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In this research work, the authors have presented a water-ethylene glycol-based hybrid nanofluid flow which contains MoS2 and GO nanoparticles on a stretching surface. The fluid flow has been examined under the consequences of velocity and thermal slip conditions, magnetic field, and exponential heat source/sink. The hybrid-based fluid flow is composed of 50% water and 50% ethylene glycol. The purpose of this investigation is to propose a comparative analysis among the pure fluid, GO nanofluid, and hybrid nanofluid. A suitable set of variables has been used to convert the leading equation to dimensionless notation. The bvp4c Matlab built-in package is utilized to compute a numerical solution of the suggested model. A comparison of the resultant data with published results exhibits a significant agreement. The outcomes of the present work show that GO nanofluid flow has a greater velocity profile than the hybrid nanofluid and base fluid. Temperature panels, skin friction, and thermal flow rate are much greater in the case of hybrid nanoparticles in contrast to single GO nanofluid and base fluid. Further, it has been noticed that the impact of the porosity factor and magnetic and rotation factors drops the velocity distribution, while the opposite impacts of the porosity and magnetic factors have been found on the radial velocity. [ABSTRACT FROM AUTHOR]

Nanofluid is a specially crafted fluid comprising a pure fluid with dispersed nanometer-sized particles. Incorporation these nanoparticles into pure fluid results in a fluid with improved thermal properties in comparison of pure fluid. The enhanced properties of nanofluids make them highly sought after, in diverse applications, consisting of coolant of devices, heat exchangers, and thermal solar systems. In this study hybrid nanofluid consisting of copper, alumina and titanium nanoparticles on a curved sheet has investigated with impact of chemical reactivity, magnetic field and Joule heating. The leading equations have converted to normal equations by using appropriate set of variables and has then evaluated by homotopy analysis method. The outcomes are shown through Figures and Tables and are discussed physically. It has revealed in this study that Cu-nanofluid flow has augmented velocity, temperature, and volume fraction distributions than those of Al2O3-nanofluid and TiO2-nanofluid. Also, the Cu-nanofluid flow has higher heat and mass transfer rates than those of Al2O3-nanofluid and TiO2-nanofluid. [ABSTRACT FROM AUTHOR]

This article presents the two-dimensional flow of hybrid nanofluid comprising of gyrotactic microorganisms under the consequences of multiple slip conditions, magnetic field and thermal radiation across an elongating curved surface using porous media. The nanoparticles of TiO2 and Fe3O4 have dispersed in water for composition of hybrid nanofluid. Main equations of the problem are converted to ODEs by using an appropriate set of variables. Solution of the present model is determined with the help of bvp4c technique, which is explained in detail in the coming section. Validation of the current results is done versus the published work. The effects of various emerging factors on flow distributions have been considered and explained. Additionally, the slips conditions are incorporated to analyze various flow distributions. The present outcomes show that the rising magnetic factor lessens the velocity profile, whereas rises the temperature profile. The curvature factor has supported both temperature and velocity distributions. Growth in velocity, thermal, concentration, and microorganisms slip factors reduce the corresponding distributions. The greater impact of the embedded parameters is found on hybrid nanofluid flow when matched to nanofluid flow. [ABSTRACT FROM AUTHOR]

In the present model, we have studied the water-based hybrid nanofluid flow through a revolving disk. The slip and convective constraints at boundary are carried out in the problem. In the model, aluminum Al2O3 and copper Cu nanoparticles are taken into consideration to form a hybrid nanofluid with base fluid water. An appropriate set of similarity variables are taken into consideration to transform the PDEs into ODEs. The solution to the model has been gained by taking the HAM procedure. The convergence solution of the model is presented in the Figures' form. The role of distinct factors in velocities, thermal, and mass concentration sketches are delineated via Figures and Tables. The consequences reveal that the flow profile decelerate with magnetic factor. The skin friction and Nusselt number mounted with mounting in volume fraction. The thermal and concentration distribution rises with escalating thermophoresis factor. An increasing behavior is detected in the temperature distribution with mounting in the heat source factor. The result shows that the variation in hybrid nanofluid is more than nanofluid. [ABSTRACT FROM AUTHOR]

