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Present research work explores the three‐dimensional nanofluid flow across a horizontal surface with bi‐directional deviation of velocity in power‐law index n. Porosity, the ohmic effect with other parameters, thermophoresis, Prandtl number, Schmidt number, and Brownian motion in the flow geometry are taken into consideration. Dimensional nonlinear formulations are changed into dimensionless expressions by employing the appropriate similarity transformation. Utilizing shooting procedure and the fourth‐fifth‐order Runge–Kutta integration approach, the numerical result has been achieved, and velocity, temperature, and concentration profiles are presented through graphs to illustrate the findings. The current outcome has numerous industrial applications, including the production of paper, metal extrusion, and optical fiber. The major findings of the present research are good agreement compared to the data that are accessible in the limiting instance compared with the earlier results. [ABSTRACT FROM AUTHOR]

The present study examined the relationship between upper limb muscle power and shooting velocity in elite male youth rink hockey players. Seventeen participants (age: 18.2 ± 1.44 years) underwent assessments of upper limb power and shooting velocity. Upper limb power was evaluated through bench press exercises, including indirect 1RM, mean power, and peak power. Shooting velocity was measured using a shooting test, including static drive shot, static slap shot, dynamic drive shot, and dynamic slap shot techniques. Results showed significant positive correlations between upper limb power and shooting velocity in static slap shot (r = 0.62, p = 0.04) and dynamic slap shot (r = 0.86; p < 0.01). Dynamic slap shot also correlated significantly with peak power (r = 0.63; p = 0.03). Differences in shooting velocity were observed among the techniques (F(3,64) = 23.7; p < 0.01, ηp2 = 0.56), with dynamic slap shot displaying the highest velocity and static drive shot the lowest. These findings highlight the positive association between upper limb muscle power and shooting velocity in elite youth rink hockey players. Developing upper limb power can enhance shooting performance. The choice of shooting technique significantly affects shooting velocity, underscoring the importance of optimizing technique for maximizing performance. These findings provide practical insights for coaches and practitioners, informing the design of targeted training programmes aimed at improving shooting velocity in rink hockey players. [ABSTRACT FROM AUTHOR]

The present analysis aims to scrutinize the importance of 3D viscoelastic-nanofluid having gyrotactic motile microorganisms and Cattaneo-Christov heat and mass fluxes over the Riga plate. The flow of current analysis occurs due to the stretching sheet. The Riga plate is frequently used in sophisticated sensor and magnetic lubrication structures. This is a specific electromagnetic actuator that contains a span-shaped arrangement of contrasting/alternating electrodes and a permanent magnet and allows for precise flow regulation. The technical efficiency of nanofluids is apprehended by the assessment of the Buongiorno process, which permits us to analyze the attractiveness of Brownian motion and thermophoresis diffusion. Thermal radiation has a key role in the energy equation and most of the available literature, it has been used linear. In this study, thermal radiation has been used nonlinearly. The transmuted non-linear ODE's traced with shooting technique and results of physical parameters are sketched by implementing bvp4c solver via computational software MATLAB. Numerous essential flow parameters are graphically shown to be of physical significance. The drag force, thermal gradient, concentration, and microorganism's rates are calculated under the effect of various embedded constraints. [ABSTRACT FROM AUTHOR]

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The current study presented here demonstrates the magnetohydrodynamics (MHD) Casson fluid flow within an infinite vertical plate with consequences of Brownian, thermophoresis, and chemically responsive systems. The governing equations are numerically computed by employing a sixth-order Runge–Kutta (R–K) algorithm, whereas Nachtsheim–Swigert (N–S) shooting iteration technique has been used as the main tool for calculating the current statement. The novelty of this study is dealing with the impression of Brownian and thermophoresis effect using shooting technique. The nonlinear governing problems have been transformed into coupled nonlinear ordinary differential equations using a suitable transformation. Numerical simulation is presented for the various interesting profiles. The velocity, temperature, and concentration profiles along with skin fraction, Nusselt, and Sherwood number take into account with the varying contributions of the parameters and deployed through graphs and tables. However, one of the current study's key findings is that skin friction improves with expanding values of the thermal convective parameter while diminishing with increasing values of the Casson term, magnetic factor, and Eckert number. The current research has an enormous demand for Brownian and thermophoresis effects within the fields involving cosmology, power systems, ionized studies, and nanotechnology. [ABSTRACT FROM AUTHOR]

The present study aims to investigate the steady state mixed convection flow for a viscous incompressible fluid along a cantilever shape. The study has analyzed the impact of mixed convection boundary layer flow behavior and heat transfer characteristic of the cantilever shape. The leading equations for the said problem are the Navier-Stokes and energy equations. These leading equations are converted into ordinary differential equations using the stream function formulation, and the numerical solution is obtained using the shooting technique with BVP4C and built in MATLAB program. The impact of dimensionless parameters such as n, Pr, and λ on the velocity and temperature profile within the boundary layer of the cantilever cylinder is presented graphically. The results for velocity slope and temperature gradient under the effects of various emerging parameters are presented in tables. The study has concluded that mixed convection parameter has a significant impact on the velocity and temperature distribution, as well as on the velocity slope and temperature gradient rates along a cantilever shape geometry. The outcomes of the current study can be utilized for the design and optimization of various engineering devices involving cantilever shapes. Further, research regarding the impact of other parameters on the cantilever shape including heat transfer characteristics can be conducted using the approach presented in this study. The novelty of the current work can be claimed by saying that for reduced gravity, other forces involved in the flow model induced the fluid motion and temperature gradient.

