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Exploration related to chemical processes in nanomaterial flows contains astonishing features. Nanoparticles have unique physical and chemical properties, so they are continuously used in almost every field of nanotechnology and nanoscience. The motive behind this article is to investigate the Cross nanofluid model along with its chemical processes via auto catalysts, inclined magnetic field phenomena, heat generation, Brownian movement, and thermophoresis phenomena over a symmetric shrinking (stretching) wedge. The transport of heat via nonuniform heat sources/sinks, the impact of thermophoretic diffusion, and Brownian motion are considered. The Buongiorno nanofluid model is used to investigate the impact of nanofluids on fluid flow. Modeled PDEs are transformed into ODEs by utilizing similarity variables and handling dimensionless ODEs numerically with the adoption of MATLAB's developed bvp4c technique. This software performs a finite difference method that uses the collocation method with a three-stage LobattoIIIA strategy. Obtained outcomes are strictly for the case of a symmetric wedge. The velocity field lessens due to amplification in the magneto field variable. Fluid temperature is amplified through the enhancement of Brownian diffusion and the concentration field improves under magnification in a homogeneous reaction effect. [ABSTRACT FROM AUTHOR]

Highlights: The stagnation point of heat transfer and hybrid nanofluid flow using the Powell-Eyring model toward stretching/shrinking surface problem is studied. The metal particles used are GO and Fe2O4 and Ethylene Glycol (EG) as base fluid. The analysis of entropy when the surface shrunk is highlighted. The thermal radiation and magnetic effects are also investigated. The heat transmission in a non-Newtonian hybrid nanofluid that combines particles of graphene oxide (GO) and iron dioxide (Fe2O4) with the base fluid chosen as ethylene glycol (EG) is analyzed, including the effects of radiation and magnetic influence. The hybrid nanofluid flow is assumed to be asymmetric because it flows along a horizontal shrinking surface in response to external inducements. The mathematically modelled partial differential equations (PDEs) form is then derived into ordinary differential equations (ODEs) by implementing a proper similarity transformation to the PDEs. The mathematical formulation is then algorithmically estimated employing the bvp4c solver in MATLAB. The parameters' effects on the skin friction measurement, local Nusselt number, entropy generation, velocity profile, and temperature profile are investigated and explained. This finding illustrated that the skin friction is augmented between 13.7% and 66.5% with the magnetic field, velocity slips, and the concentration of GO particles. As for the heat transmission ratio, only thermal radiation and velocity slip effects will affect the heat upsurge with the range of 99.8–147% for taken parameter values. The entropy for the shrinking case is found to increase between 16.6% and 43.9% with the magnetic field, velocity slip, and Eckert number. [ABSTRACT FROM AUTHOR]

Heat transfer in a symmetrical cavity with two semi-cylinders was explored in this study. Several parameters, such as ( 10 3 ≤ R a ≤ 10 6 ), ( 10 − 5 ≤ D a ≤ 10 − 2 ), ( 0.02 ≤ ϕ ≤ 0.08 ), ( 0.2 ≤ ε ≤ 0.8 ), and ( 0 ≤ H a ≤ 100 ) were selected and evaluated in this research. The outcome of the magnetic field and the temperature gradient on the nanofluid flow is considered. The geometric model is therefore described using a symmetry technique. The flow issue for the governing equations has been solved using the Galerkin finite element method (G-FEM), and these solutions are presented in dimensionless form. The equations for energy, motion, and continuity were solved using the application of the COMSOL Multiphysics® software computer package. According to the results, there is a difference in the occurrence of the magnetic parameter and an increase in heat transmission when the right wall is recessed inward. The heat transmission is also significantly reduced when the right wall is exposed to the outside. The number of Nusselt grows directly proportional to the number of nanofluids in the environment. In contrast, all porous media with low Darcy and Hartmann numbers, high porosity, and low volume fraction have high Nusselt numbers. It is found that double streamlines for the hot side and single cooling for Darcy, Rayleigh, and Hartmann numbers. A cold isotherm at various physical parameters is needed in the top cavity. Rayleigh's number and a solid volume fraction raise Darcy's number, increasing heat transmission inside the cavity and thermal entropy determines entropy components. [ABSTRACT FROM AUTHOR]

