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The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively.

The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers.

A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall.

This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.

The purpose of this study is to provide the full-state mathematical model and devise a nonlinear controller for a balloon-supported unmanned aerial vehicle (BUAV).

Newtonian mechanics is used to establish the nonlinear mathematical model of the proposed vehicle assembly which incorporates the dynamics of both balloon and quadrotor UAV. A controllable form of the nine degrees of freedom model is derived. Backstepping control is designed for the proposed model and simulations are performed to assess the tracking performance of the proposed control.

The results show that the proposed methodology works well for smooth trajectories in presence of wind gusts. Moreover, the final mathematical model is affine and various nonlinear control techniques can be used in the future for improved system performance.

Multi-rotor unmanned aerial vehicles (MUAVs) are equipped with controllers but are constrained by smaller flight endurance and payload carrying capability. On the contrary, lighter than air (LTA) aerial vehicles have longer flight times but have poor control performance for outdoor operations. One of the solutions to achieve better flight endurance and payload carrying capability is to augment the LTA balloon to MUAV. The novelty of this research lies in full-order mathematical modeling along with transformation to controllable form for the BUAV assembly.

This paper aims to explore the flow of nanofluid over bi-directional stretching sheet in the presence of magnetic field and linear thermal radiation.

In this study, water is taken as a base fluid, and copper is diluted in the base fluid. Further, four different shapes of nanoparticles are considered for the analysis. The governing nonlinear partial differential equations are transformed into the system of ordinary differential equations after using the feasible similarity transformations. Solution of the model is then performed by means of Runge–Kutta scheme.

Influence of the emerging dimensionless parameters on velocity, temperature, skin friction coefficient and local rate of heat transfer are studied with the help of graphs.

The study is presented in this paper is original and has not been submitted to any other journal for the publication purpose. The contents are original, and proper references have been provided wherever applicable.

This paper aims to propose a method by merging Legendre wavelets method and quasilinearization technique to tackle with the nonlinearity and to get better and more accurate results.

To test the significance of the proposed scheme, the authors applied the method on the model representing magneto-hydrodynamic squeezing flow of a viscous fluid between two parallel infinite disks, where one disk is impermeable and the other is porous with either suction or injection of the fluid. For the sake of comparison, numerical solution by using RK-4 is also computed. From the graphs and tables, it is evident that the proposed method shows an excellent accordance with the numerical solution.

The solution converges to the numerical solution when the degree of Legendre polynomials m is increased. For m = 20 in all the three cases, for different values of S, M and A, the graphs of solutions obtained by Legendre wavelet quasilinearization technique show an excellent agreement with numerical solution. Also, it is evident from figures that suction and injection affects the velocity profile in opposite way. For suction, maximum velocity is seen to be at the center of the channel. Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.

Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.

The purpose of this paper is to assess the flow of a nanofluid over a porous moving wedge. The passive control model along with the magnetohydrodynamic (MHD) effects is used to formulate the problem. Furthermore, in energy equation, the non-linear thermal radiation has also been incorporated. The equations governing the flow are transformed into a set of ordinary differential equations by using suitable similarity transforms. The reduced system of equations is then solved numerically using a well-known Runge–Kutta–Fehlberg method coupled with a shooting technique. The influence of parameters involved on velocity, temperature and concentration profiles is highlighted with the help of a graphical aid. Expressions for skin-friction coefficient, local Nusselt number and Sherwood number are obtained and presented graphically.

Numerical solution of the problem is obtained using the well-known Runge–Kutta–Fehlberg method.

The analysis provided gives a clear description that the increase in m and magnetic parameter M results in an increased velocity profile. Both these parameters normalize the velocity field. Radiation parameter, Rd, increases the temperature and concentration of the system so does the temperature ratio θ_ω reduces the heat transfer rate at the wall for both stretching and shrinking wedge.

In the study presented, the flow of nanofluid over a moving permeable wedge is considered. The solution of the equations governing the flow is presented numerically. For the validity of results obtained, a comparison is also presented with already existing results. To the best of the authors’ knowledge, this investigation is the first of its kind on the said topic.

The purpose of this paper is to explore the impact of thermal radiation, viscous dissipation and Joule heating effects on the flow of a magneto-nanofluid between two horizontally placed plates. Three distinct shapes of nanoparticles in a base fluid (water) are considered to compose the nanofluid.

