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In addition to solar water heating and transformers, these applications of research include heat exchangers and braking fluids, as well as acoustics and microelectronics. The mathematical model of Poiseuille hybrid nanofluid flow through a microchannel is considered with differing thermal conductivity and viscosity parameters. This mathematical model has mainly been developed to cater to the diversity of the hybrid nanofluid properties, which contains oxide and metal nanoparticles, for example, Cu and Al2O3 immersed in water (H2O) and Ethylene glycol (EG) as the base liquid. The substructure for hybrid nanofluid abides by the mixture of 20% water while the rest is filled with EG. Moreover, the perception of entropy is analyzed. The dimensional form of the current problem is deformed into a non-dimensional form using the appropriate choice of similarity transformation. Thence, the Runge–Kutta-Fehlberg method is being used to treat the numerical solution for the problem. The graphs spectacle the entropy, Bejan numbers, and physical behavior of the contributing factors to the flow phenomena. The numerical results of the rate coefficients for these parameters are shown in the table below. Furthermore, a comparison analysis is conducted to confirm the current result with prior work demonstrating a higher degree of concordance. [ABSTRACT FROM AUTHOR]

The purpose of the present investigation is to examine the heat, mass and microorganism concentration transfer rates in the magnetohydrodynamics (MHD) stratified boundary layer flow of tangent hyperbolic nanofluid past a linearly, uniform stretching surface comprising gyrotactic microorganisms as well as nanoparticles. The governing PDEs with relevant end point conditions are molded into a non-dimensional ordinary differential equation (ODE) form by means of the similarity transformation. The numerical solution of dimensionless problem is acquired within the frame of robust Keller-Box technique. The velocity, temperature, mass and motile microorganism density are investigated graphically within the context of different significant parameters. Numerical results have been inspected via plots and table (namely as the local Nusselt number, the local wall mass flux and the local microorganisms wall flux). This article proves that the energy, concentration and motile microorganism density reduce with increase in thermal, solutal and motile density stratification parameters. The asserted outcomes are beneficial to enhance the cooling and heating processes, energy generation, thermal machines, solar energy systems, industrial processes etc.

Household warming, distillation, cooling systems, manufacturing heat, power plants, and irrigation water pumps are all applications for a parabolic trough surface accumulator (PTSC). This research examines the consequences of mixing nanosolid materials on PTSC installed on a solar aircraft wing, as well as the production of entropy. The Newtonian nanofluid model was used to investigate the consequences of thermal radiative fluxing, changing thermal conductivity, and upstream magnetism force limitations. Thermal radiative, and variable thermal conducting, the heat transfer discharge from solar aircraft wings is enhanced. Ordinary differential equations (ODEs) are numerically treated using a method known as the Keller-box method. Thermal radiative and thermal conducting effect adjustments that are positive develop the heat transference coefficient of solar aircraft wings. It is thought that graphene oxide (GO) based kerosene oil (K) can help with PTSC performance monitoring. We will also experiment with different nanoparticle concentrations to see how they affect the system's active characteristics. The thermodynamic performance of GO-K nanofluid has been described better than that of base nanofluid. GO-K has a heat transition rate of 15.03% higher than conventional fluid without GO. Theoretical simulations with documentation can be more useful in improving solar thermal energy schemes. [ABSTRACT FROM AUTHOR]

Researchers across the world have tried to explore the impact of various hybrid nanoparticles in the case of fluid moving over a disk with the inclusion of various effects to investigate heat and made transfer analyses of fluid. The present article is designed to scrutinize the influence of Diathermic oil (DO) with the inclusion of tri-hybrid nanoparticles by adopting a tri-hybrid Yamada-Ota and Xue nanofluid model. The article is novel in the sense that the extension in Yamada-Ota and Xue nanofluid models in the case of tri-hybrid nanoparticles has never studied before in the existing literature. Diathermic oil (DO) is a great quality mineral oil that has been refined to assure long-term service due to its outstanding resistance to thermal cracking and chemical oxidation; also, its high specific heat and thermal conducting offer fast heat loss. Our goal in this work is to compare the concert of the Yamada-Ota and Xue representations for a nanofluid movement between two revolving disks in a spongy medium in light of these astonishing physiognomies. The entire scenario is thought out with different traits. Using the Keller box approach, the governing system's numerical solution is achieved. The feature consequences of ascending constraints solid nanoparticles capacity fraction (0.005 ≤ ϕ = ϕ 1 + ϕ 2 + ϕ 3 ≤ 0.15) , heat ratio θ w , fluid parameter β , porosity parameter M , temperature generating and sink having varieties A ∗ , and B ∗ , radiative parameter Rd , and Eckert number Ec between 0.1 and 2, versus connected outlines are examined. When the variable viscosity parameter (for gases) is positive, the axial velocity decreases; however, when the varying viscidness parameter is negative, the rapidity distribution increases (liquids). [ABSTRACT FROM AUTHOR]

