal coaxially porous disks into ordinary differential equations via similarity transformations. These equations are solved using the shooting method, and parametric studies are conducted to observe the impact of varying important parameters. The resulting data sets are used to train, validate and test the LM-ANN model, which ensures high predictive accuracy. Machine learning and curve-fitting techniques further enhance the model’s capability to generate detailed visualizations.

The findings of this study indicate that increased nanolayer thickness (0.4–1.6) significantly improves thermal performance, while changes in the chemical reaction parameter (0.2–1) have a notable effect on enhancing the Sherwood number. These results highlight the critical role of morphological nanolayers in optimizing thermal and mass transfer efficiency in MHD nanofluids.

This research provides a novel neurocomputational framework for understanding the thermal and mass transfer dynamics in MHD nanofluids by incorporating the effects of interfacial nanolayers, an aspect often overlooked in conventional studies. The use of LM-ANN trained on computational data sets enables high-fidelity predictive analysis, offering new insights into the enhancement of thermal and mass transfer efficiency in hybrid nanofluid systems.

High surface area-to-volume ratios make nanoparticles ideal for cancer heat therapy and targeted medication delivery. Moreover, ternary nanofluids (TNFs) may possess superior thermophysical properties compared to mono- and hybrid nanofluids due to their synergistic effects. In light of this information, the objective of this article is to examine the blood-based TNF flow within convergent/divergent channels under velocity slip and temperature jump.

Leading partial differential equations corresponding to the problem are transformed into a system of nonlinear ordinary differential equations by using similarity variables. The bvp4c code that uses the finite difference method is used to obtain a numerical solution.

The effect of nanoparticles may change depending on the characteristics of flow near the wall. The properties and proportions of the used nanoparticles become important to control the flow. When TNF was used, an increase in the Nusselt number between 4.75% and 6.10% was observed at low Reynolds numbers. At high Reynolds numbers, nanoparticles reduce the Nusselt number and skin friction coefficient values under some special flow conditions. Importantly, the effects of second-order slip on engineering parameters were also investigated. Furthermore, the Nusselt number increases with increasing shape factor.

Obtained results of the study can be beneficial in both nature and engineering, especially blood flow in veins.

The main innovations of this study are the usage of blood-based TNF and the examination of the effect of shape factor in convergent/divergent channels with second-order velocity slip.