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The purpose of this study is to analyze the transportation of heat and mass in three-dimensional (3D) shear rate-dependent viscous fluid. Thermal enhancement plays a significant role in industrial and engineering applications. For this, the authors dispersed trihybrid nanoparticles into the fluid to enhance the working fluid’s thermal enhancement.

The finite element method is a numerical scheme and is powerful in achieving convergent and grid-independent solutions compared with other numerical techniques. This method was initially assigned to structural problems. However, it is equally successful for computational fluid dynamics problems.

Wall shear stress has shown an increasing behavior as the intensity of the magnetic field is increased. Simulations have predicted that Ohmic heat in the case of trihybrid nanofluid (MoS₂–Al₂O₃–Cu/C₂H₆O₂) has the greatest value in comparison with mono and hybrid nanofluids. The most significant influence of chemical reaction on the concentration in tri-nanofluid is noted. This observation is pointed out for both types of chemical reaction (destructive or generative) parameters.

Through a literature survey, the authors analyzed that no one has yet to work on a 3D magnetohydrodynamics Carreau–Yasuda trihybrid nanofluid over a stretched sheet for improving heat and mass transfer over hybrid nanofluids. Herein, molybdenum disulfide (MoS₂), aluminum oxide (Al₂O₃) and copper (Cu) nanoparticles are mixed in ethylene glycol (C₂H₆O₂) to study the thermal enhancement and mass transport of their corresponding resultant mono (Cu/C₂H₆O₂), hybrid (Al₂O₃–Cu/C₂H₆O₂) and trihybrid (MoS₂–Al₂O₃–Cu/C₂H₆O₂) nanofluids.

The present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and entropy generation. Brick-shaped nanoparticles (zinc-oxide and ceria) are suspended in water, serving as the base-fluid to observe the performance of the hybrid mixture. The Maxwell thermal conductivity relation is employed to link the thermophysical attributes of the hybrid mixture with the host liquid. Additionally, a heat source/sink term is incorporated in the energy balance to enhance the impact of the investigation. Both prescribed-surface-temperature (PST) and prescribed-heat-flux (PHF) conditions are applied to inspect the thermal performance of the hybrid nanofluid.

The transport equations in Cartesian configuration are transformed into ordinary differential equations (ODEs), and an efficient method, namely the Keller-Box method (KBM), is utilized to solve the transformed system. Postprocessing is conducted to visually represent the velocity profile, thermal distribution, skin-friction coefficients, Bejan number, Nusselt number and entropy generation function against the variations of the involved parameters.

It is observed that more entropy is generated due to the increases in temperature difference and radiation parameters. The Bejan number initially declines but then improves with higher estimations of unsteadiness and Hartmann number. Overall, the thermal performance of the system is developed for the PST scenario than the PHF scenario for different estimations of the involved constraints.

To the best of the authors' knowledge, no investigation has been reported yet that explains the bidirectional flow of a CeO2-ZnO/water hybrid nanofluid with the combined effects of prescribed thermal aspects (PST and PHF) and entropy generation.

The purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.

The first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.

It is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al₂O₃ and Fe₃O₄ are nanoparticles, H₂O − C₂H₆O₂ (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.

The results can be very helpful to improve the energy efficiency of thermal systems.

The hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.

This study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

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.

This study aims to delve into the coupled mixed convective heat transport process within a grooved channel cavity using CuO-water nanofluid and an inclined magnetic field. The cavity undergoes isothermal heating from the bottom, with variations in the positions of heated walls across the grooved channel. The aim is to assess the impact of heater positions on thermal performance and identify the most effective configuration.

Numerical solutions to the evolved transport equations are obtained using a finite volume method-based indigenous solver. The dimensionless parameters of Reynolds number (1 ≤ Re ≤ 500), Richardson number (0.1 ≤ Ri ≤ 100), Hartmann number (0 ≤ Ha ≤ 70) and magnetic field inclination angle (0° ≤ γ ≤ 180°) are considered. The solved variables generate both local and global variables after discretization using the semi-implicit method for pressure linked equations algorithm on nonuniform grids.