The flow of a fluid across a revolving disc has several technical and industrial uses. Examples of rotating disc flows include centrifugal pumps, viscometers, rotors, fans, turbines, and spinning discs. An important technology with implications for numerous treatments utilized in numerous sectors is the use of hybrid nanofluids (HNFs) to accelerate current advancements. Through investigation of ternary nanoparticle impacts on heat transfer (HT) and liquid movement, the thermal properties of tri-HNFs were to be ascertained in this study. Hall current, thermal radiation, and heat dissipation have all been studied in relation to the use of flow-describing equations. The ternary HNFs under research are composed of the nanomolecules aluminum oxide (Al2O3), copper oxide (CuO), silver (Ag), and water (H2O). For a number of significant physical characteristics, the physical situation is represented utilizing the boundary layer investigation, which produces partial differential equations (PDEs). The rheology of the movement is extended and computed in a revolving setting under the assumption that the movement is caused by a rotatingfloppy. Before the solution was found using the finite difference method, complicated generated PDEs were transformed into corresponding ODEs (Keller Box method). A rise in the implicated influencing factors has numerous notable physical impacts that have been seen and recorded. The Keller Box method (KBM) approach is also delivered for simulating the determination of nonlinear system problems faced in developing liquid and supplementary algebraic dynamics domains. The rate of entropy formation rises as the magnetic field parameter and radiation parameter increase. Entropy production rate decreases as the Brinkman number and Hall current parameter become more enriched. The thermal efficiency of ternary HNFs compared to conventional HNFs losses to a low of 4.8% and peaks to 5.2%. [ABSTRACT FROM AUTHOR]

Solar radiation, which is emitted by the sun, is required to properly operate photovoltaic cells and solar water pumps (SWP). A parabolic trough surface collector (PTSC) installation model was created to investigate the efficacy of SWP. The thermal transfer performance in SWP is evaluated thru the presence of warmth radiation and heat cause besides viscid dissipation. This evaluation is performed by measuring the thermal transmission proportion of the selected warmth transmission liquid in the PTSC, known as a hybrid nano-fluid. Entropy analysis of Oldroyd-B hybrid nano-fluid via modified Buongiorno's model was also tested. The functions of regulating parameters are quantitatively observed by using the Keller-box approach in MATLAB coding. Short terms define various parameters for tables in velocity, shear pressure and temperature, gravity, and Nusselt numbers. In the condition of thermal radiation and thermal conductivity at room temperature, the competence of SWP is proven to be enhanced. Unlike basic nano-fluids, hybrid nano-fluids are an excellent source of heat transfer. Additionally, with at least 22.56% and 35.01% magnitude, the thermal efficiency of AA7075–Ti–6Al–4 V/EO is higher than AA7075–EO. [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]

It is well known that solar energy is the main source of thermal energy coming from the sun responsible for huge operations in engineering studies. It can be seen in the technology of photovoltaic cells, solar streetlights, solar energy plates, and solar water pumping. This study is for investigating solar radiation as well as a method to improve the performance of the solar water pump (SWP) with the use of solar radiation along with nanotechnology. The thermal transfer performance of the pump is checked for the case of many impacts including heat radiations and variable thermal conductivity. An Oldroyd‐B nanofluid with entropy production analysis has been scrutinized as a working coolant liquid in the system. Graphene oxide (GO) and Cu nanoparticles have been employed in engine oil (EO) as the base liquid. It is noticed that the heat transfer performance of SWP increases in the case of amplification in thermal radiation and temperature‐dependent thermal conductivity characteristics. In comparison to low thermal conductivity nanofluid, high thermal conductivity nanofluid provides the best capability for heat transmission. The thermal efficiency of the used (GO/EG) nanofluid has been enhanced by between 7.70% and 26.68% than (Cu/EO) nanofluid. [ABSTRACT FROM AUTHOR]

