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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.

This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena.

The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions.

The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers.

A comparison between oval shape and concentric circular concentric cylinder was investigated.

In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors’ knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity).

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.

The investigation has appraised the problem of an incompressible laminar steady magnetohydrodynamic (MHD) nanofluid stream over three distinct slendering thin isothermal needles of paraboloid, cylindrical and cone shapes. Water as a base liquid is assumed in this flow model. The influences of the Hall current and variable sorts of magnetic forces have enriched our investigation. Energy and concentration expressions consist of thermophoresis and Brownian migration phenomena. The analysis of thermal and mass slips of the presumed model has also been performed.

A relevant transformation is implemented for the alteration of the leading partial differential equations (PDEs) to the equations with nonlinear ordinary form. Due to the strong nonlinearity of the foremost equations, the problem is solved numerically by embedding the well-known RK-4 shooting practice. The software MAPLE 2017 has been exploited in reckoning the entire computation. To enunciate the investigated upshots, some graphical diagrams have been regarded here. According to technological interest, we measured the engineering quantities like the Sherwood number, the coefficient of drag friction and the Nusselt number in tabular customs.

The obtained consequences support that Hall current intensifies fluid movement when the needle is in a cone shape, while the superior velocity is noticed for cylindrical-shaped needles. The transference of heat responds inversely along with the growths of thermal and mass slip factors.

No work has been performed on the flow model of radiated nanofluid over a variable-shaped thin needle under Hall current, the variable magnetic field and different slip factors.

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.

This study aims to undertake a comprehensive examination of heat transfer by convection in porous systems with top and bottom walls insulated and differently heated vertical walls under a magnetic field. For a specific nanofluid, the study aims to bring out the effects of different segmental heating arrangements.

An existing in-house code based on the finite volume method has provided the numerical solution of the coupled nondimensional transport equations. Following a validation study, different explorations include the variations of Darcy–Rayleigh number (Ra_m = 10–10⁴), Darcy number (Da = 10^–5–10^–1) segmented arrangements of heaters of identical total length, porosity index (ε = 0.1–1) and aspect ratio of the cavity (AR = 0.25–2) under Hartmann number (Ha = 10–70) and volume fraction of φ = 0.1% for the nanoparticles. In the analysis, there are major roles of the streamlines, isotherms and heatlines on the vertical mid-plane of the cavity and the profiles of the flow velocity and temperature on the central line of the section.

The finding of a monotonic rise in the heat transfer rate with an increase in Ra_m from 10 to 10⁴ has prompted a further comparison of the rate at Ra_m equal to 10⁴ with the total length of the heaters kept constant in all the cases. With respect to uniform heating of one entire wall, the study reveals a significant advantage of 246% rate enhancement from two equal heater segments placed centrally on opposite walls. This rate has emerged higher by 82% and 249%, respectively, with both the segments placed at the top and one at the bottom and one at the top. An increase in the number of centrally arranged heaters on each wall from one to five has yielded 286% rate enhancement. Changes in the ratio of the cavity height-to-length from 1.0 to 0.2 and 2 cause the rate to decrease by 50% and increase by 21%, respectively.

Further research with additional parameters, geometries and configurations will consolidate the understanding. Experimental validation can complement the numerical simulations presented in this study.

This research contributes to the field by integrating segmented heating, magnetic fields and hybrid nanofluid in a porous flow domain, addressing existing research gaps. The findings provide valuable insights for enhancing thermal performance, and controlling heat transfer locally, and have implications for medical treatments, thermal management systems and related fields. The research opens up new possibilities for precise thermal management and offers directions for future investigations.