International Journal of Modern Physics B

In this paper, we get certain the lump-trigonometric solutions and rogue waves with predictability of a (2+1)-dimensional Konopelchenko–Dubrovsky equation in fluid dynamics with the assistance of Maple based on the Hirota bilinear form. We first construct a general quadratic form to get the general lump solution for the referred model. At the same time the lump-trigonometric solutions are concluded with plenty of solutions, in which the lump solution localized in all directions in space. The analytical solutions obtained are employed in the investigation of the impacts of the parameters on type of solutions. Moreover, when the lump solution is cut by twin-solitons, the special rogue waves are also introduced. Furthermore, we obtain a new sufficient solutions containing breather wave, cross-kink, periodic-kink, multi-waves and solitary wave solutions. The developed models in this work will serve as the basis for comparisons for the analytical solutions of the subsequent works on the performance of mentioned equation. It is worth noting that the emerging time and place of the rogue waves depend on the moving path of lump solution.

The invention of Chirped Pulse Amplification lasers along with the development of fast ignition methods have made fuels such as proton–boron-11 seem promising nuclear fusion energy sources because of their lack of high-energy neutrons and abundance of constituent isotopes. This paper investigates the transport of charged particles in proton–boron-11 fuel. In this study, the confinement parameter has been estimated as $\rho R=12$ g/cm² with the help of a proton driver in the fast ignition method for proton–boron-11 fuel pellets, with a ratio of boron-11 to proton $𝜀=0.3$. Subsequently, using the Li–Petrasso stopping-power model, the energy deposition coefficients of the accelerated proton-beam driver were calculated by the Target Normal Sheath Acceleration method with 1 MeV energy. The obtained results show that at a temperature of about 65 keV, the proton-beam driver with 1 MeV energy deposits about 85% of its energy in the hot spot area of 2.5 $\mu$m depth from the surface of the fuel pellet to ignite the proton–boron-11 fuel pellet.

The axially accelerating beam systems are widely used in engineering fields, which have abundant dynamical phenomena. In this work, we studied the periodic orbits and the phenomena of multistability of the system. The necessary and sufficient conditions for the existence of periodic orbits are derived by Schauder’s fixed point theorem and the averaging method. The theoretical results are in good agreement with the numerical analysis. Multistability is discussed in some set of parameter values. To predict the dynamical behaviors of the system in the long-term run, the effects of external excitation amplitude on the structures of basins of attraction are studied. The results reveal the influences of the physical parameters and initial values on the complex dynamical behaviors of the system, which can offer some guidance for selecting parameter values in engineering application of axially accelerating beams.

In this study, through the $(m+\frac{1}{G^{\prime }})$-expansion method, we extract soliton solutions to the coupled-Higgs equation. The studied nonlinear model is known to describe Higgs mechanism. The Higgs mechanism is essential to explain the generation mechanism of the property “mass” for gauge bosons. The proposed method is one of the most powerful methods for constructing soliton solutions for nonlinear partial differential equations. The obtained wave solutions include exponential, hyperbolic, and distinct structures of complex function solutions. The presented results may be helpful in explaining the physical features of various nonlinear physical phenomena. In order to analyze the dynamic behavior of all obtained solutions, we plot three-dimensional and two-dimensional graphs for the obtained solutions.

This investigation aims to inspect the flow and thermal characteristics of hybrid nanoparticles under the effect of thermophoresis and Brownian motion. The hybrid nanofluid is formed by dispersing the silver nanoparticles into the base fluid composed of tungsten oxide and water. The resulting hybrid nanofluid is assumed to flow over a moving wedge. The wedge is a geometry that can be commonly seen in many manufacturing industries, moulding industries, etc., where friction creates more heat and cooling becomes a necessary process. This study currently focuses on such areas of the industries. In this regard, the flow expressions in the form of Partial Differential Equations (PDEs) are obtained by incorporating the modified Buongiorno’s model and using boundary layer approximations. The modified Buongiorno model helps us analyze the impact of volume fraction along with the slip mechanisms. Suitable transformations are used to achieve the nondimensional form of governing equations, and further, it transforms the PDE to Ordinary Differential Equation (ODE). The RKF-45 is used to solve the obtained ODE and the boundary conditions. Furthermore, graphic analysis of the solutions for fluid velocity, energy distributions and dimensionless concentration is provided. It was noted that the behavior of the Nusselt and Sherwood numbers was determined by analyzing numerous parameters. The conclusions show that they decrease with greater values of the stratification factors. Additionally, with higher values of the wedge parameter, the magnitude of the velocity field and the thermal boundary layer diminish.