Introducing feasible similarity variables, the flow model is transformed into a nonlinear and coupled system of ordinary differential equations. The consequent system is solved by using homotopy analysis method.

Furthermore, the influence of embedded parameters on velocity and temperature profiles is highlighted graphically. The same is done for showing the variations in skin friction coefficient and local rate of heat transfer. Under certain conditions, present results compared with already existing results in the literature. Some main findings are pinpointed in the last section before the bibliography. From presented work, it is analyzed that the velocity field along y-axis and x-axis are increasing and decreasing functions of suction/injection parameter. The velocity of the fluid starts increases for Reynolds number and declines for volumetric fraction of the nanoparticles. Significant variations in angular velocity are observed for volumetric fraction and Reynolds number, respectively. Thermal field increases rapidly for brick-shaped nanoparticles, and for platelet-shaped nanoparticles, it decreases rapidly. Local rate of heat transfer increases for radiation and Reynolds number and starts decreasing for Eckert number.

The study presented is original and has not been submitted to any other journal for the publication purpose. The contents are original and proper references have been provided wherever applicable.

The purpose of this study is to investigate numerically the influence of nonlinear thermal radiation on the flow of a viscous fluid. The flow is confined in a channel with deformable porous walls.

Two numerical schemes, namely, Galerkin’s method (GM) and Runge–Kutta–Fehlberg (RKF) method have been used to obtain solutions after reducing the governing equations to a system of nonlinear ordinary differential equations.

Heat transfer rate falls at the upper wall owing to the decreasing values of the permeability parameter. However, at the lower wall, the same rate rises. Increment in θ_w increases the rate of heat transfer at both walls. Nusselt number also increases with the increasing values of Rd. Rd also uplifts the temperature distribution, except for the case where it falls near the lower wall owing to the contraction coupled with injection.

It is confirmed that the presented work is original.

In this current study, the authors aim to analyze non-linear radiative squeezed flow in a rotating frame of viscous fluid.

The Radioactive nature of the fluid is taken into consideration. The reduced form of equations governing the flow are developed by the implementation of similarity transformations. The coupled system thus obtained is solved by using the homotopy analysis method (HAM).

Augmentation in velocity and temperature profiles is discussed graphically by varying various involved parameters. The total error of the system is discussed in Table I. The cases of linear radiation and non-linear radiation are also discussed in Tables II and III.

The study presented in this paper is original and it has not been submitted to any other journal for publication purpose. The contents are original and proper references have been provided wherever applicable.

The aim of this manuscript is to study the flow of a nanofluid through a porous channel under the influence of a transverse magnetic field. Permeability of the walls is considered to be different, which results in an asymmetric nature of the flow. The height of the channel is variable, and it dilates or squeezes at a uniform rate.

A numerical solution (Runge–Kutta–Fehlberg) has been obtained after reducing the governing equations to a system of nonlinear ordinary differential equations using some suitable similarity transforms, both in time and space.

An increase in absolute values of the permeability parameter results in an enhanced mass transfer rate at both the walls, while the rate of heat transfer also increases at the lower wall. Few graphs are also dedicated to see the behavior of Nusselt and Sherwood numbers following the variations in flow parameters.

A pictorial description of the flow and effects of emerging parameters on the temperature and nanoparticle concentration profiles is presented to analyze the flow behavior. It is established that the asymmetry of the channel affects the flow quite significantly.

The purpose of this study is to analyze thermo-diffusion and diffusion-thermo effects, combined with first-order chemical reaction, in the flow of a micropolar fluid through an asymmetric channel with porous boundaries. Suction/injection velocities of upper and lower walls are taken to be different from each other. The channel exhibits a parting or embracing motion and the fluid enters, or leaves, the channel because of suction/injection through the permeable walls.

The solution of the problem is obtained by using the fourth-order Runge-Kutta method combined with the shooting technique.

The asymmetric nature of the channel that is caused by the different permeabilities of the walls deeply influences the flow. The temperature of the fluid rises significantly by increasing the absolute value of A for both Case I and Case II. While, for the concentration profile, the concentration drops near the lower vicinity of the center in Case I, and, it falls near the lower wall of the channel in Case II. Stronger Dufour effects increase the temperature of the fluid except for Case 1 at the center of the channel and for Case II in lower quarter of the channel.

It is confirmed that the presented work is original and is not under consideration by any other journal.