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Inclination angle has been reported to have an enhancing effect on the thermal-hydraulic characteristics and entropy of some thermal systems. Therefore, this paper aims to numerically investigate the effects of inclination angle, volume concentration and Reynolds number on the thermal and hydraulic characteristics and entropy generation rates of water-based Al₂O₃ nanofluids through a smooth circular aluminum pipe in a turbulent flow.

A constant heat flux of 2,000 Watts is applied to the circular surface of the tube. Reynolds number is varied between 4,000 and 20,000 for different volume concentrations of alumina nanoparticles of 0.5%, 1.0% and 2.0% for tube inclination angles of ±90o, ±60o, ±45o, ±30o and 0o, respectively. The simulation is performed in an ANSYS Fluent environment using the realizable kinetic energy–epsilon turbulent model.

Results show that +45o tube orientation possesses the largest thermal deviations of 0.006% for 0.5% and 1.0% vol. concentrations for Reynolds numbers 4,000 and 12,000. −45o gives a maximum pressure deviation of −0.06% for the same condition. The heat transfer coefficient and pressure drop give maximum deviations of −0.35% and −0.39%, respectively, for 2.0% vol. concentration for Reynolds number of 20,000 and angle ±90o. A 95%–99.8% and 95%–98% increase in the heat transfer and total entropy generation rates, respectively, is observed for 2.0% volume concentration as tube orientation changes from the horizontal position upward or downward.

Research investigating the effect of inclination angle on thermal-hydraulic performance and entropy generation rates in-tube turbulent flow of nanofluid is very scarce in the literature.

This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source.

This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios.

The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes.

This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.

This paper aims to perform the lattice Boltzmann simulation of conjugate natural convection heat transfer, heat flow visualization via heatlines approach and entropy generation in a partitioned medium filled with Ag-MgO (15-85%)/water.

The lattice Boltzmann method (LBM) is used to predict the dynamic and thermal behaviors. Experimental correlations for dynamic viscosity and thermal conductivity versus solid volume fraction are used. The study is conducted for the ranges of Rayleigh number 10³ ≤ Ra ≤ 10⁶, the partitioner thickness 0.01 ≤ δ ≤ 0.9, its position 0.15 ≤ X_s ≤ 0.85 and the hybrid nano-suspensions volume fraction 0% ≤ ϕ ≤ 2%.

The effects of varying of controlling parameters on the convective flow patterns, temperature contours, heat transfers, the heatlines and the entropy generation are presented. It has been found that the maximum rate of heat transfer enhancement occurs for low Ra numbers (10³) and is close to 13.52%. The solid thickness d and its horizontal position X_s have a substantial influence on the heat transfer rate, flow structure, heatline, total entropy generation and Bejan number. Besides, the maximum heat transfer is detected for high Ra and δ ≈ 1 and the percentage of augmentation is equal to 65.55% for ϕ = 2%. According to the horizontal position, the heat transfer remains invariant for Ra = 10³ and takes a maximum value near the active walls for Ra ≥ 10⁴. The total entropy generation increases with Ra and decreases with ϕ for Ra = 10⁶. The increase of ϕ from 0 to 2% leads to a reduction in close to 40.76%. For this value of Ra, the entropy is the maximum for δ = 0.4 and X_s = 0.35 and X_s = 0.65%. Moreover, as the Ra increases the Bejan number undergoes a decrease. The Bejan number is the maximum for Ra = 10³ independently to δ and X_s. The superior thermal performance manifests at low Ra and high value of δ independently to the positions of the conducting body.

The originality of this paper is to analyze the hybrid nano-additive effects on the two-dimensional conjugate natural convection in a partitioned medium using the LBM. The experimental correlations used for the effective thermal conductivity and dynamic viscosity give credibility to our study. Different approaches such as heatlines and entropy generation are used.

The purpose of this paper is to numerically investigate the hybrid nanofluid flow with the imposition of magnetohydrodynamic (MHD) and radiation effects alongside the convective boundary conditions over a permeable stretching/shrinking surface.

The mathematical model is formulated in the form of partial differential equations (PDEs) and are then transformed into the form of ordinary differential equations (ODEs) by using the similarity variables. The deriving ODEs are solved numerically by using the bvp4c solver in MATLAB software. Stability analysis also has been performed to determine the stable solution among the dual solutions obtain. For method validation purposes, a comparison of numerical results has been made with the previous studies.

