Efficient Shooting Research Articles

Multiple slips on Darcy–Forchheimer unsteady flow manifested with Cattaneo–Christov heat flux over a stretching sheet

This primary goal of this analysis is to investigate how several slips affect the flow, heat, and mass performance of Darcy–Forchheimer unstable behavior beyond a stretching sheet using a numerical analysis of the Soret effect. The novel constitutive model Cattaneo–Christov is illustrated to analyze the features of thermal relaxation time. The Cattaneo–Christov method is used to predict heat and mass transport. A surface that slanders and has varying thicknesses propels the flow. Through the use of local similarity transformations, the governing nonlinear partial differential equations reduce to the coupled ordinary differential equations and include the momentum, energy, and concentration equations. The altered ODEs are calculated numerically using the Runge–Kutta Fehlberg scheme and an efficient shooting procedure. The physical properties of the temperature, concentration, and fluid velocity profiles are shown visually and shed light on the change of several governing parameters. For example, in comparison to the classical Fourier’s heat model, our result suggests that the Cattaneo–Christov heat flux constitution has lower temperature and thermal boundary layer thickness. In the meantime, a high wall thickness parameter greatly upgrades the rate of heat transfer, and thermal relaxation has the opposite effect. Discussion is held regarding the effects of various miscellaneous variables on temperature, concentration, and velocity.

Illustration of thermal buoyancy on the flow of MHD Casson CNT–water nanofluids over a vertical stretching surface

This study addresses the applications of non-uniform heat source/sink and viscous dissipation in the magnetohydrodynamic (MHD) flow of Casson nanoparticles toward a porous stretchable sheet. The free convective flow for the inclusion of thermal buoyancy along with dissipative heat encourages the flow phenomena. The governing equations of the flow model are presented in terms of partial differential equations and then transformed into a system of ordinary differential equations using similarity transformations. These systems of equations are solved numerically by using the Runge–Kutta fourth-order method with a very efficient shooting technique. The effects of various parameters such as the Casson parameter, elastic parameter, porosity parameter, Prandtl number, non-uniform heat source/sink constant, Eckert number, skin fraction and Nusselt number on the flow area are computed and represented graphically. The present results reflect that the velocity of nanoparticles declined effectively with the porosity parameter and nanoparticle volume fraction. The temperature profile is increased with the elastic parameter and heat source parameter while decreasing with the Eckert number and Casson fluid parameter. Moreover, it is observed that when the Hartmann number is maximum, a retardation in wall shear force against nanoparticles volume fraction is marked.

A SHOOTING METHOD SOLUTION FOR A CONVECTIVE-RADIATIVE STRAIGHT LONGITUDINAL FIN WITH VARIABLE THERMAL PROPERTIES AND NONLINEAR BOUNDARY CONDITIONS

We develop in this work a simple and highly efficient shooting approach for solving the fin energy equation with multiple nonlinearities. The present fin problem is characterized by temperature-dependent thermal conductivity, heat transfer coefficient, and surface radiation emissivity, where the fin base is imposed to a constant temperature and the fin tip is subjected to a combination of convective and radiative heat losses. The governing fin boundary value problem is first reduced into an equivalent initial value problem and then integrated using the fourth-order Runge-Kutta method. The temperature gradient at the tip is approximated by a five-point backward finite difference formula, and computed iteratively using the secant method on the base, which is decisive for numerical integration. The fin problem is solved and compared for two cases of tip boundary condition: an adiabatic fin tip and a convective-radiative fin tip. A thermal analysis is performed using Biot number, Stark number, and the geometrical number that stands for the ratio of fin surface area to its cross-sectional area. Solutions are computed and compared to those obtained by the boundary value problem method, Galerkin method, and the Adomian decomposition method under the assumption of adiabatic fin tip. The accuracy of the nonlinear shooting method is checked by evaluating the absolute errors. Comparative results show that the fin temperature distribution and the fin efficiency are significantly impacted not only by Biot number, Stark number, and geometrical number but also by the type of the tip boundary condition, which could dramatically degrade the fin efficiency mainly for small values of geometrical number.

Acceleration of shooting and bouncing ray method based on OptiX and normal vectors correction.