This research aims to study the 3D magnetohydrodynamics stagnation-point flow (SPF) over a horizontal plane surface (HPS) carrying water-based graphene oxide (GO) nanoparticles caused by an irregular heat source/sink used in heat transfer procedures. In addition, a Tiwari–Das model is used to inspect the dynamics of fluid flow behavior and heat transmission features of the nanoparticles with experiencing the impacts of thermal radiation. The acquired nonlinear set of partial differential equations (PDEs) is transfigured to a system of ordinary differential equations (ODEs) using similarity transformations. The accumulative dimensionless ODEs are then further tackled in MATLAB using the bvp4c solver. Tables and figures are prepared for the execution of several relevant constraints along with nodal/saddle indicative parameter, internal heat source/sink parameter, radiation parameter and nanoparticles volume fraction which divulges and clarify more accurately the posited quantitative data and graphical findings. Also, the velocity profile decelerated in the axial and transverse coordinate axes for a higher value of the nanoparticle volume fraction but the dimensionless temperature distribution is augmented. Additionally, thermal boundary layer thickness and profile of temperature enriches with higher impressions of radiation constraint. However, the internal heat sink factor declines the profiles of temperature while escalating with the superior value of the internal heat source parameter.

This thermal case pronounced the stability framework for stagnation point flow of magnetized alumina and copper nanoparticles with due exponentially shrinking permeable surface. The thermal stability and enhancement of water base liquid had been taken into account with uniform impulsion of hybrid nanomaterials. The induced flow results via exponentially shrinking permeable surface. The similarity transformation simplifies the mathematical model where governing formulated system for hybrid nanofluid is altered into the nondimensional form. A numerical solver called bvp4c is employed in MATLAB software to aid in the problem-solving process, and dual branches have been found. The significance of pertaining parameters associated to the flow model is inspected in view of thermal properties. The findings show that there are two branches for suction strength $(S>S_c)$ and magnetic strength $(M>M_c)$. The bifurcation values $S_c$ and $M_c$ reduce for the occurrence of dual branches as the solid volume percentages of copper increase. Furthermore, for the upper branch solutions, the skin friction and heat transfer rate rise as ${\varnothing }_{\mathrm{\text{Cu}}}$ increases. The temporal stability analysis determines the stability of the dual branches, and it is discovered that only one of them is stable and physically applicable. The presence of suction parameter effectively controls the thermal transportation phenomenon.

In this paper, a special integrable negative-order Calogero–Bogoyavlenskii–Schiff equation (nCBS) in fluid mechanics is studied by means of the symmetry reduction method and consistent tanh expansion method. The Painlevé integrability is investigated to confirm the compatibility conditions. This integrable nCBS equation has been transformed into different reduction equations and the corresponding invariant solutions with arbitrary functions are obtained. The corresponding structures of the invariant solutions for the nCBS equation are also shown graphically. At last, new types of soliton–cnoidal interaction solutions for the nCBS equation are presented through the consistent tanh expansion method on the basis of the truncated Painlevé expansion.

In the past few years, many technical strategies, such as molding, condenser heat exchanger, liquefied metal filtration, fusion control and nuclear reactor coolant, that involve hydromagnetic fluxes and thermal intensification in porous media have been observed. This study investigates the Carreau nanofluid of nanobiofilm through stretching/shrinking sheet with a stagnant point flow, nanoparticles and convecting microbes. The orthogonal ($90^{\circ }$ impinge) coating stagnant point circulation of a medium is considered, although the sheet may be stretched/shrinked as the procedure utilized in industry. The variations in the fluid (dynamic viscosity, thermal conductivity, mass permeability) and microbes are utilized. The similarity transformation factors are used to transform the system of partial differential equations into a nonlinear system of ordinary differential equations. To find the solution of a system of equations, the Runge–Kutta method with shooting technique has been used. The flow rate, temperature and concentration, as well as the heat transfer rate, and the physical quantities have been discussed. The nanoparticle volume fraction increases with the increasing effect of activating energy as well as thermophoresis parameter, but it decreases with the enhancing effect of Lewis number (Le) and Brownian motion parameter (Nb). The graphs and tables display the illustration of the influence of different parameters.

Over the last 10 years, heat transfer performance in immediate cooling and heating applications has grown into the foremost concern for heat transfer practitioners in Engineering and manufacturing practices. Henceforward, the study in new heat transfer fluids is extremely intense and challenging. This study examines flow and thermal management in axisymmetric hydrodynamic pure water-based hybrid solid nanoparticles in a flow induced by a swirling cylinder with Fourier Heat source. Flow and heat transfer are analyzed and compared for ${\text{CNT+Graphene+Al}}_2{\mathrm{\text{O}}}_3$ and Paraffin wax+Sand+AA7072 hybrid nanofluid flow. Shooting technique (R-K 4th order) is applied to work out the flow equations numerically. Simulated results are exhibited through graphs and tables. The computational results are statistically validated with the published research work and a modest concurrence is found. The main outcome of this study is found to be in Multi-regression analysis, where the $\mathrm{\Lambda }$ w.r.t $Pr$ has higher domination compared to $\mathrm{\Phi }$ w.r.t $Pr$. Also, it is interesting to know that $\mathrm{\Phi }$ w.r.t Re has more rate of heat transfer compared to $\mathrm{\Phi }$ w.r.t $M$. As the volume fraction rises, the size of the particle is less and Reynolds number dominated the flow, due to this, a decrement is seen in the friction values. Overall, it is observed that heat transfer rate is higher in CNT+Graphene+Al₂O₃ compared with Paraffin wax+Sand+AA7072.