Cooling and heating are two critical processes in the transportation and manufacturing industries. Fluid solutions containing metal nanoparticles have higher thermal conductivity than conventional fluids, allowing for more effective cooling. Thus, the current paper is a comparative exploration of the time-independent buoyancy opposing and heat transfer flow of alumina nanoparticles scattered in water as a regular fluid induced via a vertical cylinder with mutual effect of stagnation-point and radiation. Based on some reasonable assumptions, the model of nonlinear equations is developed and then tackled numerically employing the built-in bvp4c MATLAB solver. The impacts of assorted control parameters on gradients are investigated. The outcomes divulge that the aspect of friction factor and heat transport upsurge by incorporating alumina nanoparticles. The involvement of the radiation parameter shows an increasing tendency in the heat transfer rate, resulting in an enhancement in thermal flow efficacy. In addition, the temperature distribution uplifts due to radiation and curvature parameters. It is discerned that the branch of dual outcomes exists in the opposing flow case. Moreover, for higher values of the nanoparticle volume fraction, the reduced shear stress and the reduced heat transfer rate increased respectively by almost 1.30% and 0.0031% for the solution of the first branch, while nearly 1.24%, and 3.13% for the lower branch solution. [ABSTRACT FROM AUTHOR]

Bioconvection research is essential due to its widespread use in the domains of biofuels and bioengineering. This study investigates the numerical behavior of megnetohydrodynamic bioconvection boundary layer flow of motile microorganisms in upper convected Maxwell fluid via a renewed bvp4c-based Lobatto IIIA solver. To stabilize the nanoparticles in suspension, microorganisms are used that cause bioconvection. The flow past stretchable sheets is under the influence of heat and mass transfer, nonlinear thermal radiation, and viscous dissipation. Suitable similarity transformations are adopted to amend PDEs' system of governing equations into ODEs' system. Visualize graphical and numerical presentations that show the influence of physical parameters, such as flow rate, temperature gradient, nanofluid concentration, and gyrotactic motile microorganism concentration. Physical quantities such as skin friction, Nusselt number, Sherwood number, and local density of microorganisms are also taken into consideration. [ABSTRACT FROM AUTHOR]

Iron oxide Fe 3 O 4 and magnesium oxide MgO are important biological agents that have an essential role in medical processes. The deficiency of these biological agents in the human body causes severe diseases like chronic anemia, heartburn, acid indigestion, sour stomach, etc. The existing article is concerned with the study of the mixed convection flow of micropolar Carreau–Yasuda hybrid nanoliquid at a stagnation point past a convectively heated Riga plate. The thermal and mass transport features are enhanced by applying the theory of Cattaneo–Christov thermal and mass flux. For the treatment of the above-mentioned diseases, the blood is considered a base fluid and magnesium oxide MgO and iron oxide Fe 3 O 4 are injected into the blood as nanoparticles. The thermal radiation, chemical reaction, Brownian, and thermal diffusivity influences are taken into account. Further, thermal and solutal stratification effects are implemented on the current flow problem. A higher-order PDE is utilized for the formulation of the existing model. Applicable similarity variables are utilized for the conversion of these nonlinear PDE's into nonlinear ODE's. With the aid of the homotopy analysis method (HAM), the simulation of these ensuing higher-order ODEs is carried out for the analytical outcomes of the existing hybrid nanoliquid model. The fluctuation in different flow profiles is computed under different flow parameters. Drag forces and rate of thermal and mass transport with respect to various pertinent parameters are deliberated in the form of tables. The key result of the existing study is that the temperature rises due to enhancing the estimations of the radiation parameter and nanoparticle's volume fraction. The hybrid nanoliquid's velocity enhances with the enhancement of the Weissenberg number. The hybrid nanofluid velocity declined because of the amplification of the nanoparticle's volume fraction. The hybrid nanoliquid temperature is enhanced for a thermal stratification parameter. The hybrid nanoliquid's concentration diminishes against the enhancing estimations of chemical reaction factor. [ABSTRACT FROM AUTHOR]

This study looks at the natural convections of Cu + Al2O3/H2O nanofluid into a permeable chamber. The magnetic field is also executed on the flow field and the analysis has been approached numerically by the control volume method. The study of hybrid nanofluid heat in terms of the transfer flux was supplemented with a wide range of parameters of hybrid nanofluid fractions, Rayleigh numbers Hartmann numbers and porosity factor. It's also determined that the flow and thermal distribution are heavily affected by the concentration of the nanoparticles. The concentration of nanoparticles increases the transport of convective energy inside the enclosure. The primary findings demonstrate that a rise in both the Rayleigh number and Darcy number leads to an improvement in convective heat transfer within the enclosure. However, the porosity has a negligible effect. Additionally, the rotation in a clockwise direction has a beneficial impact on the dispersion of heat transfer throughout the cavity. Furthermore, it is concluded that hybrid nanofluids are more reliable than conventional fluids in improving thermal properties. [ABSTRACT FROM AUTHOR]