The present study aims to investigate the steady state mixed convection flow for a viscous incompressible fluid along a cantilever shape. The study has analyzed the impact of mixed convection boundary layer flow behavior and heat transfer characteristic of the cantilever shape. The leading equations for the said problem are the Navier-Stokes and energy equations. These leading equations are converted into ordinary differential equations using the stream function formulation, and the numerical solution is obtained using the shooting technique with BVP4C and built in MATLAB program. The impact of dimensionless parameters such as n , Pr, and λ on the velocity and temperature profile within the boundary layer of the cantilever cylinder is presented graphically. The results for velocity slope and temperature gradient under the effects of various emerging parameters are presented in tables. The study has concluded that mixed convection parameter has a significant impact on the velocity and temperature distribution, as well as on the velocity slope and temperature gradient rates along a cantilever shape geometry. The outcomes of the current study can be utilized for the design and optimization of various engineering devices involving cantilever shapes. Further, research regarding the impact of other parameters on the cantilever shape including heat transfer characteristics can be conducted using the approach presented in this study. The novelty of the current work can be claimed by saying that for reduced gravity, other forces involved in the flow model induced the fluid motion and temperature gradient. [ABSTRACT FROM AUTHOR]

Carbon nanotubes are very desirable for use in the production of electrochemical appliances due to their attractive properties, which include strong tensile strength, high conductivity of electricity, and chemical, thermal, and mechanical durability. Considering these fascinating properties of carbon nanotubes, we set out to investigate the numerical analysis for the steady 3D magnetic effects of heat and mass transmission on the flow of a Casson (non-Newtonian) hybrid nanofluid consisting of SWCNT and MWCNT combined with water as the base fluid across a permeable stretched sheet. The heat transfer induced by a rotating inclined stretched sheet is analyzed in relation to significant factors such as the rotational parameter, heat generation/absorption, the inclination angle parameter, heat radiation, and homogeneous–heterogeneous reactions. Also, the efficiency of hybrid nanofluid is studied with different shape factors. The physical flow model is then described as a set of partial differential equations that are subsequently transferred into an appropriate system of coupled nonlinear ordinary differential equations using the requisite similarity variables. In order to compute the transformed non-dimensional BVP model, the Runge–Kutta fourth-order methodology is used in conjunction with the shooting procedure. The graphical result shows that raising the heat source parameter and the Biot number increase the temperature profile, which improves the thermal boundary layer. The key characteristics of important flow variables are shown in graphs and tables, and the present findings are compared to prior studies, which show significant agreement. Nusselt number and friction drag analysis are also examined for fluid flow behavior. The results might help increase the performance of thermal engineering engines and equipment in a variety of industrial and thermal systems. [ABSTRACT FROM AUTHOR]

AbstractThe nanofluids exclusively enhance the thermal significance of many engineering and industrial processes including the manufacturing processes, chemical reactions, polymers, thermal devices, heating systems, solar energy etc. The presence of porous medium and suction/injection phenomenon incorporates key importance in the petroleum engineering and plasma physics. The objective of current work is to present a theoretical analysis for investigating the bioconvective flow of Maxwell nanofluid with applications of suction/injection effects. The flow is causing by porous moving surface. The radiative phenomenon with nonlinear expressions is adopted. The chemical reaction features are used for analysis of concentration phenomenon. Modified Cattaneo–Christov approach is followed to model the problem. A set of dimensionless variables are used for simplifying the modeled equations. The solution procedure is subject to implementation of shooting scheme. Graphical explanation of problems is presented in order to evaluates the role of different parameters. Physical behavior of problem is focused and justified in details. It is noted that heat and mass transfer enhances due to suction/injection parameter. The temperature profile reduces due to thermal relaxation parameter. Current results reveal significance in the ehat exchangers, improving the sustainability of thermal systems, controlling the cooling processes, fertilizes, biofuels etc. [ABSTRACT FROM AUTHOR]

The purpose of this study was to analyse the differences on the shooting score and shooting technical parameters with 50 m rifle three positions, and to find the key technical factors of shooting performance in international-level 50 m rifle shooters. A SCATT MX-02 optoelectronic shooting test system was used to collect shooting score and shooting technical variables. There was a significant effect of shooting position in shooting performance, aiming accuracy, stability of hold, stability of triggering (ANOVA, position, p < 0.05). PCA identified four principal components from 8 shooting technical variables, namely stability of hold, aiming accuracy, stability of triggering and aiming time. PCR indicated that these four components were able to account for 67.1% of the variance in standing shooting, 75.9% in kneeling, and 80.2% in prone. From these, the aiming ability was the most important component, which could explain 28.5% of the variance in standing shooting, 38.4% in kneeling, and 33.8% in prone. With the help of optoelectronic training system, these components should be in focus by coaches and athletes when conducting tests and training. [ABSTRACT FROM AUTHOR]