The present paper deals with a new efficient shooting and bouncing ray (SBR) method based on OptiX and normal vectors correction. The basic idea is to make full use of the computing resources of the RTX series graphics cards. For ray tracing, the algorithm uses OptiX to invoke the built-in RT Cores of hardware. Thus, a fast intersection test can be implemented. To reduce the error of ray tracing caused by the facetted surface characterizing the curved surface, the direction of the reflected ray is corrected by normal vectors correction. Additionally, multiple GPU cores are invoked to accelerate the calculation of far-field integration of millions of ray tubes, which can improve the efficiency of the algorithm while reducing the data transmission time of heterogeneous devices. Simulation results show that the ray path after normal vectors correction is consistent with the theoretical results, and the algorithm can predict the RCS of arbitrary facetted geometries, which is 60 times faster than the SBR method based on kd-tree.

Melting heat transfer of MHD stagnation point flow of non-Newtonian fluid due to an elastic sheet

This paper sheds light on the numerical investigation of 2D flow and melting heat transport of an electrically conducting boundary layer stagnation-point flow of Casson fluid in the direction of stretching sheet. Suitable changes are made in rehabilitating the flow governing partial differential equations into dimensionless ordinary differential equations and afterwards solved these ordinary differential equations by the fourth order Runge-kutta numerical method by utilising the most efficient shooting technique. The influence of melting heat transfer, magnetic field, Prandtl number, Rayleigh number and Schmidt number on velocity, energy and concentration distributions, are studied through graphically drawn results.

A Hybrid Camera System for High-Resolutionization of Target Objects in Omnidirectional Images

Recent improvements in cameras and image processing techniques have advanced research on object detection and classification. The cameras capable of capturing omnidirectional images are advantageous for detecting surrounding objects, we focus on their usage method. Omnidirectional camera images generally have lower resolution than available cameras, leading to difficulty in identifying objects farther from the camera. To address this problem, we propose a hybrid camera system that first detects indistinct target regions during omnidirectional viewing, then uses a pan-tilt camera to capture a high-resolution image of the target. We also propose an algorithm for reducing the number of required complementary shots to realize efficient shooting.

Double‐diffusive natural convective stream due to moving vertical plate with nonlinear thermal radiation and Newton's boundary constraint

AbstractThis article investigates the heat and mass transmission of the double‐diffusive convective stream over a moving vertical plate with nonlinear thermal radiation and newton boundary conditions. The governing partial differential equations of the stream, heat, and concentration profiles were transformed into a system of nonlinear ordinary differential equation by utilizing resemblance transformation. This system was then resolved numerically by applying the fourth order Runge‐Kutta method with most efficient shooting technique. The effect of convection, buoyancy ratio, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number are graphically scrutinized. The numerical results are obtained for velocity, temperature, and concentration profiles. It is found that when the velocity profile increases, heat and mass transfer rate decreases with an increase in the parametric value of buoyancy ratio parameter. It is found that the effect of nonlinear thermal radiation stabilizes the thermal boundary layer growth. The skin friction coefficient decreases with an increase in Prandtl number. However, the Nusselt number increases with an increase in the local convective heat transfer rate. The present results are very much promising, and further, there is a very good agreement of results when compared with earlier published results for some limiting conditions.

Adoption of Machine Learning Algorithm-Based Intelligent Basketball Training Robot in Athlete Injury Prevention.

In order to effectively prevent sports injuries caused by collisions in basketball training, realize efficient shooting, and reduce collisions, the machine learning algorithm was applied to intelligent robot for path planning in this study. First of all, combined with the basketball motion trajectory model, the sport recognition in basketball training was analyzed. Second, the mathematical model of the basketball motion trajectory of the shooting motion was established, and the factors affecting the shooting were analyzed. Thirdly, on this basis, the machine learning-based improved Q-Learning algorithm was proposed, the path planning of the moving robot was realized, and the obstacle avoidance behavior was accomplished effectively. In the path planning, the principle of fuzzy controller was applied, and the obstacle ultrasonic signals acquired around the robot were taken as input to effectively avoid obstacles. Finally, the robot was able to approach the target point while avoiding obstacles. The results of simulation experiment show that the obstacle avoidance path obtained by the improved Q-Learning algorithm is flatter, indicating that the algorithm is more suitable for the obstacle avoidance of the robot. Besides, it only takes about 250 s for the robot to find the obstacle avoidance path to the target state for the first time, which is far lower than the 700 s of the previous original algorithm. As a result, the fuzzy controller applied to the basketball robot can effectively avoid the obstacles in the robot movement process, and the motion trajectory curve obtained is relatively smooth. Therefore, the proposed machine learning algorithm has favorable obstacle avoidance effect when it is applied to path planning in basketball training, and can effectively prevent sports injuries in basketball activities.