The purpose of this research was to estimate the thermal characteristics of tri-HNFs by investigating the impacts of ternary nanoparticles on heat transfer (HT) and fluid flow. The employment of flow-describing equations in the presence of thermal radiation, heat dissipation, and Hall current has been examined. Aluminum oxide (Al2O3), copper oxide (CuO), silver (Ag), and water (H2O) nanomolecules make up the ternary HNFs under study. The physical situation was modelled using boundary layer analysis, which generates partial differential equations for a variety of essential physical factors (PDEs). Assuming that a spinning disk is what causes the flow; the rheology of the flow is enlarged and calculated in a rotating frame. Before determining the solution, the produced PDEs were transformed into matching ODEs using the second order convergent technique (SOCT) also known as Keller Box method. Due to an increase in the implicated influencing elements, several significant physical effects have been observed and documented. For resembling the resolution of nonlinear system issues come across in rolling fluid and other computational physics fields. [ABSTRACT FROM AUTHOR]

The main feature of the current investigation is to analyze the magnetohydrodynamic mixed convection flow of Cross fluid. Flow is due to a movable thin needle with Soret and Dufour effect. Heat generation/absorption and nonlinear heat radiation are used in the energy equation. Characteristics of the chemical reaction and thermal activation are given special attention. Appropriate variables are introduced for the transformation of partial differential equations to ordinary differential equations. With the assistance of Runge–Kutta Fehlberg's fourth- fifth-order method with the shooting technique, we determined the prominent result numerically. The prominent examined parameters range is velocity and temperature ratios, heat generation, Dufour, Hartmann, Schmidt numbers ( 0.1 ≤ λ , θ w , Q , D u , M , S c ≤ 0.7 ), needle thickness ( 0 ≤ a ≤ 15 ), radiative parameter ( 5 ≤ R d ≤ 8 ), and Weissenberg number ( 0.01 ≤ W e ≤ 0.09 ), respectively. Graphs for velocity, thermal, concentration, Skin friction coefficient, and heat and mass transport rates are displayed and analyzed for physical parameters. A similar observation of mixed convection and needle thickness parameter is seen on the velocity field. Temperature and heat transfer rate are reverse behavior in the frame of the Dufour effect. Moreover, an enhancement in chemical reaction shows decay to the concentration field. [ABSTRACT FROM AUTHOR]

Diesel engine characteristics were investigated experimentally while adding different concentrations of third generation biodiesel spirulina algae methyl ester (SAME). Three volumetric blends of SAME are added to standard Iraqi diesel, namely 10% SAME, 20% SAME, and 30% SAME. The properties of the fuels were found according to the American Society for Testing and Materials standards (ASTM). Experimental work was conducted on a single-cylinder diesel engine under variable load and compression ratio. Three compression ratios are used, starting from 14.5, 15.5, and 16.5. Based on the results obtained, the presence of SAME along with diesel caused an increase in Brake specific fuel consumption (BSFC), carbon dioxide (CO2), and nitrogen oxides (NOx) while decreasing both brake thermal efficiency (BTE) and exhaust gas temperature (EGT). Hydrocarbon (HC) emissions decreased by 7.14%, 8.57%, and 10.71%, for 10% SAME, 20% SAME, and 30% SAME, respectively, compared to the original neat diesel fuel. The dramatic carbon monoxide (CO) emission reduction was at full load point. The addition of SAME from (10 to 30)% reported a decrease in CO by (6.67–20)%. NOx, as well as CO2 emission, are increased as a result of SAME addition. The compression ratio change from (14.5/1 to 16.5/1) led to increased BTE, NOx, and decreased BSFC and all carbon emissions. The experimental results are validated with other studies' findings, and minor divergence is reported. [ABSTRACT FROM AUTHOR]