This study investigates the heat transmission during the flow of nanofluid (CNTs + Pure Water) in the presence of partial slip boundary conditions. Flow analysis is explored through the examination of velocity slip and stagnation-point. To analyze heat transport, the energy equation considers the impacts of thermal radiation and viscous dissipation. The nanofluid is considered over a vertically stretched cylinder subjected to thermal and velocity slips. Additionally, the presence of heat sources and sinks is also reported. The partial differential equations arising from the problem are obtained through mathematical modeling and then transformed into ordinary differential equations (ODEs) using appropriate dimensionless variables. Finally, the solutions to the governing system of ODEs and boundary conditions are obtained graphically through the shooting technique (bvp4c). As significant results, it is found that the velocity of nanofluid (CNTs + Pure Water) increases for a higher amount of nanoparticles, curvature, mixed convection, and velocity ratio parameters. At the same time, it decays against the velocity slip parameter. An increase in velocity ratio, thermal slip, and heat sink parameters causes a decline in the temperature of the nanofluid (CNTs + Pure Water). At the same time, it is boosted through a higher heat source, thermal radiation, curvature parameters, Eckert number, and a higher amount of nanoparticles. The coefficient of skin friction is minimized by using higher velocity slip and mixed convection parameters while it increases for a higher amount of nanoparticles. A higher amount of nanoparticles and thermal radiation parameters intensifies the Nusselt number, and it is reduced through increments in the Eckert number and thermal slip parameter. In overall observation, the impacts of MWCNTs are efficient. [ABSTRACT FROM AUTHOR]

This article explains the MHD Casson nanofluid flow in the presence of chemical reaction coefficient past a linear stretching surface along with the slip condition. Mainly, the analysis of heat and mass transfer in the presence of Brownian motion and the thermophoretic diffusion effect is performed. Mathematical modeling for the law of conservation of mass, momentum, hear and concentration of nanoparticles is executed. Governing nonlinear partial differential equations are transformed into the dimensionless nonlinear ordinary differential equations by using appropriate transformations. To achieve numerical solution for the considered model, shooting technique and Adams-Moulton method of fourth order are used to obtain the numerical results via the computational program language FORTRAN. Comparison between the obtained results and previous works are well in agreement was observed. For the velocity, temperature, and concentration profiles, numerical computations are conducted. The effects slip parameter, velocity ratio parameter, Casson parameter, Casson parameter taken the problem. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed. It is noted that the skin-friction coefficient decreases for the larger values of velocity ratio parameter, slip parameter, and increases with an increasing value of Casson parameter. It is also found that enhancing the chemical reaction parameter leads to decrease in concentration profile. In addition, physical quantities of absorption like skin friction, local Nusselt and Sherwood numbers are also shown graphically.

The present study examined the relationship between upper limb muscle power and shooting velocity in elite male youth rink hockey players. Seventeen participants (age: 18.2 ± 1.44 years) underwent assessments of upper limb power and shooting velocity. Upper limb power was evaluated through bench press exercises, including indirect 1RM, mean power, and peak power. Shooting velocity was measured using a shooting test, including static drive shot, static slap shot, dynamic drive shot, and dynamic slap shot techniques. Results showed significant positive correlations between upper limb power and shooting velocity in static slap shot (r = 0.62, p = 0.04) and dynamic slap shot (r = 0.86; p < 0.01). Dynamic slap shot also correlated significantly with peak power (r = 0.63; p = 0.03). Differences in shooting velocity were observed among the techniques (F(3,64) = 23.7; p < 0.01, ηp2 = 0.56), with dynamic slap shot displaying the highest velocity and static drive shot the lowest. These findings highlight the positive association between upper limb muscle power and shooting velocity in elite youth rink hockey players. Developing upper limb power can enhance shooting performance. The choice of shooting technique significantly affects shooting velocity, underscoring the importance of optimizing technique for maximizing performance. These findings provide practical insights for coaches and practitioners, informing the design of targeted training programmes aimed at improving shooting velocity in rink hockey players.

This study aimed to report the shooting velocities and to assess the differences in shot velocity according to the techniques used in elite youth male rink hockey players. Fifteen rink hockey players (age = 18.40 ± 1.44 year; body mass = 73.52 ± 6.02 kg; height = 1.76 ± 0.06 m; BMI = 23.61 ± 2.12; sports experience = 6.44 ± 1.76 years) participated in this cross-sectional study. Shooting velocities were assessed for four techniques: slap shot without approach run, drive shot without approach run, slap shot with approach run, and drive shot with approach run. Shooting velocity measurements were conducted using a radar Stalker ATS systemTM. The results demonstrated that drive shots consistently achieved higher velocities compared to slap shots (F(3,56) = 23.9 p < 0.01, ηp2 = 0.58). Additionally, incorporating an approach run significantly increased shooting velocities for both techniques (p < 0.01). These findings hold significant implications for coaches and players seeking to optimize shooting performance in rink hockey.

This study investigates the impact of radiative heat flux phenomena and magnetized Casson nanofluid flow on boundary layer flow along a non-linear stretching surface. Brownian motion and thermophoresis effects are used to highlight the properties of the nanofluid, including electrical conductivity. The flow curves and fluid behavior of particle suspensions in lithographic coatings used to make printing paints are well-described by the nonlinear Casson framework. Suction, chemical reaction, and a homogeneous magnetic field are all considered. An effective Levenberg-Marquardt Methodology (LMM) for artificial neural networks (ANNs) method is presented in this article. The LMM is one of the back-propagation algorithms with the lowest nonlinear latency. The required changes are necessary to convert a quasi-network of partial differential equations (PDEs) expressing the chemical reaction of the Casson nanofluid and radiative heat flux into a set of standards. The couple system regarding the model are facilitated via numerical shooting algorithm The compared to prior findings, the current ones have a very high degree of accuracy. The effects of different factors on the rate of heat transfer, the skin friction coefficient, the concentration of nanoparticles, the Sherwood number, the velocity, and the temperature profiles are illustrated in a tabular and visual form. The temperature and concentration fields exhibit the opposite effect on velocity as magnetic parameters change. The fluid's velocity is slowed down by a Lorentz force that is stronger at greater values of the magnetic field. Due to the suction parameter, the thickness of the momentum, temperature, and concentration boundary layers decreases. In physical terms, pressure forces are generated in the flow when the suction parameter is positive, and the opposite occurs when the suction parameter is negative. It is revealed that enhancement in thermal and concentration phenomenon is predicted by increasing Casson fluid parameter. For ANN analysis, the gradient numerical values reduced upon enhancing the number of epoch.