In order to understand the characteristics of bio-convection and moving microorganisms in flows of magnetized Walters-B nano-liquid, we developed a model employing Riga plate with stretchy sheet. The Buongiorno phenomenon is likewise employed to describe nano-liquid motion in the Walters-B fluid. Expending correspondence transformations, the partial differential equation (PDE) control system has been transformed into an ordinary differential equation (ODE) control system. The COMSOL program is used to generate mathematical answers for non-linear equations by employing the Galerkin finite element strategy (G-FEM). Utilizing logical and graphical metrics, temperature, velocity, and microbe analysis are all studied. Various estimates of well-known physical features are taken into account while calculating nanoparticle concentrations. It is demonstrated that this model's computations directly relate the temperature field to the current Biot number and parameter of the Walters-B fluid. The temperature field is increased to increase the approximations of the current Biot number and parameter of the Walters-B fluid. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explore the behavior of Sutterby nanofluid passed a sloping sheet with a tendency to fluctuate thermal conductivity, radiation and a magnetic field. In a solar parabolic trough collector (PTC) for solar cooling and hydrogen generation, a nanofluid is employed as the running fluid. The Koo-Kleinstreuer-Li (KKL) model is used to calculate effective thermal conductivity and viscosity. The advance results are differentiate with the Lobatto 111A method which strengthens the integration reliability of the current liquid system. Copper oxide-engine oil (CuO-EO) is taken into consideration to address the performance analysis of the current study. The skin coefficient and the local Nusselt number are expressed numerically in the form of a table, whereas other dominant competent parameters on the speed and temperature profiles are discussed numerically and graphically. The radiation parameter slows the rate of heat transfer while increasing the velocity gradient. To test the effect on many device performance parameters, nanoparticle absorption also varies with the growth of Reynolds and Brinkman numbers, entropy creates growth. The thermodynamic action of copper oxide-engine oil (CuO-EO) nanofluid is more noticeable than engine oil (EO) nanofluid oil under similar conditions. CuO-based EO nanofluid system had the best heat transmission efficiency and hydrogen generation. The thermal effectiveness of CuO-EO over EO is characterized by a minimum of 2.89% and a magnitude of 14.79%. Written theory simulations may be more effective in developing solar thermal energy systems. • Here Sutterby nanofluid passed a sloping sheet with radiation, and magnetic field is addressed. • Effective thermal conductivity and viscosity by Koo-Kleinstreuer-Li (KKL) model is used. • Copper oxide-engine oil (CuO-EO) with Lobatto 111A method is considered. • Total entropy rate is calculated through second law of thermodynamics. • Device performance is studied via different parameters. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamics (MHD) viscous Jeffrey heat transport flow past a permeable extending sheet is analyzed. The Alumina ( A l 2 O 3 ) is chosen as nanoparticles immersed in sodium alginate ( SA ) as the based fluid. The effect of heat generation, Ohmic heating and viscous dissipation are also being investigated adopting Tiwari and Das model. The adequate similarity transformation is used to convert the governing equations to non-linear of higher-order ordinary differential equations (ODEs). The numerical solution of the transformed ODEs is accomplished using a finite-difference technique. The results are described in graphs according to selected parameters' values provided. The flow velocity reductions when the porosity parameter is augmented. The thermal distribution is affected by the presence of Pr , M , β , γ ∗ , δ ∗ and ϕ . Deborah number and the volume fraction of nanoparticles affect the skin friction coefficient in opposite ways. A higher volume percentage of nanoparticles and a higher Deborah number are both shown to boost the rate of heat transfer. These findings suggest that the concentration of nanoparticles can be used to manipulate heat transport and nanofluid motions. [ABSTRACT FROM AUTHOR]