Current investigation emphasizes the evaluation of entropy in a porous medium of Williamson nanofluid (WNF) flow past an exponentially extending horizontal plate featuring Parabolic Trough Solar Collector (PTSC). Two kinds of nanofluids such as copper-methanol (Cu-MeOH) and alumina-methanol (Al2O3-MeOH) were tested, discussed and plotted graphically. The fabricated nanoparticles are studied using different techniques, including TDDFT/DMOl3 method as simulated and SEM measurements as an experimental method. The centroid lengths of the dimer are 3.02 Å, 3.27 Å, and 2.49 Å for (Cu-MeOH), (Al2O3-MeOH), and (Cu-MeOH-αAl-MOH), respectively. Adequate similarity transformations were applied to convert the partial differential equation (PDEs) into nonlinear ordinary differential equations (ODEs) with the corresponding boundary constraints. An enhancement in Brinkmann and Reynolds numbers increases the overall system entropy. WNF parameter enhances the heat rate in PTSC. The thermal efficiency gets elevated for Cu-MeOH than that of Al2O3-MeOH among 0.8% at least and 6.6% in maximum for varying parametric values. [ABSTRACT FROM AUTHOR]

In process engineering as chemical and biotechnological industry, agitated vessels are commonly used for various applications; mechanical agitation and mixing are performed to enhance heat transfer and improve specific Physico-chemical characteristics inside a heated tank. The research subject of this work is a numerical investigation of the thermo-hydrodynamic behavior of viscoplastic fluid (Casson–Papanastasiou model) in a stirred tank, with introducing a new anchor impeller design by conducting some modifications to the standard anchor impeller shape. Four geometry cases have been presented for achieving the mixing process inside the stirred vessel, CAI; classical anchor impeller, AI1; anchor impeller with added horizontal arm blade, AI2 and AI3 anchor impeller with two and three added arm blades, respectively. The investigation is focused on the effect of inertia and plasticity on the thermo-hydrodynamic behavior (flow pattern, power consumption, and heat transfer) by varying the Reynolds number (Re = 1, 10, 100, 200), Bingham number (Bn = 1, 10, 50), in addition to the effect of geometry design in the overall stirred system parameters. The findings revealed an excellent enhancement of flow pattern and heat transfer in the stirred system relatively to the increase of inertia values. Also, an energy reduction has been remarked and the effect of anchor impeller shape. AI3 geometry design significantly improves the flow pattern and enhances heat transfer by an increased rate of 10.46% over the other cases. [ABSTRACT FROM AUTHOR]

The current evaluation described the flow features of Darcy Forchhemier hybrid nanoliquid across a slender permeable stretching surface. The consequences of magnetic fields, second order exothermic reaction, Hall current and heat absorption and generation are all accounted to the fluid flow. In the working fluid, silicon dioxide (SiO2) and titanium dioxide (TiO2) nano particulates are dispersed to prepare the hybrid nanoliquid. TiO2 and SiO2 NPs are used for around 100 years in a vast number of diverse products. The modeled has been designed as a nonlinear set of PDEs, Which are degraded to the dimensionless system of ODEs by using the similarity transformation. The reduced set of nonlinear ODEs has been numerically estimated through bvp4c package. The outcomes are tested for validity and consistency purpose with the published report and the ND solve technique. It has been noted that the energy curve lessens with the influence of thermodiffusion, Brownian motion and rising number of nanoparticles, while boosts with the result of magnetic field. Furthermore, the concentration outline of hybrid nanoliquid improves with the upshot of chemical reaction. [ABSTRACT FROM AUTHOR]

This contribution examines a highly forced convection situation due to the movements of two adjacent wavy and straight walls of two-sided wavy enclosures. An adiabatic obstacle is located within the domain and the top boundary is partially heated. The included porous medium is assumed to be radiant and the two-energy equations system is applied for this proposed. An inclined magnetic force together with heat generation sources is inclusive in the flow area. The governing equations have been solved utilizing the characteristic-based split algorithm under the spirit of finite-element method. Numerical outcomes for the flow and heat transfer for the fluid and solid phases are determined for miscellaneous combinations of the physical factors. Graphical and tabular findings pointing out interesting features of the physics of the problem are presented and discussed. The forced convection mode is dominant at higher values of the undulation parameter λ and low values of the Hartmann number Ha. Also, the radiative porous medium reduces the Nusselt coefficient for the solid phase. Furthermore, the rate of the heat transfer is reduced by 80% when the values of the Darcy coefficient are decreased from 10 - 2 to 10 - 5 . [ABSTRACT FROM AUTHOR]