Several industrial fields require mixing and mechanical agitation processes. This operation is mainly used to enhance heat and mass transfer inside stirred tank systems and improve the degree of homogeneity to obtain a high-quality final product. The main goal of this research paper is to analyze the thermal and hydrodynamic behavior of non-Newtonian nanofluid (Bingham–Papanastasiou–Al2O3) inside a symmetrically stirred tank. A 3D numerical study has been conducted for a stationary laminar flow inside a symmetric cylindrical vessel under influencing parameters, including the inertia parameter ( R e = 1 ,   20 ,   100 ) and the volume fraction of nanoparticles ( Ø = 0.02 ,   0.06 ,   0.1 ) with different geometric configurations, has been introduced into the stirring system. According to the findings, with high inertia ( R e = 100 ), the heat transfer inside the stirred tank is enhanced. Furthermore, increasing the nanoparticle fraction volume had a significant impact on the acceleration of heat transfer along the stirred vessel. It has been also found that the geometric configuration of an anchor with added arm blade (Case 2) is more efficient compared with the rest of the anchor agitator. [ABSTRACT FROM AUTHOR]

In a cylindrical cavity, the convection and entropy of the hybrid nanofluid were studied. We have introduced a rectangular fin inside the cylinder; the fin temperature is at T h . The right waving wall is cooled to T c . The upper and lower walls are insulated. This study contains the induction of a constant magnetic field. The Galerkin finite element method (GFEM) is utilized to treat the controlling equations obtained by giving Rayleigh number values between R a (103–106) and Hartmann number ratio H a (0, 25, 50, 100) and Darcy ranging between D a (10−2–10−5) and the porosity ratio is ε (0.2, 0.4, 0.6, 0.8), and the size of the nanoparticles is ϕ (0.02, 0.04, 0.06, 0.08). The range is essential for controlling both fluid flow and the heat transport rate for normal convection. The outcomes show how Da affects entropy and leads to a decline in entropy development. The dynamic and Nusselt mean diverge in a straight line. The domain acts in opposition to the magnetic force while flowing. Highest entropy-forming situations were found in higher amounts of R a , D a , and initial values of H a . Parameters like additive nanoparticles (ϕ) and porosity (ε) exert diagonal dominant trends with their improving values. [ABSTRACT FROM AUTHOR]

In (Al2O3-Cu/H2O) hybridized nanofluid (HYNF) is an unsteady electro-hydrodynamic stagnation point flow. A stretchable (shrinkable) surface that was convectively heated was studied in the past. In addition to the traditional nonslip surface, the heat generating (absorbing) and the velocity slippage constraints are deliberated in this research. An obtained nonlinear scheme is resolved by the homotopy analysis method. Governing parameters are the electric field parameters, that is, the dimensionless parameters including the magnetic parameter, Prandtl quantity, heat generating factor, Eckert quantity, and unsteady factor. We discuss in detail the effects of these variables on the movement of problems and thermal transmission characteristics. Increasing the values of the magneto and electric force parameters increased the temperature. Increasing the Prandtl number lowered the temperature. For the Eckert parameter, an increase in temperature was recognized. The symmetric form of the geometry model displayed improved the fluid flow by the same amount both above and below the stagnation streamline, while it decreased the flow pressure by the same level. The more heat source uses to increase the temperature of the HYNF over the entire area, the more heat is supplied to the plate, but with a heat sink, the opposite effect is observed. [ABSTRACT FROM AUTHOR]

Cross nanofluid possesses an extraordinary quality among the various fluidic models to explore the key characteristics of flowing fluid during very low and very high shear rates and its viscosity models depend upon shear rate. The current study establishes the numerical treatment regarding variable viscosity-based mixed convective inclined magnetized Cross nanofluid with varying thermal conductivities over the moving permeable surface. Along with variable thermal conductivities, we considered thermal radiation, thermophoresis, and the Brownian motion effect. An inclined magnetic field was launched for velocity scrutiny and the heat transfer fact was numerically seen by mixed convective conditions. Similarity variables were actioned on generated PDEs of the physical model and conversion was performed into ODEs. Numerical results showed that the frictional force and Nusselt quantity considerably influence the skinning heat transfer processes over the geometry of a moving permeable surface. Furthermore, less velocity was noticed for the greater suction parameter and the Brownian motion parameter corresponds to lower mass transport. [ABSTRACT FROM AUTHOR]