The aggregation of nanoparticles is a major phenomenon having broad consequences in many fields. In order to fully utilize the capabilities of nanoparticles in a variety of applications and to evaluate the effects that they will have on the environment and biological systems, it is crucial to comprehend and manage aggregation. To develop and improve nanoparticle-based technology, researchers are still learning more about the aggregation processes. Thus, the present study investigates the combined effects of velocity slip and nanoparticle aggregation on Heat transfer (HT) analysis of MHD nanofluid (i.e., TiO2-C2H6O2) flow between porous convergent, divergent channel. The modified Krieger–Dougarty and Maxwell–Bruggeman models were utilized for nanoparticle aggregation. The modeling is based on nonlinear PDEs such as continuity, momentum, and heat equations. These equations are transformed into a system of nonlinear ODEs using similarity transformations and then solved numerically and analytically. The analytical solution has been constructed using the ADM method. The present results in particular cases are compared to results obtained by the HAM- package and by the Runge- Kutta Fehlberg 4th–5th order (RKF-45) for validation. The effects of active parameters on the velocity, temperature, concentration, skin friction, and Nusselt numbers are investigated. It is found that nanoparticle aggregation can limit fluid velocity in converging channels by increasing flow resistance through aggregate formation. Individual nanoparticles generate friction and lower velocity, while aggregated nanoparticles boost fluid density and velocity. In addition, it is found that the magnetic field lowers skin friction and increases HT due to Lorentz force, while porosity increases friction and HT. Nanoparticle concentration inversely affects friction, increasing friction without aggregation and decreasing friction with aggregation, with the HT rate rising with increased nanoparticle concentrations.

Blade coating is a technique for coating the moving substrate with a protective fluid layer through the blade as a common smoothing device. The heat transfer and slip effects of the rheological Sisko fluid model for plane coater are considered under blade coating process. This model combines the power-law and Newtonian fluids and taken as the limiting behavior of a blade coating in the stiff blade limit. The flow of greases is the most significant example of this type of fluid, which is easily found in nature and has many practical uses. To solve the non-linear expressions, LAT (Lubrication Approximation Theory) is applied, and a shooting technique is used for numerical solutions. The impacts of several parameters on flow characteristics, particularly the velocity ratio K, the Sisko fluid parameter b, the power-law index n, and the slip parameter α are investigated. The effects of both shear-thinning and shear-thickening behaviors are also investigated. The lubrication pressure and temperature increase with the Sisko fluid parameter b and decrease with the slip parameter α. As material parameter b increases from (0.001–1), 20.7% reduction in coating thickness and a 53.2% pressure reduction is noted as compared to the Newtonian case. [ABSTRACT FROM AUTHOR]

This study aimed to report the shooting velocities and to assess the differences in shot velocity according to the techniques used in elite youth male rink hockey players. Fifteen rink hockey players (age = 18.40 ± 1.44 year; body mass = 73.52 ± 6.02 kg; height = 1.76 ± 0.06 m; BMI = 23.61 ± 2.12; sports experience = 6.44 ± 1.76 years) participated in this cross-sectional study. Shooting velocities were assessed for four techniques: slap shot without approach run, drive shot without approach run, slap shot with approach run, and drive shot with approach run. Shooting velocity measurements were conducted using a radar Stalker ATS systemTM. The results demonstrated that drive shots consistently achieved higher velocities compared to slap shots (F(3,56) = 23.9 p < 0.01, ηp2 = 0.58). Additionally, incorporating an approach run significantly increased shooting velocities for both techniques (p < 0.01). These findings hold significant implications for coaches and players seeking to optimize shooting performance in rink hockey. [ABSTRACT FROM AUTHOR]

In this article, the ways where thermal radiation, besides other sources of heat, influence the magnetohydrodynamic stream of a Jeffery nanofluid across a widening sheet is investigated. To recover the accuracy of the nanofluid model, the effects of viscous indulgence, chemical response, Brownian motion, and thermophoresis have all been incorporated. The mathematical model of this system is first determined in PDEs format and then turned into ODEs format by similarity process. The numerical simulation of the ensuing nonlinear ODEs with subsequent periphery conditions is established by employing the Runge-Kutta fourth-order integration scheme with the shooting technique. The role of various stream considerations on stream, temperature, nanoparticle concentration, skin friction coefficient, Nusselt and Sherwood quantities are conveyed and explored in graphs and tables. In a limiting sense, the legitimacy of computational outcomes is assessed by comparing them to previously published data. The stream distribution quickens as the Deborah quantity accumulates, whereas the temperature and concentration profiles reflect the downward pattern. [ABSTRACT FROM AUTHOR]