The time-fractional derivative based on the Grunwald–Letnikove derivative of the 2D-ISPH method is applying to emulate the dual rotation on MHD natural convection in a hexagonal-shaped cavity suspended by nano-encapsulated phase change material (NEPCM). The dual rotation is performed between the inner fin and outer hexagonal-shaped cavity. The impacts of a fractional time derivative α 0.92 ≤ α ≤ 1 , Hartmann number Ha 0 ≤ H a ≤ 80 , fin length 0.2 ≤ L Fin ≤ 1 , Darcy parameter Da 10 - 2 ≤ D a ≤ 10 - 4 , Rayleigh number Ra 10 3 ≤ R a ≤ 10 6 , fusion temperature θ f 0.05 ≤ θ f ≤ 0.8 , and solid volume fraction φ 0 ≤ φ ≤ 0.06 on the velocity field, isotherms, and mean Nusselt number Nu ¯ are discussed. The outcomes signaled that a dual rotation of the inner fin and outer domain is affected by a time-fractional derivative. The inserted cool fin is functioning efficiently in the cooling process and adjusting the phase change zone within a hexagonal-shaped cavity. An increment in fin length augments the cooling process and changes the location of a phase change zone. A fusion temperature θ f adjusts the strength and position of a phase change zone. The highest values of Nu ¯ are obtained when α = 1 . An expansion in Hartmann number Ha reduces the values of Nu ¯ . Adding more concentration of nanoparticles is improving the values of Nu ¯ . [ABSTRACT FROM AUTHOR]

The current study treats the magnetic field impacts on the mixed convection flow within an undulating cavity filled by hybrid nanofluids and porous media. The local thermal non-equilibrium condition below the implications of heat generation and thermal radiation is conducted. The corrugated vertical walls of an involved cavity have T c and the plane walls are adiabatic. The heated part is put in the bottom wall and the left-top walls have lid velocities. The controlling dimensionless equations are numerically solved by the finite volume method through the SIMPLE technique. The varied parameters are scaled as a partial heat length (B: 0.2 to 0.8), heat generation/absorption coefficient (Q: − 2 to 2), thermal radiation parameter (Rd: 0–5), Hartmann number (Ha: 0–50), the porosity parameter (ε: 0.4–0.9), inter-phase heat transfer coefficient (H*: 0–5000), the volume fraction of a hybrid nanofluid (ϕ: 0–0.1), modified conductivity ratio (kr: 0.01–100), Darcy parameter D a : 1 0 - 1 to 1 0 - 5 , and the position of a heat source (D: 0.3–0.7). The major findings reveal that the length and position of the heater are effective in improving the nanofluid movements and heat transfer within a wavy cavity. The isotherms of a solid part are significantly altered by the variations on Q , R d , H ∗ and k r . Increasing the heat generation/absorption coefficient and thermal radiation parameter is improving the isotherms of a solid phase. Expanding in the porous parameter ε enhances the heat transfer of the fluid/solid phases. [ABSTRACT FROM AUTHOR]

The entropy generation from convective hybrid nanofluid flow within the odd-shaped geometries using the finite element method is examined is examined. The flow domain is filled by variable porosity and permeability porous media. Also, the thermal conductivity is assumed to be heterogeneous, and the Brinkman extended non-Darcy model is applied to simulate the porous medium. The geometry is considered partially/fully filled by the porous medium and four cases are assumed, namely, only the horizontal channel is a porous (case 1), only the vertical channel is a porous (case 2), the entire domain is a porous (case 3) and the entire domain is a non-porous (case 4). Different designs of the odd-geometry are taken into account based on the aspect ratio. The characteristic-based split (CBS) based on semi-implicit (SI) scheme is used to treat the governing equations. Simulations are carried out for various values of the maximum Darcy parameter Da max , alumina-copper volume fraction ϕ Al , ϕ Cu and different conditions of the porous domain. It is noted that the case of the heterogeneous thermal conductivity maximizes the irreversibility from heat transfer and total entropy generation. Also, a weakness in values of the average Bejan number is obtained as the Rayleigh number is grown, regardless the porous conditions. [ABSTRACT FROM AUTHOR]

