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This study explains the steady flow of a hybrid nanofluid due to a permeable shrinking sheet close to a stagnation region with suction/injection. By proper transformations, the leading differential equations, partial in nature, are reduced to nonlinear differential equations with a single independent variable. A combination of the Runge–Kutta method and a shooting technique is applied to unravel those nonlinear equations. The effects of various parameters on the flow and thermal fields are presented graphically and analyzed. Also, for various physical parameters, wall shear stress, and the heat transport coefficient are computed numerically and discussed in detail. For the boundary value problem, multiple (two) solutions are obtained for a definite choice of governing parameters. Hence, a stability analysis is carried out, indicating that the first branch of the solution is stable and physically realistic. The unsteady equations are considered for implementing the stability analysis. Furthermore, in a hybrid nanofluid flow, a higher heat transfer rate than a nanofluid is observed. The separation of the boundary layer occurs. Also, with a rise in the value of the nanoparticle volume fraction of Al2O3, the critical value of the suction parameter increases. [ABSTRACT FROM AUTHOR]

In this analysis, a numerical investigation of hybrid nanofluid flow composed of copper and alumina nanoparticles over an extending sheet is deliberated. The sheet surface is assumed to be heated by considering the convective condition, and there is no mass flow at the sheet surface by assuming the zero flux of mass constraints. The modeled ordinary differential equations, which are obtained by transforming the partial differential equations using suitable similarity variables, are evaluated numerically by adopting the bvp4c scheme. The main theme of this analysis is to investigate the applications of an inclined magnetic field toward the hybrid nanofluid flow over a convectively heated surface. The results obtained from this analysis show that the dragging force at the sheet's surface has been greatly increased by the magnetic factor and angle of inclination. Additionally, the angle of inclination greatly influenced the heat transfer rate, temperature, and concentration distributions when α = 900 as compared to α < 900. [ABSTRACT FROM AUTHOR]

The boundary-layer flow on a shrinking/contracting sheet has abundant industrial applications, which include continuous glass casting, metal or polymer extrusions, and wire drawing. In this regard, the present analysis focuses the hybrid nanofluid flow on an exponentially extending sheet. The water-based hybrid nanofluid flow contains CoFe2O4 and TiO2 nanoparticles. Heat transfer rate analysis involves the utilization of the Cattaneo–Christov heat flux model. Moreover, the Brownian motion and thermophoresis effects are used in this novel work. The mathematical model is presented in the form of system of partial differential equations, which is then transformed into system of ordinary differential equations (ODEs) using the similarity variables. The system of ODEs is evaluated by homotopy analysis method. The variation in the flow profiles has been investigated using figures and tables. The conclusions demonstrate that the effect of magnetic parameter is 52% better for hybrid nanofluid flow than for the pure water. Conversely, the increasing magnetic parameter diminishes the thermal transfer rates for water, TiO2–H2O, CoFe2O4–H2O, and TiO2–CoFe2O4/H2O. The increasing thermophoresis parameter upsurges the thermal flow rate of nanofluids and hybrid nanofluid, while the increasing Brownian motion parameter lessens the thermal transfer rates of nanofluids and hybrid nanofluid. The increasing effect of thermophoresis parameter is 39% better for hybrid nanofluid than for the base fluid. However, the declining impression of Brownian motion factor is 48% greater for hybrid nanofluid related to pure water.