This study investigates the impact of radiative heat flux phenomena and magnetized Casson nanofluid flow on boundary layer flow along a non-linear stretching surface. Brownian motion and thermophoresis effects are used to highlight the properties of the nanofluid, including electrical conductivity. The flow curves and fluid behavior of particle suspensions in lithographic coatings used to make printing paints are well-described by the nonlinear Casson framework. Suction, chemical reaction, and a homogeneous magnetic field are all considered. An effective Levenberg-Marquardt Methodology (LMM) for artificial neural networks (ANNs) method is presented in this article. The LMM is one of the back-propagation algorithms with the lowest nonlinear latency. The required changes are necessary to convert a quasi-network of partial differential equations (PDEs) expressing the chemical reaction of the Casson nanofluid and radiative heat flux into a set of standards. The couple system regarding the model are facilitated via numerical shooting algorithm The compared to prior findings, the current ones have a very high degree of accuracy. The effects of different factors on the rate of heat transfer, the skin friction coefficient, the concentration of nanoparticles, the Sherwood number, the velocity, and the temperature profiles are illustrated in a tabular and visual form. The temperature and concentration fields exhibit the opposite effect on velocity as magnetic parameters change. The fluid's velocity is slowed down by a Lorentz force that is stronger at greater values of the magnetic field. Due to the suction parameter, the thickness of the momentum, temperature, and concentration boundary layers decreases. In physical terms, pressure forces are generated in the flow when the suction parameter is positive, and the opposite occurs when the suction parameter is negative. It is revealed that enhancement in thermal and concentration phenomenon is predicted by increasing Casson fluid parameter. For ANN analysis, the gradient numerical values reduced upon enhancing the number of epoch. [ABSTRACT FROM AUTHOR]

Mathematical models and numerical solutions of Williamson fluid flow under influences of various boundary conditions provide important support to experimental studies in the solar energy field. Therefore, the present study is concerned with the effects of forced convection of the viscoelastic boundary layer on a horizontal plate embedded in saturated porous media subjected to constant surface temperature. The study explores the profiles of shear stress, velocity, temperature, and heat transfer coefficient. The governing equations in nondimensional forms are obtained by using a model of Darcy–Forchheimer–Brinkman and finally are solved numerically by using bvp4c with MATLAB package. The results of the numerical solution show an insignificant rise in the distribution of the velocity boundary layer and shear stress profile as the Darcy parameter is increased, while a decrease in the temperature and Nusselt numbers are found. On the other hand, as the viscoelastic parameter is increased, the Darcy parameter shows a reverse response. Finally, insignificant increases in profiles of boundary layer velocity, temperature, shear stress, and Nusselt number are observed at high values of the Forchheimer number. [ABSTRACT FROM AUTHOR]

This investigation peruses the features of temperature and mass transport of the non-Newtonian third-order liquid over an absorbent convective temperature shrinking sheet. The sheet is packed with silver nanoparticles. The Buongiornos modelling uses a particular non-Newtonian third-order liquid with the Brownian movement and the thermophoresis consequences using the non-linear radiation. The non-linear partial differential equations are changed to the ordinary differential equations with similarity transformations. The changed system of equations is then resolved using the numerical Shooting method and the sixth-order Runge-Kutta’s method. The numerically obtained solutions of the velocity profiles, temperature distributions, and concentrations of nanoparticles are discussed graphically. Also, the non-Newtonian parameter reduced the velocity of the liquid, increased the temperature and the concentration profiles throughout the fluid. Ultimately, the qualified systematic analysis is built by the preceding study in restrictive cases and displaingy the best correlation.

Numerical study for flow of a hybrid nanofluid between two coaxial cylinders organized. Nanomaterial consists of graphene oxide (GO) and copper (Cu) nanoparticles in Kerosene oil basefluid. This hybrid nanofluid is taken between two coaxial cylinders. Inner cylinder is fixed while the outer cylinder exhibits rotation. A uniform magnetic field is taken along radial direction for examining flow and heat transfer characteristics. Joule heating is also accounted. Mathematical modeling is terms of ODEs (Ordinary Differential Equations) is constructed. These ODEs are non-dimensionalized through appropriate variables. Such ODEs are then numerically tackled by bvp4c (built-in-shooting technique along with RK-4 algorithm) for solutions developed. Fluid velocity, pressure, skin friction, fluid temperature and Nusselt number are evaluated graphically under the effects of sundry variables. Higher magnetic parameter cause decline in velocity of both hybrid nanofluid (GO + Cu/Kerosene oil) and nanofluid (Cu/Kerosene oil). Temperature of both hybrid nanofluid (GO + Cu/Kerosene oil) and nanofluid (Cu/Kerosene oil) boosts for higher magnetic and Brinkman parameters. Decay in temperature in noticed against higher nanoparticle volume fraction for cupper. Nusselt number intensifies for nanoparticle volume fractions for both copper and graphene oxide nanoparticles.