This work deals with natural convection flow resulting from rotating circular cylinders in a horizontal wavy cavity fully filled by nanofluid. The horizontal wavy cavity was saturated by three layers of heterogeneous porous media. Incompressible smoothed particle hydrodynamics (ISPH) method is used to solve the non-dimensional governing equations of the current physical problem. Three circular cylinders are carrying a hot temperature with a uniform circular velocity inside a horizontal wavy cavity. Effects of physical parameters including circular cylinder radius (0.05 ≤ R c ≤ 0.3) , Darcy parameter (10 - 3 ≤ Da ≤ 10 - 5) , Rayleigh number (10 3 ≤ Ra ≤ 10 5) , nanoparticles volume fraction (0 ≤ ϕ ≤ 6 %) , and paddle lengths (0.05 ≤ L paddl ≤ 0.2) on fluid flow and heat transfer were examined. Results revealed that an increase on radius of inner cylinders rises temperature distributions and nanofluid flow. A decrease on Darcy parameter weakens fluid flow. A growth on paddle lengths enhances velocity field in all the porous layers. In the current simulations, ISPH method showed a well performance in simulating natural convection flow of nanofluid inside a novel geometry (horizontal wavy cavity). [ABSTRACT FROM AUTHOR]

In this study, 3D-SIMPLE algorithm in the finite volume method (FVM) is introduced for investigating the convective flow of a power-law nanofluid within a cubic enclosure. The three-dimensional domain is filled by a heat-generating and 3D-heterogeneous porous media. The non-Newtonian power-law nanofluid is simulated using the two-phase model and case of the shear thickening fluids is considered. Three different levels of heterogeneous porous media and three values of power-law indices are investigated on the temperature, streamlines, nanoparticle volume fraction, isosurfaces of temperature and vertical velocity W. The obtained results indicated that with a homogeneous porous medium and Newtonian fluid, the temperature and nanoparticle volume fraction distributions are raising inside the cubic enclosure. Variations on the nanoparticle volume fraction under impacts of buoyancy ratio and thermophoresis parameters are reflecting the essential of the non-homogeneous distributions of the nanoparticle volume fraction. The maximum temperature rose in the cases of Newtonian fluid and homogeneous porous medium. [ABSTRACT FROM AUTHOR]

This correction notice addresses an error in the affiliation details of the second author, Izharul Haq, in an article titled "Analysis of thermally stratified micropolar Carreau–Yasuda hybrid nanofluid flow with Cattaneo–Christov heat and mass flux." The original article incorrectly listed the affiliation as 'College of Sciences and Human Studies (CSHS), Mohammad Bin Fahd University, Al Khobar Dammam, Saudi Arabia,' when it should have been 'College of Sciences and Human Studies (CSHS), Prince Mohammad Bin Fahd University, Al Khobar Dammam, Saudi Arabia.' The correction has been made to the original article. The publisher, Springer Nature, maintains a neutral stance on jurisdictional claims and institutional affiliations. [Extracted from the article]

This document is a retraction note from the journal Scientific Reports. The article in question, titled "Second-order convergence analysis for Hall effect and electromagnetic force on ternary nanofluid flowing via rotating disk," has been retracted by the editors due to concerns raised about nonsensical phrases, irrelevant references, and issues with authorship. The authors have not provided satisfactory responses to these concerns, leading the editors to lose confidence in the results and conclusions presented. Some of the authors have not confirmed their agreement or disagreement with the retraction, while others have not responded to correspondence from the editors. [Extracted from the article]

Nanofluids hold paramount importance in various fields, notably in thermal engineering, due to their exceptional thermal conductivity and heat transfer properties. This heightened efficiency makes nanofluids invaluable in enhancing the performance of cooling systems, heating processes, and thermal management applications. Keeping in view these important applications, this study involves the analysis of ternary hybrid nanofluid containing Cu\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{Cu}}$$\end{document}, TiO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{TiO}}_{2}$$\end{document}, and SiO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{SiO}}_{2}$$\end{document} in water on a porous stretchy three-dimensional surface incorporating thermal radiation, thermophoretic forces, chemical reaction, Joule heating with convective and mass flux conditions. The leading equations rendered to dimensionless notation through the application of similarity transformation. Subsequently, the solution to the transformed equation is acquired using the bvp4c method. As outcome of the work, an elevated thermophoresis factor leads to an expansion of the concentration, whereas a lessening tendency is noted for Schmidt number, Brownian motion and chemical reactivity factor. The thermal efficiency of the ternary nanofluid is enhanced by factors such as thermophoresis thermal radiation, Biot number, Eckert number, and magnetic field. The computed estimates of drag force at surface reveal the impact of various parameters, indicating that an increase in the porosity parameter leads to a reduction in the surface drag force in x-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$x -$$\end{document} as well as y-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$y -$$\end{document} directions. Conversely, advancement in the magnetic factor causes an escalation in surface drags force along the y-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$y -$$\end{document} direction. Higher Biot number and radiation parameter values enhance the heat transference proportion, whereas higher Brownian motion, thermophoresis, and Eckert number decrease the thermal flow rate. Additionally, escalation in chemical reaction, Schmidt number, and Brownian motions enhances the mass transfer rate. The numerical code for this work has satisfactory promise with the already published work. The insights gained from this analysis can be applied to enhance the efficiency of engineering processes where convective heat transfer is a critical factor, thereby improving the performance of various applications like cooling systems, heat exchangers, and other thermal management systems. The research findings have practical implications for industries seeking to optimize energy utilization and improve the thermal performance of their systems through the utilization of advanced nanofluid dynamics. [ABSTRACT FROM AUTHOR]