A novel hybrid nanofluid was explored in order to find an efficient heat-transmitting fluid to replace standard fluids and revolutionary nanofluids. By using tangent hyperbolic hybrid combination nanoliquid with non-Newtonian ethylene glycol (EG) as a basis fluid and a copper (Cu) and titanium dioxide (TiO2) mixture, this work aims to investigate the viscoelastic elements of the thermal transferring process. Flow and thermal facts, such as a slippery extended surface with magnetohydrodynamic (MHD), suction/injection, form factor, Joule heating, and thermal radiation effects, including changing thermal conductivity, were also integrated. The Keller–Box method was used to perform collective numerical computations of parametric analysis using governing equivalences. In the form of graphs and tables, the results of TiO2–Cu/EG hybrid nanofluid were compared to those of standard Cu/EG nanofluid in important critical physical circumstances. The entropy generation study was used to examine energy balance and usefulness for important physically impacting parameters. Detailed scrutiny on entropy development get assisted with Weissenberg number, magnetic parameter, fractional volumes, injection parameter, thermal radiation, variable thermal conductivity, Biot number, shape variation parameter, Reynolds and Brinkman number. Whereas the entropy gets resisted for slip and suction parameter. In this case, spotted entropy buildup with important parametric ranges could aid future optimization. [ABSTRACT FROM AUTHOR]

Prandtl–Eyring hybrid nanofluid (P-EHNF) heat transfer and entropy generation were studied in this article. A slippery heated surface is used to test the flow and thermal transport properties of P-EHNF nanofluid. This investigation will also examine the effects of nano solid tubes morphologies, porosity materials, Cattaneo–Christov heat flow, and radiative flux. Predominant flow equations are written as partial differential equations (PDE). To find the solution, the PDEs were transformed into ordinary differential equations (ODEs), then the Keller box numerical approach was used to solve the ODEs. Single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) using Engine Oil (EO) as a base fluid are studied in this work. The flow, temperature, drag force, Nusselt amount, and entropy measurement visually show significant findings for various variables. Notably, the comparison of P-EHNF's (MWCNT-SWCNT/EO) heat transfer rate with conventional nanofluid (SWCNT-EO) results in ever more significant upsurges. Spherical-shaped nano solid particles have the highest heat transport, whereas lamina-shaped nano solid particles exhibit the lowest heat transport. The model's entropy increases as the size of the nanoparticles get larger. A similar effect is seen when the radiative flow and the Prandtl–Eyring variable-II are improved. [ABSTRACT FROM AUTHOR]

As a try, this work has been focused in the way towards the effective contribution in the field of solar aviation using renowned nanotechnology. After realizing the causes and effects of traditionally used energy forms, the search of cost-efficient, eco-friendly, and most prominent renewable source leads us back to the solar utilities. Research era of solar radiation-powered aircraft has been in trend. Focusing on that, an efficient numerical model representing the flow and thermal aspects of a parabolic trough surface collector (PTSC) embedded on solar aircraft wings has been adopted for this study. As the first time with the note, an eminent and leading form of thermal efficient fluid of kind, the Casson hybrid nanofluid has been engaged with the expectations of enhanced performance in the solar aircraft wings. To test it, a trending reputable numerical scheme of the Keller-box method has been utilized and the parametrical studies were carried out. The upshots of those studies provide the affable proofs in favor of our expectations towards the improved solar wings with better thermal efficiency. The glimpse of those successes in the parametrical level has been showcased in the forms of tables and graphs. The lateral "x" direction significant about the inertial forces, suspended particle ratio, and skin resistance phenomena, while for the transverse fluidity in the "y" direction were has to be concern about the magnetic interactions, rotational coordinates, viscous nature of the fluid along with the porous states. The power of hybrid nanofluid combos was exposed in higher notes in a unique state of solar aircraft wings. Furthermore, the thermal efficiency of hybrid nanofluids over nanofluids got down to a minimal level of 6.1% and peaked up to 21.8%. [ABSTRACT FROM AUTHOR]

Solar thermal collectors distribute, capture, and transform the solar energy into a solar thermal concentration device. The present paper provides a mathematical model for analyzing the flow characteristics and transport of heat to solar collectors (SCs) from non-Newtonian nanofluids. The non-Newtonian power-law scheme is considered for the nanofluid through partial slip constraints at the boundary of a porous flat surface. The nanofluid is assumed to differ in viscosity and thermal conductivity linearly with temperature changes and the magnetic field is appliqued to the stream in the transverse direction. The method of similarity conversion is used to convert the governing structure of partial differential formulas into the system of ordinary differential ones. Using the Keller box procedure, the outcoming ordinary differential formulas along with partial slip constraints are numerically resolved. A discussion on the flowing and heat transport characteristics of nanofluid influenced by power law index, Joule heating parameter, MHD parameter and slip parameters are included from a physical point of view. Comparison of temperature profiles showed a marked temperature increase in the boundary layer due to Joule heating. The thickness of the motion boundary-layer is minimized and the transport of heat through boundary-layer is improved with the partial slip velocity and magnetic parameters rising. Finally, With an increase in the Eckert number, the distribution of temperature within boundary layer is increased. [ABSTRACT FROM AUTHOR]