The flow and the heat transfer of the fluid at the boundary layer are described through the plot of the velocity profile, temperature profile, skin friction coefficient and local Nusselt number that are presented graphically. Dual solutions are obtained, but only the first solution is stable. For the realizable solution at the shrinking surface, the proliferation of nanoparticle volume fraction (copper) and magnetic (magnetohydrodynamics) parameters can impede the boundary layer separation. Also, Biot number could enhance the temperature profile and the heat transfer rate at the shrinking surface region. The incrementation of 0.1% of Biot number has enhanced the heat transfer rate by approximately 0.1% and the incrementation of 0.5% volume fraction for copper has reduced the heat transfer rate by approximately 0.17%.

The presented model and numerical results are original and new. It can be used as a future reference for further investigation and related practical application. The main contribution of this investigation includes giving the initial prediction and providing the numerical data for the other researchers for their future reference regarding the impacts of nanoparticles volumetric concentration towards the main physical quantities of interest in the presence of magnetic and radiation parameters with the convective boundary conditions.

This paper aims to explore on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder by adding the effect of chemical reaction, B together with the magnetic field, M.

A set of reduced ordinary differential equations from the governing equations of partial differential equations is obtained through similarities requirements. The resulting equations are solved using bvp4c in MATLAB2019a. The impact of various physical parameters such as curvature parameter, ϒ, chemical reaction rate, B, magnetic field, M and Schmidt numbers, Sc on shear stress, f′′0 local heat flux, -θ′(0) and mass transfer, -∅′(0) also for velocity, f′(η), temperature, θ(η) and concentration, ∅(η) profiles have been plotted and briefly discussed. In this work, some vital characteristics such as local skin friction, Cf, local Nusselt number, Nux and local Sherwood number, Shx are chosen for physical and numerical analysis.

The findings expose that the duality of solutions appears in a shrinking region ( ε < 0). The value of skin friction, heat transfer rate and mass transfer rate reduction for existing of M, but in contrary result obtain for larger ϒ, B and Sc. Furthermore, the hybrid nanofluid demonstrates better heat transfer compared to nanofluid.

The hybrid nanofluid has widened its applications such as in electronic cooling, manufacturing, automotive, heat exchanger, solar energy, heat pipes and biomedical, as their efficiency in the heat transfer field is better compared to nanofluid.

The findings on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder with the effect of chemical reaction, B and magnetic field, M is new and the originality is preserved for the benefits of future researchers.

The flow and heat transfer of a hybrid nanofluid composed of kerosene and ZnO-Al2O3 nanoparticles (NPs) is investigated. The flow occurs over complex surfaces with stretching and shrinking features. The base fluid is electrically conducting, and an external magnetic field is added so that the nanofluid and the electric field are in equilibrium. Irrotational flow with viscous dissipation effects is considered.

The governing equations of the system are formulated, and a similarity transformation is used to convert the system of equations into ordinary differential equations, which are solved numerically. The friction coefficient of the flow and the Nusselt number are calculated for a wide range of parameters, and the results are presented in graphical form. In addition, dual solutions of the problem were noticed to occur for a certain range of the unsteadiness parameter. A stability analysis has been performed and presented to elucidate the behavior of these dual solutions.

For the solution of the upper branch, the velocity and temperature profiles of the nanofluid are enhanced by increasing the magnetic field parameter M, but the same variables decrease in the solution of the lower branch. The same trend is detected for the velocity of the fluid with the suction parameter. The temperature of the nanofluid decreases in both branches of the solution by increasing the Prandtl number. Similarly, they decrease with the suction parameter. The temperature of the nanofluid slightly increases in both branches of the solution by increasing the Eckert number. With the stability analysis the authors performed, it was determined that the solution is stable in the upper branch, but unstable in the lower branch.

The kerosene nanofluid with hybrid Zinc/Aluminum-oxide is presented for the first time in the literature.

The purpose of this paper is to review previous research studies on mathematical models for entropy generation in the magnetohydrodynamics (MHD) flow of nanofluids. In addition, the influence of various parameters on the velocity profiles, temperature profiles and entropy generation was studied. Furthermore, the numerical methods used to solve the model equations were summarized. The underlying purpose was to understand the research gap and develop a research agenda.