The study reveals that optimal heat transfer occurs when the heater is positioned at the right corner of the grooved cavity. Heat transfer augmentation ranges from 0.5% to 168.53% for Re = 50 to 300 compared to the bottom-heated case. The magnetic field’s orientation significantly influences the average heat transfer, initially rising and then declining with increasing inclination angle. Overall, this analysis underscores the effectiveness of heater positions in achieving superior thermal performance in a grooved channel cavity.

This concept can be extended to explore enhanced thermal performance under various thermal boundary conditions, considering wall curvature effects, different geometry orientations and the presence of porous structures, either numerically or experimentally.

The findings are applicable across diverse fields, including biomedical systems, heat exchanging devices, electronic cooling systems, food processing, drying processes, crystallization, mixing processes and beyond.

This work provides a novel exploration of CuO-water nanofluid flow in mixed convection within a grooved channel cavity under the influence of an inclined magnetic field. The influence of different heater positions on thermomagnetic convection in such a cavity has not been extensively investigated before, contributing to the originality and value of this research.

This paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel.

The treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method.

Analysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances.

Linear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation.

This paper aims to study numerically the flow, heat transfer, and entropy generation of aqueous copper oxide-silver hybrid nanofluid over a down-pointing rotating vertical cone, with linear surface temperature (LST) and linear surface heat flux (LSHF), in the presence of a cross-magnetic field. In industrial applications, such as oil and gas plants, food industries, steel factories and nuclear packages, the real bodies may contain nonorthogonal walls and variable cross-section three-dimensional forms which this issue can clarify the importance of selective geometry in the present research.

The mass-based scheme is accomplished for the simulation, and the entropy generation and Bejan number will be analyzed in conjunction with the aforementioned model. It has been hypothesized that two types of boundary conditions (LST and LSHF) as well as five nanoparticle shapes (sphere, brick, cylinder, platelet and disk) present a collection of crucial results. The overseeing PDEs are changed over completely to the dimensionless ODEs, and these are solved by Runge–Kutta–Fehlberg approach combined with a shooting methodology for certain values of physical parameters.

Subsequent to the fantastic compromise of the computational outcomes with past reports, the outcomes are introduced to conduct the investigation of the hydrodynamics/thermal boundary layers, the skin friction and the Nusselt number, as well as entropy generation and Bejan number. A state of hybrid nanofluid, which exhibits a remarkable increase in heat transfer in comparison to the states of mono-nanofluid and regular fluid, has been found to have the highest Nusselt number; however, the skin friction values should always be taken into account and managed. The entropy generation improves with the mass of the second nanoparticle (silver), while the opposite pattern is exhibited for the Bejan number. Furthermore, the lowest value of entropy generation number belongs to the cylindrical shape of nanoparticles in the LST case. In final, a significant accomplishment of the current study is the accurate output of the mass-based scheme for an entropy analysis problem.

To the best of the authors’ knowledge, for the first time, in this study, a new development of natural convective flow of a hybrid nanofluid about the warmed (LST and LSHF) and down-pointing rotating vertical cone by the mass-based algorithm has been presented. The applied methodology considers the masses of base fluid (water) and nanoparticles (Ag and CuO) as an alternative to the first and second nanoparticles volume fraction. Indeed, the combination use of the Tiwari–Das nanofluid model and the mass-based hybridity algorithm for the entropy generation analysis can be the main novelty of this work.

The purpose of the paper is to conduct a numerical and experimental investigation into the properties of nanofluids containing spherical nanoparticles of random sizes flowing through a porous medium. The study aims to understand how the thermophysical properties of the nanofluid are affected by factors such as nanoparticle volume fraction, permeability of the porous medium, and pore size. The paper provides insights into the behavior of nanofluids in complex environments and explores the impact of varying conditions on key properties such as thermal conductivity, density, viscosity, and specific heat. Ultimately, the research contributes to the broader understanding of nanofluid dynamics and has potential implications for engineering and industrial applications in porous media.