Survey of literature unveils that nanofluids are more efficient for heat transport in comparison to the traditional fluids. However, the enlightenment of developed techniques for the augmentation of heat transport in nanomaterials has considerable gaps and, consequently, an extensive investigation for aforementioned models is vital. The ongoing investigation aims to study the 2-D, incompressible Jeffrey nanofluid heat transference flow due to a stretchable surface. Furthermore, the effect of dispersion of graphene nanoparticles in base liquid ethylene glycol (EG) on the performance of flow and heat transport using the Tawari-Das model in the existence of Ohmic heating (electroconductive heating) and viscous heat dissipation is contemplated. The boundary-layer PDEs are reconstituted as ODEs employing appropriate similarity transformation. Keller-Box Method (KBM) is utilized to determine the numerical findings of the problem. Graphene conducts heat greater in rate than all of the other materials and it is a good conductor of electrical energy. Graphene/EG nanofluid is employed to look out the parametric aspects of heat transport flow, drag coefficient, and heat transference rate phenomena with the aid of graphs and tables. The numerical outcomes indicate that concentration and magnetic field abate the shear stresses for the nanofluid. An increase of Graphene nanoparticle volume fraction parameter can boost the heat transport rate. The effect of Prandtl Number is to slow down the rate of heat transport as well as decelerate the temperature. Additionally, the rate of heat transportation augments on a surface under Deborah's number. Results indicate that the temperature of the graphene-EG nanofluid is greater than the convectional fluid hence graphene-EG nanofluid gets more important in the cooling process, biosensors and drug delivery than conventional fluids. [ABSTRACT FROM AUTHOR]

The present article presents a novel idea regarding the implementation of Tiwari and Das model on Reiner-Philippoff fluid (RPF) model by considering blood as a base fluid. The Cattaneo-Christov model and thermal radiative flow have been employed to study heat transfer analysis. Tiwari and Das model consider nanoparticles volume fraction for heat transfer enhancement instead of the Buongiorno model which heavily relies on thermophoresis and Brownian diffusion effects for heat transfer analysis. Maxwell velocity and Temperature slip boundary conditions have been employed at the surface of the sheet. By utilizing the suitable transformations, the modeled PDEs (partial-differential equations) are renewed in ODEs (ordinary-differential equations) and treated these equations numerically with the aid of bvp4c technique in MATLAB software. To check the reliability of the proposed scheme a comparison with available literature has been made. Other than Buongiorno nanofluid model no attempt has been made in literature to study the impact of nanoparticles on Reiner-Philippoff fluid model past a stretchable surface. This article fills this gap available in the existing literature by considering novel ideas like the implementation of carbon nanotubes, CCHF, and thermal radiation effects on Reiner-Philippoff fluid past a slippery expandable sheet. Momentum, as well as temperature slip boundary conditions, are never studied and considered before for the case of Reiner-Philippoff fluid past a slippery expandable sheet. In the light of physical effects used in this model, it is observed that heat transfer rate escalates as a result of magnification in thermal radiation parameter which is 18.5% and skin friction coefficient diminishes by the virtue of amplification in the velocity slip parameter and maximum decrement is 67.9%. [ABSTRACT FROM AUTHOR]

Nowadays, with the advantages of nanotechnology and solar radiation, the research of Solar Water Pump (SWP) production has become a trend. In this article, Prandtl–Eyring hybrid nanofluid (P-EHNF) is chosen as a working fluid in the SWP model for the production of SWP in a parabolic trough surface collector (PTSC) is investigated for the case of numerous viscous dissipation, heat radiations, heat source, and the entropy generation analysis. By using a well-established numerical scheme the group of equations in terms of energy and momentum have been handled that is called the Keller-box method. The velocity, temperature, and shear stress are briefly explained and displayed in tables and figures. Nusselt number and surface drag coefficient are also being taken into reflection for illustrating the numerical results. The first finding is the improvement in SWP production is generated by amplification in thermal radiation and thermal conductivity variables. A single nanofluid and hybrid nanofluid is very crucial to provide us the efficient heat energy sources. Further, the thermal efficiency of MoS2–Cu/EO than Cu–EO is between 3.3 and 4.4% The second finding is the addition of entropy is due to the increasing level of radiative flow, nanoparticles size, and Prandtl–Eyring variable. [ABSTRACT FROM AUTHOR]