Hybrid nanofluid problems are used for augmentation of thermal transportation in various industrial applications. Therefore, the present problem is studied for the heat and mass transportation features of hybrid nanofluid caused by extending surface along with porous media. In this investigation, the authors have emphasized to analyze hybrid nanofluid flow containing diamond and copper nanoparticles on an extending surface. Furthermore, the velocity, temperature, and concentration slip constraints are adopted to examine the flow of fluid. Heat source, chemical reactivity, thermal radiation, Brownian motion and effects are taken into consideration. Nonlinear modeled equations are converted into dimensionless through similarity variables. By adopting the homotopy analysis method, the resulting equations are simulated analytically. The impacts of various emerging factors on the flow profiles (i.e., velocities, temperature, concentration, skin frictions, local Nusselt number, and Sherwood number) are shown using Figures and Tables. The major key findings reveal that the hybrid nanofluid temperature is higher but the concentration is lower for a Brownian diffusivity parameter. Moreover, increment role of heat transport is achieved due to the increment in radiation factor, thermophoresis, Brownian motion factors, and Eckert number. It has also been observed that velocity in x-direction converges in the region −0.8≤ℏf≤0.5-0.8\le {\hslash }_{\text{f}}\le 0.5, in y-direction velocity is convergent in the zone −0.6≤ℏg≤0.35-0.6\le {\hslash }_{\text{g}}\le 0.35, while temperature converges in the region −0.6≤ℏθ≤0.4-0.6\le {\hslash }_{\text{θ}}\le 0.4 and concentration converges in the region −0.5≤ℏφ≤0.4-0.5\le {\hslash }_{\text{φ}}\le 0.4.

The heat and mass transportation for nanofluid across a swirling cylinder under the actions of magnetic effects and Cattaneo–Christov heat flux is reported in the current analysis. The objective of this study is to examine the energy and mass transmissions through hybrid nanofluid under the influence of heat source/sink and reactive species. The hybrid nanoliquid has been prepared by the dispersion of silver (Ag) and gold (Au) nanoparticles (NPs) in the base fluid ethylene glycol (C2H6O2). The flow phenomena are expressed in the form of nonlinear partial differential equations and are converted to a nondimensional form, by employing the similarity substitution. For the computational estimation of the problem, the parametric continuation method is employed. The demonstration of velocity, mass, and energy outlines versus distinct physical factors is exposed in the form of figures. It has been perceived that the axial and swirling velocity outline drops with the influence of the Reynolds number, magnetic effect, and the insertion of Au and Ag NPs in C2H6O2. Furthermore, the hybrid nanofluid energy curve declines with the effect of the Reynolds number, thermal relaxation factor, and the volume friction of NPs.

An induced magnetic field is produced owing to an electric current flowing through the conductor. The induced magnetic field and the length of the conductor are in direct proportion. The current study examines the comparison of Yamada-Ota and Xue thermal conductivity models for a mixed convective hybrid nanoliquid flow through the permeable vertical channel influenced by an induced magnetic field. The projected model is supported by the combination of thermal radiation and heat generation and multiple slip conditions imposed on the walls. The Tiwari and Das model is adopted considering engine oil as a working liquid with immersed multiwalled and single-walled carbon nanotubes (CNTs) nanoparticles. The unique combination of strength, conductivity, and other properties make CNTs a promising material for an extensive variety of applications. These governing partial differential equations undergo conversion to ordinary differential equations via the similarity transformation and are then numerically processed with the bvp4c technique of the MATLAB program. The outcomes are deliberated logically via illustrations and tables. It is perceived that fluid velocity is compromised by strengthening the induced magnetic field. Nevertheless, an opposing trend is witnessed for the enhanced values of the Prandtl number. [ABSTRACT FROM AUTHOR]

In this article, the authors have presented the MHD hybrid nanoliquid flow comprised of CuO and Ag nanoparticles (nps) over a rotating disk under the effects of thermophoresis, Brownian motion, activation energy, heat source and chemical reaction. The flow is considered over a spinning disc with convective conditions. The proposed model is solved with the help of HAM. The convergence of the HAM is also shown in order to verify the convergence of the modeled problem. The effects of embedded parameters on the velocity, energy and mass profiles of the magnetohydrodynamic flow of hybrid nanoliquid are shown with the help of Figures. Also, the effects of embedded parameters on skin friction, heat and mass transfer rate are calculated with the help of Tables. The results showed that the velocity and energy profiles are augmented with the increasing solid volume fraction. The increasing magnetic parameter reduces both the radial and tangential velocities of the hybrid nanofluid flow. The increasing effects of heat source, thermophoresis and Brownian motion factors on energy profiles are found. The increasing influence of thermophoresis and activation energy factors on concentration profile of the hybrid nanofluid flow is found, while the increasing Brownian motion, chemical reaction and Schmidt number reduce the concentration profile. [ABSTRACT FROM AUTHOR]