The purpose of the present communication is to investigate the flow of a radiative electromagnetic-Casson nanofluid past a stretching sheet under the impacts of a chemical reaction and nonlinear thermal radiation. To enrich the blood flow, a modulated viscosity/thermal conductivity dependent temperature/nanoparticles concentration parameter is included in the governing equations. The system of PDEs is transformed to ODEs by invoking similarity transformations and then solved numerically by the well-known fourth-order Runge-Kutta integration scheme based on shooting approach. The main factors affecting the Casson fluid's temperature profiles are revealed. [ABSTRACT FROM AUTHOR]

The differential equation φ′′′ + φφ′′ + α(φ′2 - 1) = 0 where α > 0 is appeared for studying the boundary layer flow past a semi infinitewedge. As a means to prove the existence of solutions verifying (0) = α ≥ √ 1/1-α, φ′(0) = b ≥ 0 and φ′(𝑡) → 1 or - 1 as t → +∞ for 0 < α < 1. We utilize shooting technique and consider the initial conditions φ (0) = α, φ′(0) = b and φ" (0) = c. We demonstrate that there exists an infinitely many solutions where φ′(+∞) = 1. [ABSTRACT FROM AUTHOR]

The present article concentrates on the consequences of melting heat transfer on the chemically reactive flow of Eyring-Powell liquid flow via a semi-permeable curved channel in presence of applied magnetic field. The impacts of two types of chemical reaction namely, homogeneous and heterogeneous are considered in the concentration equation. In addition, the characteristics of heat transport phenomena is also examined with the application of thermal radiation. By adopting a scheme of curvilinear coordinates system along with some appropriate similarity conversions a nonlinear ordinary differential equations is attained. The numerical simulation of the determined velocity and transport equations are estimated by using the shooting procedure. The influence of pertinent factors on the flow equations, surface drag force and rate of heat transport are thoroughly discussed via graphs and table. It is noted from the current study that surface drag force and concentration of the liquid are rises with a rising value of the melting parameter, while fluid velocity and its temperature decreases. [ABSTRACT FROM AUTHOR]

Williamson fluid flux and heat transfer characteristics over horizontal plate via a saturated porous medium at constant surface temperature are examined in this study to determine the impact of forced viscous dissipation. The flow is modeled using a Darcy-Forchheimer-Brinkman model based on conservation laws and associated governing equations. Using appropriate dimensionless variables, the modeled governed equations are transformed into dimensionless differential forms. The higher constrained coupled non-linear differential equations have been reduced to the first order differential equations to find a reliable numerical solution. The Runge-Kutta method and the built-in Matlab function bvp4c are applied in the shooting method to produce a numerical solution. The impact of λx, ϵ, ζx, βx on the velocity profile, temperature, shear stress, and skin friction are illustrated graphically. It is found that the increasing of the Darcy number leads to enhance both velocity and shear stress while the temperature and the Nusselt number are diminished inside the boundary layer. Additionally, it is found that the raising Williamson's parameter causes the temperature to rise while decreasing velocity, shear stress, heat transfer coefficient, and Nusselt number inside the boundary layer. The method applied in the current work is supported by earlier research.

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.

The classical theory of elasticity relies on the perfect structure of matter. No matter how small a medium is, it always stays homogeneous—but the reality is different. Even though the classical continuum mechanics suffices well for describing phenomena that evolve at super‐microscopic scales, it ceases to reproduce reasonable responses when the size effects are pronounced. It is due to the local constitutive equations of classical continuum mechanics, which are devoid of any length scales associated with the underlying microstructure. The gradient‐dependent theory of elasticity redresses this shortcoming by incorporating the kinematic quantities of the corresponding representative volume element by enriching the differential equations with higher‐order spatial and temporal derivatives. In this study, the scaled boundary finite element method is formulated for the equations of motion with higher‐order inertia terms. To this end, the semi‐discretized scaled boundary finite element equations of the medium are derived by introducing the scaled boundary transformation of geometry to the gradient‐enriched equations of motion and applying the Galerkin method of weighted residuals. It is shown that the well‐established available solution methods are incapable of handling the frequency‐domain representation of the derived formulation. Accordingly, a numerical solution method based on the shooting technique is proposed. The solution procedure is formulated for general numerical integration schemes via the infinite Taylor series. The evolution of the impedance‐diffusion matrix and contribution of inter‐subdomain forces and tractions are extracted. Four different numerical integration methods are employed to describe the solution procedure. In addition, a comparison regarding their computational efficiency is presented. For the sake of verification, the scaled boundary finite element solutions of three numerical examples are compared with reference solutions that are obtained using finite element models with extremely fine meshes. The convergence trends are also presented for both h$$ h $$‐ and p$$ p $$‐refinement methods. The results demonstrate the capability of the proposed formulation in reproducing accurate responses. [ABSTRACT FROM AUTHOR]

Our key objective in the present work is to elaborate the concept of activation energy in chemically reactive flow with the help of modeling and computation. The model investigated is fluid flow over a vertical cylinder in the porous medium with chemical reaction and radiation effect. The similarity transform converted the resulting constitutive equations and partial differential equations (PDEs) into ordinary differential equations (ODEs). The resulting non-linear momentum, heat transfer, and mass transfer coupled equations are computed with the Range–Kutta–Fehlberg method. Both assisting and non-assisting buoyant flow conditions are considered, and observed numeric solutions vary with the transport properties. Characteristics of momentum, heat, and concentration under the applied boundary conditions are analyzed. In addition, the increment in activation energy parameters boosts the Lorentz force and mass transfer rate.