This paper reviews 141 journal articles published between 2010 and 2022 on topics related to mathematical models used to assess the impacts of various parameters on the entropy generation, heat transfer and velocity of the MHD flow of nanofluids.

This review clarifies the application of entropy generation mathematical models, identifies areas for future research and provides necessary information for future research in the development of efficient thermodynamic systems. It is hoped that this review paper can provide a basis for further research on the irreversibility of nanofluids flowing through different channels in the development of efficient thermodynamic systems.

Entropy generation analysis and minimization constitute effective approaches for improving the performance of thermodynamic systems. A comprehensive review of the effects of various parameters on entropy generation was performed in this study.

The purpose of this study is to investigate the Cattaneo-Christov double diffusion, multiple slips and Darcy-Forchheimer’s effects on entropy optimized and thermally radiative flow, thermal and mass transport of hybrid nanoliquids past stretched cylinder subject to viscous dissipation and Arrhenius activation energy.

The presented flow problem consists of the flow, heat and mass transportation of hybrid nanofluids. This model is featured with Casson fluid model and Darcy-Forchheimer model. Heat and mass transportations are represented with Cattaneo-Christov double diffusion and viscous dissipation models. Multiple slip (velocity, thermal and solutal) mechanisms are adopted. Arrhenius activation energy is considered. For graphical and numerical data, the bvp4c scheme in MATLAB computational tool along with the shooting method is used.

Amplifying curvature parameter upgrades the fluid velocity while that of porosity parameter and velocity slip parameter whittles down it. Growing mixed convection parameter, curvature parameter, Forchheimer number, thermally stratified parameter intensifies fluid temperature. The rise in curvature parameter and porosity parameter enhances the solutal field distribution. Surface viscous drag gets controlled with the rising of the Casson parameter which justifies the consideration of the Casson model. Entropy generation number and Bejan number upgrades due to growth in diffusion parameter while that enfeeble with a hike in temperature difference parameter.

To the best of the authors’ knowledge, this research study is yet to be available in the existing literature.

The purpose of this paper is to study the flow, heat and mass transfer of MHD Casson nanofluid due to an inclined stretching sheet using similarity transformation, the governing PDE’S equations of flow, heat and mass transfer are converted into ODE’S. The resulting non-linear ODE’S are solved numerically using an implicit finite difference method, which is known as Kellor-box method. The effects of various governing parameters on velocity, temperature and concentration are plotted for both Newtonian and non-Newtonian cases. The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters. It is noticed that the effect of angle of inclination enhances the temperature and concentration profile whereas velocity decreases. The temperature decreases due to the increase in the parametric values of Pr and Gr due to thickening in the boundary layer.

Numerical method is applied to find the results.

Flow and heat transfer analysis w.r.t various flow and temperature are analyzed for different values of the physical parameters.

The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters.

The study of the boundary layer flow, heat and mass transfer is important due to its applications in industries and many manufacturing processes such as aerodynamic extrusion of plastic sheets and cooling of metallic sheets in a cooling bath.

Here in this paper the authors have investigated the MHD boundary layer flow of a Casson nanofluid over an inclined stretching sheet along with the Newtonian nanofluid as a limited.

The purpose of this paper is to investigate the heat transfer of laminar and turbulent pulsating Al203/water nanofluid flow in a two-dimensional channel. In the laminar flow range, with increasing Reynolds number (Re), the velocity gradient is increased. Also, the Nusselt number (Nu) is increased, which causes increase in the overall heat transfer rate. Additionally, in the change of flow regime from laminar to turbulent, average thermal flux and pulsation range are increased. Also, the effect of different percentage of Al₂O₃/water nanofluid is investigated. The results show that the addition of nanofluids improve thermal performance in channel, but the using of nanofluid causes a pressure drop in the channel.

The pulsatile flow and heat transfer in a two-dimensional channel were investigated.

The numerical results show that the Al₂O₃/Water nanofluid has a significant effect on the thermal properties of the different flows (laminar and turbulent) and the average thermal flux and pulsation ranges are increased in the change of flow regime from laminar to turbulent. Also, the addition of nanofluid improves thermal performance in channels.

The originality of this work lies in proposing a numerical analysis of heat transfer of pulsating Al₂O₃/Water nanofluid flow -with different percentages- in the two-dimensional channel while the flow regime change from laminar to turbulent.