In our research work, we have developed a model describing the characteristics of the bio-convection and moving microorganisms in the flows of a magnetized generalized Burgers' nanoliquid with Fourier's and Fick's laws in a stretchable sheet. Considerations have been made to Cattaneo–Christov mass and heat diffusion theory. According to the Cattaneo–Christov relation, the Buongiorno phenomenon for the motion of a nanoliquid in the generalized Burgers' fluid has also been applied. Similarity transformations have been used to convert the control system of the regulating partial differential equations (PDEs) into ordinary differential equations (ODEs). The COMSOL software has been applied to obtain mathematical results of non-linear equations via the Galerkin finite element method (G-FEM). Logical and graphical measurements for temperature, velocity, and microorganisms analysis have also been examined. Moreover, nanoparticle concentrations have been achieved by examining different approximations of obvious physical parameters. Computations of this model show that there is a direct relationship among the temperature field and thermal Biot number and parameter of the generalized Burgers' fluid. The temperature field is increased to grow the approximations of the thermal Biot number and parameter of generalized Burgers' fluid. It is reasonable to deduce that raising the chemical reaction parameter and concentricity relaxation parameter or decreasing the Prandtl number, concentricity Biot quantity, and active energy parameter can significantly increase the nanoparticles concentration dispersion. [ABSTRACT FROM AUTHOR]

Highlights: What are the main findings? The problem of 2-D Prandtl nanofluid past a moving wedge is investigated in detail; Tri-hybrid nanoparticles are considered here; Heat and mass transmission evaluations are conducted in the presence of endothermic/exothermic chemical reactions; The moving wedge is considered; What is the implication of the main finding? LobattoIIIA scheme is implemented for the numerical solution of modeled PDEs. Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick's second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ , thermal radiation R d , thermophoresis parameter N t and endothermic/exothermic reaction Ω , and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature. [ABSTRACT FROM AUTHOR]

Current research proposes a model for assessing the flow properties and heat transmission from hybridized nanofluids to solar collectors (SCs). A theoretical investigation that was based on the application of alumina-water (Al2O3-H2O) conventional nanofluid and copper/alumina-water (Cu-Al2O3/H2O) hybrid nanofluid has been considered between two rotating plates in parabolic trough solar collector (PTSC). The Cattaneo–Christov model (CCM) for heat fluxing is used for the thermal boundary layer analysis. The impact of centripetal and Coriolis forces on the swirling flow has been considered. Adequate transformations are utilised for the conversion of the regulating partial differential equations (PDEs) into a group of dimensionless ordinary differential equations (ODEs). Dimensionless ODEs are then tackled by the Keller box method (KBM) in the MATLAB program. The basic concept of this study is to inspect the influences of change in substantial factors on velocities, temperature, and heat transmission rate for both Al2O3-H2O mono nanofluid (MNF) and Cu-Al2O3/H2O hybridized nanofluid (HBNF). The striking feature of the investigation is that the hybrid nanofluid Cu-Al2O3/H2O has a less frictional force and an elevated heat transmission rate (RHT) as assessed with the traditional nanoliquid Al2O3-H2O. Consequently, the rotating factor slows RHT on the surface. In this case study, HBNF is better than the mono NF as a thermal and electrical conductor. [ABSTRACT FROM AUTHOR]

The article titled "Numerical Case Study of Chemical Reaction Impact on MHD Micropolar Fluid Flow Past over a Vertical Riga Plate" has been retracted by the Materials Editorial Office. Concerns were raised about the validity of the parameters and equations presented in the article. An investigation was conducted by the Editorial Office and Editorial Board, and despite the authors' cooperation, they were unable to explain the anomalies and validity concerns. Due to these issues, the paper has been retracted in accordance with the journal's retraction policy and the Committee on Publication Ethics guidelines. The authors of the article disagree with the retraction. [Extracted from the article]