"The author (Z. Raizah) extends her appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP.1/334/43)." now reads: "The author (Z. Raizah) extends her appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP.1/300/44)." Correction to: I Scientific Reports i https://doi.org/10.1038/s41598-023-37973-6, published online 03 July 2023 The original version of this Article contained an error in the Acknowledgements section. [Extracted from the article]

The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov–Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNFs) have several applications in various fields due to their unique properties, heat exchangers, refrigeration systems, cooling of electronic devices, solar thermal energy, geothermal energy, nuclear power plants, biomedical engineering, coatings, ceramics, environmental remediation, rocket propulsion, thermal management systems, heat shields, etc. Due to these applications, the existing problem is presented to study the flow of Maxwell HNF for the stretching sheet in a permeable medium comprising of magnesium oxide (MgO) as well as iron (I, II) oxide (Fe3O4) nanoparticles (Nps) for the improvement of heat transport. The magnetic field effects are considered on the flow behavior. Transport of heat as well as mass is computed by using the concepts of Brownian diffusivity, diffusivity due to thermophoresis, and chemical reaction under convective conditions. The flow dynamics have been designed in the form of PDEs (partial differential equations). By using the suitable variables of similarity, higher-order nonlinear PDEs have been converted into ODEs (ordinary differential equations). Simulation of these ODEs of higher order is performed by using the parametric continuation method (PCM). In this study, it is examined that the NF and HNF velocity is reduced due to greater magnetic field parameters and volume fraction of Nps. Further, the increasing role of the NF and HNF temperature is obtained for the parameters of Brownian and thermophoresis. [ABSTRACT FROM AUTHOR]

Copper Cu\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left( {{\text{Cu}}} \right)$$\end{document} and gold Au\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left( {{\text{Au}}} \right)$$\end{document} nanoparticles have been studied for a variety of applications in a base fluid blood including drug delivery is used as a carrier for drugs, allowing for targeted delivery to specific cells or tissues in the body, as a biosensors to detect specific biomolecules and pathogens in blood. These biosensors can be utilized for medical diagnostics, food safety testing and environmental monitoring. Also, copper and gold nanoparticles in blood are utilized for wound healing, cancer therapy, photothermal therapy and imaging, etc. Due to above applications, copper and gold are immersed as solid nanoparticles in blood (pure fluid) in current investigation. This article's main objective is to scrutinize the mixed convective flow of a hybrid (copper and gold/blood) nanoliquid made of micropolar Carreau–Yasuda fluid. The flow at the stagnant point passes by a Riga plate that has been convectively heated. The features of thermal and mass transportation are greatly boosted by including the model of thermal and mass flux proposed by Cattaneo–Christov. The motile microorganism mechanism is also examined on the flow behavior. The consequences of radiant heat, chemical reactions, Brownian motion, and thermal diffusivity are considered. Additionally, the outcomes of thermal and solutal stratification are applied to problem under consideration. The design of the current model uses higher-order partial differential equations (PDEs) that are shifted to ordinary differential equations (ODEs) by employing appropriate variables and then have been evaluated using homotopy analysis approach (HAM). Several flow parameters are employed to determine the variation in various flow patterns. Tables are used to discuss drag forces, heat and mass transport rates in relation to many relevant parameters. The prime outcomes of the work are that improving the estimates of nanoparticles concentration causes the thermal distribution to rise and velocity distribution to retard. The acceleration of the Weissenberg number elevates the velocity distribution. The raising of thermal stratification factor causes the hybrid nanoliquid temperature to reduce. The microorganism’s outline declines against the amplifying estimates of bioconvection Lewis number and microorganism’s stratification factor. The stretching parameter improves the velocity of nanofluid. [ABSTRACT FROM AUTHOR]