INTERVENTION IN THE TRAINING PROCESS AT JUNIOR BIATHLETES AFTER INCREASING EFFORT CAPACITY

High performance involves leading the sports training by individualizing both the means of training and the recovery process. The periodization of sports training, by intensity, respectively workload was intensively studied, in order to highlight the main forms of training, in units of time, which favor the increase of effort capacity. The aim of this research is to monitor the training process of junior biathletes after scheduling the process with very high effort parameters. The results of the research prove that the most efficient shooting and competition results of a junior biathlete is conditioned by the adaptation of the human body at maximum efforts.

Theoretical analysis of thermal characteristics of casson nano fluid flow past an exponential stretching sheet in Darcy porous media

The existent problem involves, the steady two-dimensional flow adjacent to boundary, mass as well as heat transfer of non-Newtonian Casson nano fluid in presence of an exponential stretching sheet. Then at this time work relating the BVP which forms a set of nonlinear normal differential equations, borrowed from a set of P.D.E's using similarity transformation, are cracked numerically with Runge-Kutta method of 4th order procedure with most efficient shooting technique. The brunts of an assortment of other dimensionless variables on temperature, velocity along with nano particle concentration are worked out, as well as the consequential values are depicted in graphical forms. The dimensionless variables under examination are Suction/Injection parameter F*w, Casson fluid Parameter β, Lewis number Le, Brownian Parameter Nb, Prandtl number Pr, Thermopheresis Parameter Nt, Porous parameter Kk*, whose brunt on Temperature profile G*(η), velocity profile F*(η), nanoparticle concentration profile H*(η) are exhibited in graphs in the course of Figs. 1 to 9 with detailed explanation.

MHD slip flow and convective heat transfer due to a moving plate with effects of variable viscosity and thermal conductivity

PurposeThe steady two-dimensional laminar boundary layer flow, heat and mass transfer over a flat plate with convective surface heat flux was considered. The governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations and then solved numerically by Runge–Kutta method with the most efficient shooting technique. Then, the effect of variable viscosity and variable thermal conductivity on the fluid flow with thermal radiation effects and viscous dissipation was studied. Velocity, temperature and concentration profiles respectively were plotted for various values of pertinent parameters. It was found that the momentum slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the momentum slip.Design/methodology/approachNumerical Solution is applied to find the solution of the boundary value problem.FindingsVelocity, heat transfer analysis is done with comparing earlier results for some standard cases.Originality/value100

Numerical study of slip and radiative effects on magnetic Fe3O4-water-based nanofluid flow from a nonlinear stretching sheet in porous media with Soret and Dufour diffusion