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]

This analysis elucidates the magnetized Eyring–Powell nanoliquid flow over a stratified convectively heated cylinder. Rheological flows subjected to heat transportation have crucial contributions in the modern-day industries. We considered the heat transportation under the heat source effects. In addition, the Brownian along with thermophoretic aspects of nanoliquid with thermal radiation are explored. Implementation of relevant variables yields the expressions in differential form. These expressions are evaluated analytically employing homotopy algorithm. The upshots of various parameters are revealed via graphs. A rise in Prandtl number provides less temperature but upsurges the heat transference rate. [ABSTRACT FROM AUTHOR]

In this article, thermal performance of engine oil in the presence of both single and multiple wall carbon nanotubes (SWCNTs and MWCNTs) between two concentric cylinders is presented. Flow is driven with oscillatory pressure gradient and magneto-hydrodynamics (MHDs) effects are also introduced to control the random motion of the nanoparticles. Arrived broad, it is perceived that the inclusion of nanoparticles increases the thermal conductivity of working fluid significantly for both turbulent and laminar regimes. Fundamental momentum and energy equations are based upon partial differential equations (PDEs) that contain thermos-physical properties of both SWCNTs and MWCNTs. The solution has been evaluated for each mixture, namely: SWCNT-engine oil and MWCNT-engine oil. Results are determined for each velocity, temperature, pressure and stress gradient. Graphical results for the numerical values of the emerging parameters, namely: Hartmann number ( M ), the solid volume fraction of the nanoparticles ( ϕ ), Reynolds number ( Re ω ), and the pulsation parameter based on the periodic pressure gradient are analyzed for pressure difference, frictional forces, velocity profile, temperature profile, crux, streamlines and vorticity phenomena. In addition, the assets of various parameters on the flow quantities of observation are investigated. [ABSTRACT FROM AUTHOR]

Retraction of: I Scientific Reports i https://doi.org/10.1038/s41598-021-03392-8, published online 15 December 2021 The Editors have retracted this Article. S. Suriya Uma Devi, Rabha W. Ibrahim, Faisal Shahzad, Mohamed R. Eid, Abdel-Haleem Abdel-Aty, M. Motawi Khashan, and I. S. Yahia did not reply to the correspondence about the retraction. Retraction Note: A brief comparative examination of tangent hyperbolic hybrid nanofluid through a extending surface: numerical Keller-Box scheme. [Extracted from the article]

The motive behind this article is to investigate the impact of triple diffusive convective flowing on Reiner-Philippoff (R-Ph) past a stretchable surface with Avramenko-Blinov-Shevchuk boundary restrictions. The governing determined partial differential equation (PDEs) are converted into ordinary differential equations (ODEs) with the utilization of similarity conversions and handled these equations computationally with the application of a well-recognized computational structure called Cash and Carp method. The dimensionless parameters used in figures and tables range between 0.1 ≤ γ ≤ 1.1 , 0.1 ≤ λ ≤ 2.1 , 0 ≤ Nc 1 ≤ 2 , 0.1 ≤ Nc 2 ≤ 1.3 , 0.1 ≤ Le 1 , L e 2 , Ld 1 , a n d Ld 2 ≤ 2 , 0.1 ≤ Nd 1 ≤ 0.5 , 0.1 ≤ Nd 2 ≤ 0.5 , 0 ≤ R d ≤ 3 , 0.1 ≤ ∊ ≤ 0.5 , 0 ≤ N b ≤ 1 , 0 ≤ N t ≤ 1.2. From numerical outcomes, it is revealed that the velocity field devalues outstanding to an incremental change in the Grashof number factor and the solutal profile escalates by the benefit of an intensification in the Dufour Lewis number. The heat of the fluid amplifies as a consequence of amplification in both linear heat radiation and Brownian diffusion parameters. [ABSTRACT FROM AUTHOR]