Abstract Significance Aim Methodology Results Novelty The hybrid nanofluid flow is an exciting area of research nowadays for various applications like solar thermal systems, aircrafts, heat exchangers, cooling systems and medical applications.The present research explores the numerical analysis of the three-dimensional spinning flow of a hybrid nano-liquid (NiCr + TC4) over a nonlinear stretching sheet with boundary slip.The flow equations are governed as partial differential equations (PDEs) and then converted into ordinary differential equations (ODEs) via scaling transformations. In order to compute a solution to the nonlinear ODEs, the Runge-Kutta Fehlberg scheme is used along with MATLAB.The findings demonstrate that the temperature field rises with an increase in nanoparticle volume fraction ( ϕ , NiCr ϕ T C 4 ) and falls with an increase in Prandtl number Pr. The wall shear stress in the hybrid nanofluid flow is 1.2% more than viscous fluid flow for different index parameter (n) values. In addition, thermal radiation and magnetic effects widen the study and provide useful insights into the behavior of nano-liquid under various aspects.This article explores the computational analysis of the 3D rotating flow of (NiCr + TC4)/H2O hybrid nano-liquid across a nonlinear stretching sheet under boundary slip conditions. This flow also takes into account the effect of the variable magnetic field and heat radiation. [ABSTRACT FROM AUTHOR]

The main motive of the instigated mathematical model is to observe the impact of Hall current on the hybrid nanofluid flow over a disk that is rotating. The copper and silver metal nanoparticles have been considered with volume fraction φ1=φ2=0.01(0.01)0.04 and are suspended in water to form the hybrid nanofluid. Diverse characteristics like magnetic field, thermal radiation, and (ESHS) exponential space dependent heat source are incorporated to investigate the nature of the flow. The present mathematical model is initiated with partial derivative equations (PDEs) which are redrafted as ordinary derivative equations (ODEs) with appropriate transformations of similarity. The results are attained through a blend of the Runge-Kutta method, shooting procedure, and the influences of parameters on the flow of nanofluid and hybrid nanofluid are compared and illustrated both as tables and graphs. The present numerical research is unique because by employing a complete quadratic CCD framework using the RSM strategy, the sensitivity and optimization analysis of the heat transmission improvement for the volume fraction, ESHS, and thermal radiation parameters have been performed. The R-squared and adjusted R-Squared are obtained as 100%. The residual graphs and contour diagrams of the same are also shown. The current study establishes that the Hall parameter increases the radial velocity, but it also controls the energy and cross-radial velocity. The rate of heat transmission is increased by thermal radiation even at low levels of ESHS. The rate of heat transmission is more sensitive (0.024670) to the volume fraction of the hybrid nanofluid when ESHS is at an intermediate level. The lowest sensitivity (-1.269967) value towards ESHS is observed For thermal radiation and ESHS parameter values, the heat transmission rate of the mono nanofluid is not as great as that of hybrid nanofluid. The current study finds applications in the generation of hydroelectric power, air cleansing and rotating equipment, healthcare devices, and many other industries.