The paper intends to analyze numerically the effect of forced convection with viscoelastic boundary on porous media subjected to constant heat flux on the surface. The modified Navier–Stokes equations in nondimensional forms are formulated and modeled with Darcy–Forchheimer–Brinkman to solve the equations using bvp4c with MATLAB package. The numerical results are found for local Nusselt number, shear stress, temperature distribution, and finally the velocity of the boundary layer over a horizontal plate. The analysis includes the influence of several parameters, such as Forchheimer, porous media, Nusselt number, and viscoelastic on distributions of velocity and temperature. Also, the effects comprise the friction and heat transfer coefficients. The numerical results under constant heat flux indicate an increase in shear stress and boundary layer velocity as the Darcy parameter increases and at the same time, the values of temperature and Nusselt number are decreased. A significant increase was observed for the values of Nusselt number, temperature, and shear stress under large values of the Forchheimer parameter. The numerical results show a good agreement with available previous works. [ABSTRACT FROM AUTHOR]

This article investigates the combined effects of nonlinear radiation and magnetic parameter under the velocity slip and temperature jump conditions on the boundary layer flow, arising in magnetohydrodynamics stagnation point flow toward a horizontal moving plate with constant velocity, Uw ${U}_{w}$. The governing mass, momentum, and energy equations are reduced into nonlinear ordinary differential equations with boundary conditions using the relevant similarity variables. The reduced boundary value problem is regulated by the magnetic parameter, slip parameter, temperature jump parameter, Prandtl number, radiation parameter, and temperature ratio parameter. In the absence of an analytic solution, the reduced equations are then demonstrated numerically using the shooting technique. The effects of parameters on the flow domain are analyzed using tables and figures. Moreover, two‐dimensional streamlines are plotted for visualizing fluid flow. It is found that the temperature decreases as the magnetic parameter, slip parameter, temperature jump parameter, and Prandtl number increase, but the opposite scenario is observed when the radiation parameter and temperature ratio parameter increase. [ABSTRACT FROM AUTHOR]

The objective of this paper is to prove the existence, non-existence and the sign of convex and convex-concave solutions of the third-order non-linear differential equation f‴ + f″ + βf′(f′ - 1) = 0 satisfying the boundary conditions f (0) = α ∈ ℝ, f′ (0) = b < 0 and f′ → λ as t → + ∞ where λ ∈ {0,1} and β < 0. The problematic arises in the study of the Mixed Convection Boundary Layer flow over a permeable vertical surface embedded in a Porous Medium according to the mixed convection parameter b<0, the permeable parameter α ∈ ℝ and the temperature parameter β < 0. [ABSTRACT FROM AUTHOR]

Numerical study for flow of a hybrid nanofluid between two coaxial cylinders organized. Nanomaterial consists of graphene oxide (GO) and copper (Cu) nanoparticles in Kerosene oil basefluid. This hybrid nanofluid is taken between two coaxial cylinders. Inner cylinder is fixed while the outer cylinder exhibits rotation. A uniform magnetic field is taken along radial direction for examining flow and heat transfer characteristics. Joule heating is also accounted. Mathematical modeling is terms of ODEs (Ordinary Differential Equations) is constructed. These ODEs are non-dimensionalized through appropriate variables. Such ODEs are then numerically tackled by bvp4c (built-in-shooting technique along with RK-4 algorithm) for solutions developed. Fluid velocity, pressure, skin friction, fluid temperature and Nusselt number are evaluated graphically under the effects of sundry variables. Higher magnetic parameter cause decline in velocity of both hybrid nanofluid (GO + Cu/Kerosene oil) and nanofluid (Cu/Kerosene oil). Temperature of both hybrid nanofluid (GO + Cu/Kerosene oil) and nanofluid (Cu/Kerosene oil) boosts for higher magnetic and Brinkman parameters. Decay in temperature in noticed against higher nanoparticle volume fraction for cupper. Nusselt number intensifies for nanoparticle volume fractions for both copper and graphene oxide nanoparticles. [ABSTRACT FROM AUTHOR]

In this study, the features of Maxwell fluid flow through a stretching sheet (variable thickness) with heat source/sink and melting heat transfer are analyzed. Leading equations of the course are transmuted with suitable similarity transmutations and resolved the subsequent equations mathematically with shooting technique. The effects of the valid parameters on the regular profiles (velocity, concentration, temperature) are elucidated through graphs in two cases (presence and absence of melting). And also, friction factor, transfer rates (mass, heat) are examined with the same parameters and the outcomes are presented in tabular form. A few of the findings are (a) the elastic parameter upsurges the velocity (b) heat source parameter raises the temperature (c) mass transfer rate is lowered by chemical reaction.

While the importance of optimal two-point and three-point jump-shooting performance for securing the desired game outcome on various levels of basketball competition has been well documented, there is a limited amount of scientific literature on what biomechanical adjustments in shooting technique comprise the success of each shooting attempt. Therefore, the purpose of the present study was to examine the difference in kinetic and kinematic characteristics during the preparatory and release phases of the shooting motion between made and missed jump shots. While standing on a force plate, twenty-nine recreationally active males with prior basketball playing experience attempted 10 two-point and 10 three-point jump shots, combining for a total of 580 attempts. Simultaneously, two high-definition cameras were used to capture kinematic characteristics of interest. Higher elbow positioning during the preparatory phase of the shooting motion, relative to the shooter's stature, was shown to be a critical kinematic adjustment that differentiated made from missed two-point jump shots. Alongside identical observations regarding the importance of the elbow placement, keeping the torso in a more erect position during the preparatory phase of the shooting motion, having a greater release angle and vertical jump height at the timepoint of the ball release, and attaining higher maximal trajectory height were critical kinematic adjustments that differentiated made from missed three-point jump shots. [ABSTRACT FROM AUTHOR]