The thermal control subject of heat transference encompasses the generation, use, conversion, and transportation of thermal energy. Heat transference is critical in engineering and industrial industries such as food processing, food additive manufacturing, electronic cooling, microturbines, and so on. Because of the intriguing possibilities in sectors such as polymer manufacture, paper production, crystal glass manufacturing, and so on, academics all over the globe have attempted to investigate the influence of heat transmission on fluid past an expanding surface. We constructed a symmetric system relating extended Burgers' nanofluid (BNF) with Fourier's and Fick's laws in a symmetric stretchy slip as part of our investigation. The Cattaneo-Christov mass and heat diffusions principle has been considered. The Buongiorno occurrence is also utilized for the symmetric flowing of nanofluids (NFs) in the generalized Burger's fluid, according to the Cattaneo-Christov connection (CCC). For the numerical solution, using the similarity transformations, the control system that regulates partial differential equations (PDE) was turned into ordinary differential equations (ODE). Using the COMSOL program, the Galerkin finite element method (G-FEM) is utilized to generate mathematical results for non-linear equations. We observed greater temperature and concentration for Fourier-Fick's conditions as compared to revised Fourier-Fick's scenarios. The heat field is raised to produce the calculations of the current Biot quantity and generalized BNF factor. To receive results in the form of figures and tables, the parameter values must be between 0.1 ≤ β 1 ≤ 0.5, 0.2 ≤ β 2 ≤ 0.4, 0.2 ≤ β 3 ≤ 0.4, 0.2 ≤ β 4 ≤ 0.4, 0.1 ≤ M ≤ 1.2, 0.1 ≤ Nr ≤ 0.9, 0.1 ≤ λ ≤ 0.5, 0.2 ≤ K ≤ 1.6, 0.1 ≤ Rd ≤ 1, 0.1 ≤ λ T ≤ 0.3, 0.1 ≤ δ 1 ≤ 0.3, 0.1 ≤ E ≤ 1 and 0.1 ≤ Le ≤ 0.9. The G-FEM investigation of Burgers' nanofluid (BNF) in the presence of heat source, thermal radiative heat flux and Cattaneo-Christov mass and heat flux has not been investigated yet in the available literature. [ABSTRACT FROM AUTHOR]

• Blood-based Ag, Au and TiO 2 nanoparticles are considered for pulsatile flow between concentric chambers. • Overseeing conditions of the figured-out issue are tackled to accomplish the exact solution. • Parameters at various boundaries of the perceptual flow are examined. • Blood based Ag, Au and TiO 2 has a higher hotness move rate when contrasted with the pure blood. The novel theoretical ternary hybrid nanofluid (HNF) model presented in this research focuses on the enhancement of heat transport. In this study, tri-hybrid nanoparticles made of Au, Ag, and TiO 2 are dissolved in the blood, which serves as the base fluid. The traditional Tiwari and Das HNF model has been extended to modify it for the situation of tri-HNF. As a result, A geometrical prototype is depicted utilizing proportion. We created the regulating equations for the analytic solution to this problem. The Bessel and modified Bessel functions are used to solving the velocity, temperature, and pressure fields. The outcomes are computed for each velocity, heat, pressure, as well as stress gradient. Graphic outcomes for the computational amounts of the immerged variables, notably: Hartmann quantity (M), the solid fractional size of the nanomaterial (ϕ), Reynolds quantity (R e β), and the pulsation variable focused on the periodic pressure gradient, are examined for pressure difference, frictional forces, rapidity outline, temperature outline, crux, streamlines, and vorticity phenomena. The tri-hybrid nanofluid (THNF) has better thermal conductivity than the HNF, according to the graphed results. It has also been revealed that the outside magnetic force may regulate velocity, which influences temperature outlines and consequently heat transmission, which can be improved or decreased by managing the magnetized flux. [ABSTRACT FROM AUTHOR]