This work addresses a theoretical exploration of the water-based hybrid nanofluid flow over a nonlinear elongating surface. The flow is taken under the effects of Brownian motion and thermophoresis factors. Additionally, the inclined magnetic field is imposed in the present study to investigate the flow behavior at different angle of inclination. Homotopy analysis approach is used for the solution of modeled equations. Various physical factors, which are encountered during process of transformation, have been discussed physically. It is found that the magnetic factor and angle of inclination have reducing impacts on the velocity profiles of the nanofluid and hybrid nanofluid. The nonlinear index factor has direction relation with the velocity and temperature of the nanofluid and hybrid nanofluid flows. The thermal profiles of the nanofluid and hybrid nanofluid are augmented with the increasing thermophoretic and Brownian motion factors. C u O − H 2 O nanofluid flow has enhanced heat transfer rate than A g − H 2 O nanofluid flow. On the other hand, the C u O − A g / H 2 O hybrid nanofluid has better thermal flow rate than C u O − H 2 O and A g − H 2 O nanofluids. From this table it has noticed that, Nusselt number has increased by 4% for silver nanoparticles whereas for hybrid nanofluid this incrimination is about 15%, which depicts that Nusselt number is higher for hybrid nanoparticles. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNFs) are a new breed of nanofluids that possess numerous tempting applications encompassing microfluidics, transportation, defense, medical, etc. The objective of this novel exploration is to inspect the behavior of Hamilton–Crosser (H-C) and Yamada–Ota (Y-O) HNF flow models past a stretching cylinder. The H-C model is also used to gauge which particle shape (blade, platelet, cylinder, brick) is more effective in the improvement of the heat transfer rate. The envisioned flow is influenced by the Hall current, Cattaneo–Christov (C-C) heat flux and variable thermal conductivity (TC). The uniqueness of the projected model is the notion of a heterogeneous reaction sprouting on the surface of the cylinder in the presence of an absorbent medium. Owing to this supposition, the chemical reaction occurs in the least possible time. The proposed model's novelty lies in the consideration of the surface catalyzed reaction in the HNF flow models past a stretching cylinder amalgamated with the unique impacts of the Hall current, C-C heat flux and variable TC. The thermal performance of the two renowned models H-C and Y-O is also evaluated. The MATLAB software bvp4c technique is used for numerical outcomes of this coupled system. The analysis depicts that the performance of the Y-O HNF flow model is far above the H-C HNF flow model. It is also inferred from the results that blade-shaped nanoparticles possess higher TC than the other nanoparticles. The heat transfer rate for blade-shaped nanoparticles is stronger than the other nanoparticles. The fluid concentration reduces for higher surface-catalyzed reaction parameter. The corroboration of the proposed model is also given in this study. The comparative results disclosed that in the case of the magnetic parameter M , the minimum error percentage is 0.015% for M = 0. 5 , and permeability parameter λ , the least error percentage is 0.037% for λ = 1. 0. [ABSTRACT FROM AUTHOR]

Hybrid nanofluid boundary layer flow past a stretching surface with zero mass flux boundary condition is explored in this article. The main aim of this article is to analyze the electromagnetohydrodynamic role in a hybrid nanofluid containing silver and molybdenum disulfide nanoparticles. The self‐similar solution is embedded to reduce the governing partial differential equation into algebraic equations and a shooting algorithm is applied to obtain the solution of the resultant boundary value problem. Variation in momentum, energy, and nanoparticle concentration is explained through graphical profiles. Nusselt number and drag force coefficients are computed for various flow parameters and their impact on the nanofluid and hybrid nanofluid is computed and presented and explained in a comparative fashion. It is observed that the velocity profile shows the opposite nature with respect to the electric field and magnetic field. For electric field parameter velocity accelerates whereas for magnetic parameter velocity diminishes. Nusselt number increases with electric field parameter and nanoparticle volume fraction. [ABSTRACT FROM AUTHOR]

The main purpose of the current article is to scrutinize the flow of hybrid nanoliquid (ferrous oxide water and carbon nanotubes) (CNTs + Fe 3 O 4 /H 2 O) in two parallel plates under variable magnetic fields with wall suction/injection. The flow is assumed to be laminar and steady. Under a changeable magnetic field, the flow of a hybrid nanofluid containing nanoparticles Fe 3 O 4 and carbon nanotubes are investigated for mass and heat transmission enhancements. The governing equations of the proposed hybrid nanoliquid model are formulated through highly nonlinear partial differential equations (PDEs) including momentum equation, energy equation, and the magnetic field equation. The proposed model was further reduced to nonlinear ordinary differential equations (ODEs) through similarity transformation. A rigorous numerical scheme in MATLAB known as the parametric continuation method (PCM) has been used for the solution of the reduced form of the proposed method. The numerical outcomes obtained from the solution of the model such as velocity profile, temperature profile, and variable magnetic field are displayed quantitatively by various graphs and tables. In addition, the impact of various emerging parameters of the hybrid nanofluid flow is analyzed regarding flow properties such as variable magnetic field, velocity profile, temperature profile, and nanomaterials volume fraction. The influence of skin friction and Nusselt number are also observed for the flow properties. These types of hybrid nanofluids (CNTs + Fe 3 O 4 /H 2 O) are frequently used in various medical applications. For the validity of the numerical scheme, the proposed model has been solved by another numerical scheme (BVP4C) in MATLAB. [ABSTRACT FROM AUTHOR]