Significant advances in the field of composite structures continue to be made on a variety of fronts, including theoretical studies based on advances in structural theory kinematics and computer models of structural elements employing advanced theories and unique formulations. Plate vibration is a persistently interesting subject owing to its wider usage as a structural component in the industry. The current study was carried out using the Co continuous eight-noded quadrilateral shear-flexible element having five nodal degrees of freedom, which is ground on first-order shear deformation theory (FSDT). For small strain and sufficiently large deformation, the geometric nonlinearity is integrated using the Von Kármán assumption. The governing equations in the time domain are solved employing the modified shooting technique along with an arc-length and pseudo-arc-length continuation strategy. This work explored the effect of fiber angle on the steady-state nonlinear forced vibration response. To explain hardening nonlinearity, the strain and stress fluctuation throughout the thickness for a rectangular laminated composite plate is determined. The cyclic fluctuation of the steady-state nonlinear normal stress during a time period at the centre of the top/bottom surfaces is also provided at the forcing frequency ratio of peak amplitude in a nonlinear response. Because of the variation in restoring forces, the frequency spectra for all fiber angle orientations show significantly enhanced harmonic participation in addition to the fundamental harmonic. [ABSTRACT FROM AUTHOR]

This research communicates the thermal assessment of Sutterby nanofluid containing the gyrotactic microorganisms with solutal and Marangoni boundaries. The applications of melting phenomenon and thermal conductivity are also considered. The flow is confined by a stretched cylinder. The prospective of Brownian motion and thermophoresis diffusions are also taken account via Buongiorno nanofluid model. The problem is formulated with help of governing relations and equations which are altered into dimensionless form via appropriate variables. The numerical scheme based on shooting scheme is employed to access the solution. A comparative analysis is performed to verify the approximated solution. The observations reveal that the velocity profile enhanced with the Marangoni number while a declining velocity profile has been observed with Sutterby nanofluid parameter and Darcy resistance parameter. The nanofluid temperature get rise with thermal conductivity parameter and thermal Biot number. An arising profile of nanofluid concentration is observed for concentration conductivity parameter and buoyancy ratio parameter.

To improve the heat efficiency base fluids (water, engine oil, glycol), the interaction of nanoparticles (nanotubes, droplets, nanowires, metals and non-metals) into such traditional liquids is the most frequent mechanism and attained the researchers attention, especially in current decade. The nanofluid is a suspension of submerged solid particles in base fluids. The nano-materials convinced the applications in the field of nanotechnology, thermal engineering, industrial and bio-engineering. Following to such motivating applications in mind, current research reports the stagnation point flow of radiative micropolar nanofluid over an off centered rotating disk with applications of motile microorganisms. The novel dynamic of thermal radiation and activation energy are also incorporated. The appropriate transformations are utilized to reduce the partial differential equations into dimensionless forms. A numerical shooting scheme is used to obtain the approximate solution with MATLAB software. The effects of prominent parameter on velocity profile, nanofluid temperature, concentration of nanoparticles and microorganism profile are physically incorporated.

Background and Purpose: Studying the effects of suction and injection on heat transportation in nanofluids for time-dependent boundary layer flow is a key topic in fluid dynamics. Aerodynamics and the sciences of space both make extensive use of these types of flow. In this research, nanodiamond and silver nanoparticles in water-type base-fluid nanofluids flow are analyzed under the effects of thermal radiation and non-Fourier theory.Methodology: A mathematical system having certain physical variations of the flow model is converted to a non-dimensional ordinary differential equation system via suitable similarity transformation variables. Then the flow model is numerically solved by RK4 and a shooting technique to describe the dynamics of the nanofluids under varied flow conditions. RK4 with the shooting approach gives a rapid result with high convergence accuracy. The relevant characteristics of physical quantities evaluated by an inclusive numerical scheme are observed for flow pattern, temperature distribution, and nanofluids concentration variations in the presence of suction and injection fluxes.Finding: According to the findings, both ND-H2O and Ag-H2O have outstanding thermal performance characteristics. The Ag-based nanofluid, however, has a better heat transfer capability. To validate the analysis, a graphical and tabular comparison is presented under specified assumptions. The key finding is that, with the injection effect, the heat flow rate is larger than with the suction effect. The unsteadiness parameter causes a drop in the velocity profile, whereas energy distribution rises with this parameter.

Despite its importance and significant contribution to the final game out-come, the free throw shooting motion is greatly understudied. The purpose of this study was to examine kinematic differences between proficient and non-proficient free throw shooters and to determine which variables have the greatest impact on successful free throw shooting performance. Thirteen healthy recreationally active males volunteered to participate in this study. Each participant shot three sets of ten consecutive free throws from the regulation distance from the basket. Each set was performed under 3 minutes with 1-2-minute rest between each set. A high-definition camera recording at 30 fps captured the free throw shooting motion from a sagittal point of view. Video analysis software was used to analyze the following kinematic variables: knee angle, elbow angle, hip flexion, ankle flexion, release angle, shoulder angle, hand release height, and elbow height. The findings of this study suggest that lower elbow positioning influenced by greater knee, ankle, and hip flexion during the preparatory phase of the shooting motion may lead to improvements in free throw shooting accuracy. Moreover, greater ball release height and release angle, as previously suggested, could decrease the margin of error and enhance free throw shooting performance. By using these kinematic variables to create the discriminant function projection model, it is plausible that proficient free throw shooters can be accurately classified in 94% of cases.