Increasingly sophisticated techniques are being developed for the manufacture of functional nanomaterials. A growing interest is also developing in magnetic nanofluid coatings which contain magnetite nanoparticles suspended in a base fluid and are responsive to external magnetic fields. These nanomaterials are “smart” and their synthesis features high-temperature environments in which radiative heat transfer is present. Diffusion processes in the extruded nanomaterial sheet also feature Soret and Dufour (cross) diffusion effects. Filtration media are also utilized to control the heat, mass and momentum characteristics of extruded nanomaterials and porous media impedance effects arise. Magnetite nanofluids have also been shown to exhibit hydrodynamic wall slip which can arise due to non-adherence of the nanofluid to the boundary. Motivated by the multi-physical nature of magnetic nanomaterial manufacturing transport phenomena, in this paper, we develop a mathematical model to analyze the collective influence of hydrodynamic slip, radiative heat flux and cross-diffusion effects on transport phenomena in ferric oxide ([Formula: see text]-water) magnetic nanofluid flow from a nonlinear stretching porous sheet in porous media. Hydrodynamic slip is included. Porous media drag is simulated with the Darcy model. Viscous magnetohydrodynamic theory is used to simulate Lorentzian magnetic drag effects. The Rosseland diffusion flux model is employed for thermal radiative effects. A set of appropriate similarity transformation variables are deployed to convert the original partial differential boundary value problem into an ordinary differential boundary value problem. The numerical solution of the coupled, multi-degree, nonlinear problem is achieved with an efficient shooting technique in MATLAB symbolic software. The physical influences of Hartmann (magnetic) number, Prandtl number, Richardson number, Soret (thermo-diffusive) number, permeability parameter, concentration buoyancy ratio, radiation parameter, Dufour (diffuso-thermal) parameter, momentum slip parameter and Schmidt number on transport characteristics (e.g. velocity, nanoparticle concentration and temperature profiles) are investigated, visualized and presented graphically. Flow deceleration is induced with increasing Hartmann number and wall slip, whereas flow acceleration is generated with greater Richardson number and buoyancy ratio parameter. Temperatures are elevated with increasing Dufour number and radiative parameter. Concentration magnitudes are enhanced with Soret number, whereas they are depleted with greater Schmidt number. Validation of the MATLAB computations with special cases of the general model is included. Further validation with generalized differential quadrature (GDQ) is also included.

Melting heat transfer analysis of non-Newtonian Casson fluid due to moving plate

PurposeThis paper aims to investigate laminar boundary layer flow and heat transfer from a warm laminar Casson liquid to a melting sheet moving parallel to a melting stream. The governing equations, i.e. continuity, momentum and heat transfer, are coupled non-linear partial differential equations. These equations are reduced to non-linear ordinary differential equations by means of similarity transformations, converted into first-order differential equations, and are solved numerically using the Runge–Kutta–Felhberg method with an efficient shooting technique. The velocity and temperature profiles are plotted for various values of the governing parameters, such as the moving parameter, Prandlt number, melting parameter and Casson parameter. It is found that the problem admits multiple solutions. The results of this study are validated by comparing them with the earlier published studies’ results. Thus, a good agreement is obtained.Design/methodology/approachThis study carries out numerical solution of melting heat transfer analysis.FindingsThe findings of this study show the analysis of flow and melting heat transfer characteristics.Research limitations/implicationsIn this study, analysis of dual solution is carried out.Originality/valueIn this paper, the melting heat transfer analysis on Blasius flow of a Casson fluid is taken into consideration. To the best of the author’s knowledge, no investigations have been reported on this topic.

Magneto-hydrodynamic Blasius flow and heat transfer from a flat plate in the presence of suspended carbon nanofluids

In this article, we have discussed the effect of external magnetic field and other governing parameters on the flow and heat transfer in the presence of suspended carbon nanotubes over a flat plate. The governing equations of flow and heat transfer are derived from the Navier–Stokes and Prandtl boundary layer concept. The derived governing equations of flow and energy are non-linear partial differential equation, and these equations are converted into non-linear ordinary differential equations with corresponding boundary conditions using some suitable similarity transformations and are solved numerically using fourth-order Runge–Kutta method with efficient shooting technique. Effects of governing parameters on flow and heat transfer are shown through various graphs and explained with physical interpretation in detail. This study has applications in glass-fiber production and technology. On observing the results of this study, we can conclude that external magnetic field shows opposite behaviors on velocity and temperature and it enhances the rate of heat transfer.

Effects of Variable Viscosity, Buoyancy and Variable Thermal Conductivity on Mixed Convection Heat Transfer Due to an Exponentially Stretching Surface with Magnetic Field

An analysis has been carried out to study the effects of variable fluid viscosity and variable thermal conductivity on mixed convection heat transfer due to an exponentially stretching surface with external magnetic field. The basic boundary layer equations governing the flow and heat transfer are in the form of partial differential equations. These PDE’s are converted into non-linear ordinary differential equations using the suitable similarity transformations. The resulting boundary value problems of flow and heat transfer are solved by using the Runge–Kutta Fehlberg method with efficient shooting technique. The effect of variable viscosity, variable thermal conductivity, Prandtl number, magnetic field parameter, Eckert number, and Grashof’s number (buoyancy) on velocity and temperature are plotted (for PST and PHF case) and discussed in detail.