The flow of nanofluids is of great importance because of their substantial industrial usage and alluring heat transfer capabilities. Recently, an innovative notion namely “hybrid nanofluid” has replaced the customary nanofluid flows to further enhance the heat transfer capabilities. We in this envisaged mathematical model are heading in the same direction and are intended to present a comparative analysis of the heat transfer competence of two time-dependent fluid models namely; hybrid nanofluid (Copper–Iron Oxide, Manganese- Zinc ferrite/Diathermic oil) (Cu-Fe2O4, Mn-ZnFe2O4/DO) and simple nanofluid (Mn-ZnFe2O4/DO) flows amidst two rotating disks in a porous media with Darcy-Forchheimer effect. The subject flows are assisted by the thermal stratification with nonlinear radiation effects. A blend of numerical “bvp4c” and statistical “Response Surface Method (RSM)” approaches is utilized to analyze the envisioned mathematical model. Tabulated and graphical depiction of the outcomes is given to comprehend their appraisal. It is comprehended that the radiation and thermal stratification parameters possess differing trends for the fluid temperature profile. Furthermore, it is observed that the parameter estimation and significance indicate both skin friction coefficient models are similar. The fitted model for skin friction and Nusselt number are the best fit where the normality assumption is satisfied.

The main purpose of the current article is to scrutinize the flow of hybrid nanoliquid (ferrous oxide water and carbon nanotubes) (CNTs + Fe3O4/H2O) in two parallel plates under variable magnetic fields with wall suction/injection. The flow is assumed to be laminar and steady. Under a changeable magnetic field, the flow of a hybrid nanofluid containing nanoparticles Fe3O4 and carbon nanotubes are investigated for mass and heat transmission enhancements. The governing equations of the proposed hybrid nanoliquid model are formulated through highly nonlinear partial differential equations (PDEs) including momentum equation, energy equation, and the magnetic field equation. The proposed model was further reduced to nonlinear ordinary differential equations (ODEs) through similarity transformation. A rigorous numerical scheme in MATLAB known as the parametric continuation method (PCM) has been used for the solution of the reduced form of the proposed method. The numerical outcomes obtained from the solution of the model such as velocity profile, temperature profile, and variable magnetic field are displayed quantitatively by various graphs and tables. In addition, the impact of various emerging parameters of the hybrid nanofluid flow is analyzed regarding flow properties such as variable magnetic field, velocity profile, temperature profile, and nanomaterials volume fraction. The influence of skin friction and Nusselt number are also observed for the flow properties. These types of hybrid nanofluids (CNTs + Fe3O4/H2O) are frequently used in various medical applications. For the validity of the numerical scheme, the proposed model has been solved by another numerical scheme (BVP4C) in MATLAB.

In the present study, the migration and deposition of multi-walled carbon nanotube (MWCNT)-Fe 3 O 4 nanocomposite particles in a square enclosure for natural convection hybrid nanofluid flow are analysed numerically using the Eulerian–Lagrangian model with one-way coupling. The governing equations are solved by the finite volume method and Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The location and velocity of 3000 selected composite particles in the host nanofluid are obtained by employing the Lagrangian approach. The influences of Rayleigh number and nanoparticle volume fraction on the thermal and flow behaviours of the system are presented. It is observed that the increasing volume fraction leads to a rise in the average Nusselt number at low Rayleigh numbers, while the case of ϕ =0.1% is the optimum volume fraction of nanoparticle in terms of heat transfer enhancement and strength of flow structure at R a ≥ 1 0 4 . The simulations of Lagrangian particle tracking demonstrate that the minimum deposition rate of composite particles with d p =0.5 μ m is obtained for a given Rayleigh number. The number of deposited large composite particles for the case of ϕ =0.1% is slightly more than for ϕ =0.3%, while the deposition rate of ultra-fine composite particles gets a higher value in the case of ϕ =0.3%. Moreover, the thermophoresis force plays a more significant role in small particle deposition than the Brownian random force. [ABSTRACT FROM AUTHOR]