• Current study is based on emerging technologies in nanofluid electromagnetic sensors. • Mathematical model developed for exponential Riga plate with dual stratification. • Novel radiative heat flux and hermal sink/generation is studied on typical flow. • Keller Box Finite Difference scheme solutions achieved with an excellent correlation. Motivated by emerging technologies in nanofluid electromagnetic sensor systems, a mathematical model is developed for free convective chemically reacting magnetized Buongiorno nanofluid flow along a stretching exponential Riga plate with dual (thermal and solutal) stratification. Additionally, the effects of radiative heat flux and thermal sink/generation are included. The non-dimensional boundary layer conservation equations are solved with the associated boundary constraints using the Keller Box finite difference scheme, and authentication with earlier studies is conducted. With increasing magnetization parameter, velocity is elevated whereas temperature is suppressed. Increasing Grashof number enhances velocity strongly near the sensor surface region but reduces it further towards the free stream. The heat transfer is depleted throughout the boundary layer regime with greater Grashof numbers. The thermal distribution is substantially boosted with increment in radiative flux, heat source, thermophoresis and Brownian motion parameters, whereas it is strongly decreased with increment in Prandtl numbers and thermal stratification. The nanoparticle concentration is markedly reduced with rising nanoparticle solutal stratification, Brownian motion parameter, reacting species term and Schmidt number. However, there is a considerable increment in nanoparticle concentration with high thermophoresis values. An increase magnetization parameter also elevates the drag force and wall heat transfer rate whereas it reduces the species gradient at the wall. With increasing chemical reaction, a weak rise in the wall friction and temperature gradient is noticed, but a significant rise is computed in Sherwood number. [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]

The purpose of this research study is to evaluate the solutions of Titanium and Aluminum alloy nanofluidic model with gyrotactic microorganisms (TAA-NFMGM) by applying stupendous knacks of Bayesian distributed adaptive neural structure (BDANS). The use of nanofluids containing gyrotactic microorganisms in combination with titanium and aluminum alloys have potential applications in diverse fields, including engineering, bioremediation, biomedical devices, biotechnology, and research depending on different factors like design of the system and use of certain microorganism. A dataset for BDANS is generated for the eight different events with Adam numerical technique for TAA-NFMGM by varying Prandtl number (Pr), mixed convection parameter (λ), microorganisms concentration parameter (Ω), bioconvection peclet number (Pe), and bioconvection Lewis number (Lb). The reference data set generated with Adam numerical technique is utilized for numerical calculation of different parameters on TAA-NFMGM by employing the artificial intelligence based BDANS. The accuracy and justification of the performance of BDANS is efficaciously substantiated through negligible level of MSE around 10–10 to 10–13, calculation of regression metrics and distribution of instances of error on histograms with values 10–04 to 10–09 near to reference line. [ABSTRACT FROM AUTHOR]

The communication aims to analyze the conduct of rotating Prandtl nanofluid with the inclusion of effects like MHD, variable species diffusivity, nonlinear warm radiation, convective limit conditions, velocity slip and chemical reaction on fluid moving along a stretchable surface. Buongiorno model is implemented in orde to catch the Brownian movement and thermophoresis impacts by the presence of nanofluids. The effect of viscous dissemination and Joule heating is used in the current review. Using suitable similarity variables, the governing differential conditions with respect to momentum, energy, and concentration are improved into customary, ordinary differential equations and these equations numerically with the shooting technique. The ranges of different dimensionless parameters used in our study are Prandtl fluid parameter 0 ≤ α ≤ 3.5, elastic parameter 1 ≤ β ≤ 7, thermal radiation 1 ≤ Rd ≤ 2, temperature ratio parameter 1 ≤ θ w ≤ 1.6, Eckart number 0.3 ≤ Ec ≤ 0.7, velocity slip parameter 0 ≤ γ 1 ≤ 1, thermophoresis parameter 0.1 ≤ Nt ≤ 4, Brownian motion parameter 0.1 ≤ Nb ≤ 1.5, Prandtl number 1.7 ≤ Pr ≤ −2.6, magnetic parameter 0.1 ≤ M ≤ 0.8, chemical reaction parameter 0.2 ≤ δ ≤ 1, convection parameter 0.3 ≤ γ 2 ≤ 1.1, rotational parameter 0.1 ≤ λ ≤ 0.7, Schmidt number 0.1 ≤ Sc ≤ 0.7, variable species diffusivity 0.1 ≤ ϵ ≤ 0.5 which shows up during mathematical arrangement are shown as tables and charts. These results are enhanced with the data for the heat transfer rate and skin friction coefficients. It is seen that the temperature profile enhanced on account of an increase in temperature convection boundary and mass fraction field raises due to an improvement in species diffusivity parameter. [ABSTRACT FROM AUTHOR]