The purpose of this article is to investigate the mass and heat transport phenomena associated with micropolar fluid flow created by a vertically stretched Riga surface. This is constructed using an array of irregular electrodes and permanent magnets that are oriented spanwise. Additionally, we investigate the particles' micro rotational impacts. Furthermore, the flow behaviour of the modeled problem has been numerically calculated with bvp4c solver and the obtained results are presented graphically. Numerical data are used to illustrate physical parameters such as skin friction, Nusselt, and Sherwood numbers. For precise values of different flow parameters, the characteristics of fluid velocity, angular velocity, temperature, and concentration gradients are investigated graphically. The flowing parallel to the Riga plate in a positive x –path is aided by Lorentz forces introduced into the flowing simulation by the electro-magnetic poles of the Riga plate, which produces a rapidity greater than the inner speed. It is confirmed that the numerical calculations fit well with the results of earlier published investigations. Due to the participation of the Riga plate, the updated Hartmann number has a considerable effect on flow profiles. [ABSTRACT FROM AUTHOR]

A numerical study of chemically reactive effects on Magnetohydrodynamics (MHD) free convective unsteady flowing over an inclined plate in a porousness material in the existence of viscous dissipation was studied. The nondimensional principal equations are time dependent coupled and non-linear partial differential equations (PDEs) are solved by the efficacy finite element method (FEM). As well, the computational relationships of speed, energy, and concentricity in the form of Galerkin finite element were obtained. Calculations are achieved with a wide range of key flow parameters, namely, the angle of inclination (α), permeability parameter k , magnetic parameter (M), buoyancy ratio parameter (N), Schmidt number ( S c ), Eckert number ( E c ), Prandtl number ( P r ), chemical factor ( K r ) on speed, and concentricity and temperature fields are examined in detail with the assistance of diagrams. [ABSTRACT FROM AUTHOR]

Parabolic trough solar collectors (PTSCs) are generally utilized to reach high temperatures in solar-thermal applications. The current work investigates entropy production analysis and the influence of nano solid particles on a parabolic trough surface collector (PTSC) installed within a solar powered ship (SPS). For the current investigation, the non-Newtonian Maxwell type, as well as a porous medium and Darcy–Forchheimer effects, were used. The flow in PTSC was produced by a nonlinear stretching surface, and the Cattaneo–Christov approach was used to assess the thermal boundary layer's heat flux. Similarity transformation approach has been employed to convert partial differential equations into solvable ordinary differential equations allied to boundary conditions. Partial differential and the boundary conditions have been reduced into a group of non-linear ordinary differential equations. A Keller-box scheme applied to solve approximate solutions of the ordinary differential equations. Single-walled carbon nanotubes -engine oil (SWCNT-EO) and Multiwalled carbon nanotubes/engine oil (MWCNT-EO) nanofluids have been utilized as working fluid. According to the findings, the magnetic parameter led to a reduction in the Nusselt number, as well as an increment in skin friction coefficient. Moreover, total entropy variance over the domain enhanced for flow rates through Reynolds number and viscosity fluctuations were monitored by using Brinkman number. Utilizing SWCNT-EO nanofluid increased the thermal efficiency between 1.6–14.9% in comparison to MWCNT-EO. [ABSTRACT FROM AUTHOR]

This work aims to determine how the temperature gradient orientation affects the heat exchange between two superposed fluid layers separated by zero wall thickness. The finite volume method (FVM) has been developed to solve the governing equations of both fluid layers. To achieve the coupling between the two layers, the heat flow continuity with the no-slip condition at the interface was adopted. The lower part of the space is filled with a nanofluid while the upper part is filled with a pure fluid layer. We have explored two cases of temperature gradient orientation: parallel gradient to gravity forces of our system and perpendicular gradient to gravity forces. We took a set of parameters, R i and ϕ , to see their influence on the thermal and hydrodynamic fields as well as the heat exchange rate between the two layers. The main applications of this study related to biological systems such as the cytoplasm and the nucleoplasm are phase-separated solutions, which can be useful as models for membranelles organelles and can serve as a cooling system application using heat exchange. The Richardson number and the volume of nanosolid particles have a big impact on the rate of change of heat transmission. When a thermal gradient is perpendicular to gravity forces, total heat transmission improves with increasing solid volume percentage, but when the thermal gradient is parallel to gravity forces, overall heat transfer decreases significantly. [ABSTRACT FROM AUTHOR]