Applications in research and engineering have been found for microfluidic technologies and microfluidic devices based on micro-electromechanical systems. This work investigates Darcy-Forchheimer's nanofluid flow past a spinning disk with microorganisms. The disk considers the effect of a porous medium. The energy equation incorporates heat source and thermal radiation, whereas the mass equation accounts for the impact of chemical reactions. The Buongiorno nanofluid theory is also analyzed in the viscous flow. The role of Stefan blowing is examined by analyzing the rate of transference of mass at the surface of a disk. The flow equations are initially converted into a set with one independent variable and then solved numerically using the Bvp4c method on MATLAB software, which is integrated with the shooting process. The graphical representation of momentum, thermal, mass species, and microorganisms field is used to analyze the behavior of these differentiated physical quantities. The drag force, microorganism, Sherwood number, and Nusselt number are computed for various physical factors. The findings indicate that an increase in the Stefan blowing factor results in improved gradients of radial velocity. The increasing values of the porosity number decreased the liquid velocity. The greater thermal field was a consequence of the involvement of both the thermophoretic force and Brownian motion.Graphical abstract: Applications in research and engineering have been found for microfluidic technologies and microfluidic devices based on micro-electromechanical systems. This work investigates Darcy-Forchheimer's nanofluid flow past a spinning disk with microorganisms. The disk considers the effect of a porous medium. The energy equation incorporates heat source and thermal radiation, whereas the mass equation accounts for the impact of chemical reactions. The Buongiorno nanofluid theory is also analyzed in the viscous flow. The role of Stefan blowing is examined by analyzing the rate of transference of mass at the surface of a disk. The flow equations are initially converted into a set with one independent variable and then solved numerically using the Bvp4c method on MATLAB software, which is integrated with the shooting process. The graphical representation of momentum, thermal, mass species, and microorganisms field is used to analyze the behavior of these differentiated physical quantities. The drag force, microorganism, Sherwood number, and Nusselt number are computed for various physical factors. The findings indicate that an increase in the Stefan blowing factor results in improved gradients of radial velocity. The increasing values of the porosity number decreased the liquid velocity. The greater thermal field was a consequence of the involvement of both the thermophoretic force and Brownian motion. [ABSTRACT FROM AUTHOR]

Significant applications of chemical reaction in flow using a curve sheet include metabolic, plastic extrusion and biochemical engineering. A few instances include the management of moisture and temperature supplies during an agricultural fair and the transmission of energy in a drizzly cooling tower. The current study aims to examine the heat and mass transmission for Darcy–Forchheimer flow induced by the curved stretch surface looped in a circle of radius R\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R$$\end{document}. The flow is influenced by heat generation and thermal radiation with the effects of chemical reactions. Kerosene oil (KO) is used as the base fluid while three different types of nanoparticles, GO,ZrO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{GO}}, \,{\text{ZrO}}_{2}$$\end{document} and SiO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{SiO}}_{2}$$\end{document} are mixed with it. Convective heat conditions are incorporated in this model. A curvilinear coordinates system is studied to build the mathematical model of the flow condition under certain assumptions and then solved using the bvp4c approach in MATLAB. The effects of physical and geometrical characteristics relevant to this analysis on dimensionless physical quantities of interest are discussed using the necessary graphs and tables. According to the results, the Darcy–Forchheimer and porosity parameters caused a fall in the velocity profile, whereas the curvature parameter was found to cause an enhancement in the velocity profile. Our finding exhibits that GO\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{GO}}$$\end{document} has a greater influence on ZrO2andSiO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{ZrO}}_{2} \;{\text{and}}\;{\text{SiO}}_{2}$$\end{document}. Thermal distribution augments with growth in radiative flow and Biot number while has declined with the upsurge in curvature factor. Growth in curvature factor has supported the behavior of concentration distribution and has been opposed by an upsurge in chemically reactive factor and Schmidt number. A comparison of the results obtained here with those that have already been published in the relevant literature has been made with outstanding achievement. [ABSTRACT FROM AUTHOR]