This paper investigates nanofluids with spherical nanoparticles in a porous medium, exploring thermal conductivity, density, specific heat, and dynamic viscosity. Studying three compositions, the analysis employs the classical Maxwell model and Koo and Kleinstreuer’s approach for thermal conductivity, considering particle shape and temperature effects. Density and specific heat are defined based on mass and volume ratios. Dynamic viscosity models, including Brinkman’s and Gherasim et al.'s, are discussed. Numerical simulations, implemented in Python using the Langevin model, yield results processed in Origin Pro. This research enhances understanding of nanofluid behavior, contributing valuable insights to porous media applications.

This study involves a numerical examination of nanofluid properties, featuring spherical nanoparticles of varying sizes suspended in a base fluid with known density, flowing through a porous medium. Experimental findings reveal a notable increase in thermal conductivity, density, and viscosity as the volume fraction of particles rises. Conversely, specific heat experiences a decrease with higher particle volume concentration.xD; xA; The influence of permeability and pore size on particle volume fraction variation is a key focus. Interestingly, while the permeability of the medium has a significant effect, it is observed that it increases with permeability. This underscores the role of the medium’s nature in altering the thermophysical properties of nanofluids.

This paper presents a novel numerical study on nanofluids with randomly sized spherical nanoparticles flowing in a porous medium. It explores the impact of porous medium properties on nanofluid thermophysical characteristics, emphasizing the significance of permeability and pore size. The inclusion of random nanoparticle sizes adds practical relevance. Contrasting trends are observed, where thermal conductivity, density, and viscosity increase with particle volume fraction, while specific heat decreases. These findings offer valuable insights for engineering applications, providing a deeper understanding of nanofluid behavior in porous environments and guiding the design of efficient systems in various industrial contexts.

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.

The modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and research projects have been carried out to acquire an understanding of heat transport performance for their functional application to heat conveyance augmentation. The idea of this study is to inspect the entropy production in Darcy-Forchheimer Ree-Eyring nanofluid containing bioconvection flow toward a stretching surface is the topic of discussion in this paper. It is also important to take into account the influence of gravitational forces, double stratification, heat source–sink and thermal radiation. In light of the second rule of thermodynamics, a model of the generation of total entropy is presented.

Incorporating boundary layer assumptions allows one to derive the governing system of partial differential equations. The dimensional flow model is transformed into a non-dimensional representation by applying the appropriate transformations. To deal with dimensionless flow expressions, the built-in shooting method and the BVP4c code in the Matlab software are used. Graphical analysis is performed on the data to investigate the variation in velocity, temperature, concentration, motile microorganisms, Bejan number and entropy production concerning the involved parameters.

The authors have analytically assessed the impact of Darcy Forchheimer's flow of nanofluid due to a spinning disc with slip conditions and microorganisms. The modeled equations are reset into the non-dimensional form of ordinary differential equations. Which are further solved through the BVP4c approach. The results are presented in the form of tables and figures for velocity, mass, energy and motile microbe profiles. The key conclusions are: The rate of skin friction incessantly reduces with the variation of the Weissenberg number, porosity parameter and Forchheimer number. The rising values of the Prandtl number reduce the energy transmission rate while accelerating the mass transfer rate. Similarly, the effect of Nb (Brownian motion) enhances the energy and mass transfer rates. The rate of augments with the flourishing values of bioconvection Lewis and Peclet number. The factor of concentration of microorganisms is reported to have a diminishing effect on the profile. The velocity, energy and entropy generation enhance with the rising values of the Weissenberg number.

According to the findings of the study, a slip flow of Ree-Eyring nanofluid was observed in the presence of entropy production and heat sources/sinks. There are features when the implementations of Darcy–Forchheimer come into play. In addition to that, double stratification with chemical reaction characteristics is presented as a new feature. The flow was caused by the stretching sheet. It has been brought to people's attention that although there are some investigations accessible on the flow of Ree-Eyring nanofluid with double stratification, they are not presented. This research draws attention to a previously unexplored topic and demonstrates a successful attempt to construct a model with distinctive characteristics.