Aluminum nanoparticles are suitable for wiring power grids, such as local power distribution and overhead power transmission lines, because they exhibit high conductivity. These nanoparticles are also among the most utilized materials in electrical field applications. Thus, the present study investigated the impact of magnetic field on 3D crossflow in the streamwise direction with the impacts of Dufour and Soret. In addition, the effects of activation energy and chemical reaction were incorporated. The viscosity and thermal conductivity of nanofluids were premeditated by KKL correlation. Prominent PDEs (Partial Differential Equations) were converted into highly nonlinear ODEs (Ordinary Differential Equations) using the proper similarity technique and then analyzed numerically with the aid of the built-in bvp4c solver in MATLAB. The impact of diverse important variables on temperature and velocity was graphically examined. Additionally, the influences of pertaining parameters on the drag force coefficient, Nusselt number, and Sherwood number were investigated. Inspections revealed that the mass transfer rate decreases, while the heat transport increases with increasing values of the Soret factor. However, the Nusselt and Sherwood numbers validate the differing trend for rising quantities of the Dufour factor. [ABSTRACT FROM AUTHOR]

This paper discusses the Darcy–Forchheimer three dimensional (3D) flow of a permeable nanofluid through a convectively heated porous extending surface under the influences of the magnetic field and nonlinear radiation. The higher-order chemical reactions with activation energy and heat source (sink) impacts are considered. We integrate the nanofluid model by using Brownian diffusion and thermophoresis. To convert PDEs (partial differential equations) into non-linear ODEs (ordinary differential equations), an effective, self-similar transformation is used. With the fourth–fifth order Runge–Kutta–Fehlberg (RKF45) approach using the shooting technique, the consequent differential system set is numerically solved. The influence of dimensionless parameters on velocity, temperature, and nanoparticle volume fraction profiles is revealed via graphs. Results of nanofluid flow and heat as well as the convective heat transport coefficient, drag force coefficient, and Nusselt and Sherwood numbers under the impact of the studied parameters are discussed and presented through graphs and tables. Numerical simulations show that the increment in activation energy and the order of the chemical reaction boosts the concentration, and the reverse happens with thermal radiation. Applications of such attractive nanofluids include plastic and rubber sheet production, oil production, metalworking processes such as hot rolling, water in reservoirs, melt spinning as a metal forming technique, elastic polymer substances, heat exchangers, emollient production, paints, catalytic reactors, and glass fiber production. [ABSTRACT FROM AUTHOR]

Apart from the Buongiorno model, no effort was ably accomplished in the literature to investigate the effect of nanomaterials on the Oldroyd-B fluid model caused by an extendable sheet. This article introduces an innovative idea regarding the enforcement of the Tiwari and Das fluid model on the Oldroyd-B fluid (OBF) model by considering engine oil as a conventional base fluid. Tiwari and Das's model takes into account the volume fraction of nanoparticles for heat transport enhancement compared to the Buongiorno model that depends significantly on thermophoresis and Brownian diffusion impacts for heat transport analysis. In this paper, the thermal characteristics of an Oldroyd-B nanofluid are reported. Firstly, the transformation technique is applied on partial differential equations from boundary-layer formulas to produce nonlinear ordinary differential equations. Subsequently, the Keller-box numerical system is utilized to obtain final numerical solutions. Copper engine oil (Cu–EO) and molybdenum disulfide engine oil (MoS2–EO) nanofluids are considered. From the whole numerical findings and under the same condition, the thermodynamic performance of MoS2–EO nanofluid is higher than that of Cu–EO nanofluid. The thermal efficiency of Cu–EO over MoS2–EO is observed between 1.9% and 43%. In addition, the role of the porous media parameter is to reduce the heat transport rate and to enhance the velocity variation. Finally, the impact of the numbers of Reynolds and Brinkman is to increase the entropy. [ABSTRACT FROM AUTHOR]