Slip Flow of Powell-Eyring Liquid Film Due to an Unsteady Stretching Sheet with Heat Generation

This paper is focused on the study of the viscous Powell-Eyring liquid thin film flow and heat transfer driven by an unsteady stretching sheet in the presence of slip velocity and non-uniform heat generation. A system of equations for momentum and thermal energy are reduced to a set of coupled non-linear ordinary differential equations with the aid of dimensionless transformation. The resulting seven-parameter problem has been solved numerically by using an efficient shooting technique coupled with the fourth-order Runge-Kutta algorithm over the entire range of physical parameters. To interpret various physical parameters governing the flow and heat transfer which appear in the momentum and energy equations, the results are presented graphically. The present results are compared with some of the earlier published work in some limiting cases and are found to be in an excellent agreement. This favorable comparison lends confidence in the numerical results to be reported in the present work. Furthermore, the effects of the parameters governing the thin film flow and heat transfer are examined and discussed through graphs and tables. Also, the values of the local skin-friction coefficient and the local Nusselt number for different values of physical parameters are presented through tables. Additionally, the obtained results for some particular cases of the present problem appear in good agreement with the literature review.

Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet

High Weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. The flow is considered to be steady, low inertial, and two-dimensional. Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. It is observed that, unlike the Newtonian flows, in order to maintain a potential flow, normal stresses must inevitably develop. The velocity field and stresses distributions over plate are presented for difference values of pressure gradient and Weissenberg numbers.

Effect of Viscous Dissipation and Thermal Radiation on Heat Transfer over a Non-Linearly Stretching Sheet Through Porous Medium

In this present paper, we have discussed the effects of viscous dissipation and thermal radiation on heat transfer over a non-linear stretching sheet through a porous medium. Usual similarity transformations are considered to convert the non-linear partial differential equation of motion and heat transfer into ODE’s. Solutions of motion and heat transfer are obtained by the Runge-Kutta integration scheme with most efficient shooting technique. The graphical results are presented to interpret various physical parameters of interest. It is found that the velocity profile decreases with an increase of the porous parameter asymptotically. The temperature field decreases with an increase in the parametric values of the Prandtl number and thermal radiation while with an increase in parameters of the Eckert number and porous parameter, the temperature field increases in both PST (power law surface temperature) and PHF (power law heat flux) cases. The numerical values of the non-dimensional wall temperature gradient and wall temperature are tabulated and discussed.

COMPUTATIONAL DYNAMICS OF MHD FREE CONVECTION FLOW ALONG AN INCLINED PLATE WITH NEWTONIAN HEATING IN THE PRESENCE OF VOLUMETRIC HEAT GENERATION

In this study, we examine the combined effects of a transverse magnetic field and an exponentially decaying heat source on boundary layer flow of a viscous incompressible electrically conducting fluid over an inclined plate with a Newtonian surface heating. The governing partial differential equations with the appropriate boundary conditions are reduced to a set of nonlinear ordinary differential equations using similarity transformations. The obtained differential equations are solved numerically using a fourth-order Runge-Kutta integration scheme along with an efficient shooting technique. A comparison with earlier results in the literature shows perfect agreement. Effects of various embedded parameters on the fluid velocity, fluid temperature, skin friction, plate surface temperature, and heat transfer rate are presented graphically and discussed quantitatively.

The Effects of MHD Flow and Heat Transfer for the UCM Fluid over a Stretching Surface in Presence of Thermal Radiation

An analysis is performed to investigate the effect of MHD and thermal radiation on the two-dimensional steady flow of an incompressible, upper-convected Maxwells (UCM) fluid in presence of external magnetic field. The governing system of partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and is solved numerically by efficient shooting technique. Velocity and temperature fields have been computed and shown graphically for various values of physical parameters. For a Maxwell fluid, a thinning of the boundary layer and a drop in wall skin friction coefficient is predicted to occur for the higher elastic number which agrees with the results of Hayat et al. 2007 and Sadeghy et al. 2006. The objective of the present work is to investigate the effect of elastic parameterβ, magnetic parameterMn, Eckert numberEc, Radiation parameterN,and Prandtl numberPron flow and heat transfer charecteristics.