International Journal of Modern Physics B

The time-dependent variable coefficients of Bogoyavlensky–Konopelchenko (BK) equation and generalized Bogoyavlensky–Konopelchenko (gBK) equation are considered in this paper. The integrability test by Painlevé analysis is being implemented on both the considered equations. An auto-Bäcklund transformation has been generated with the help of Painlevé analysis for both equations. Auto-Bäcklund transformation method has been used for obtaining the analytic solutions. By using auto-Bäcklund transformation method, three different analytic solution families have been derived for each of the considered equations. Multi-soliton solutions are also calculated for both the considered equations by using Hereman and Nuseir algorithm. All the results are expressed graphically in 3D by varying different functions and parametric values. These graphs reveal the physical significance of equations under consideration.

In this work, the physical features of growing epitaxial layers of new solid solutions of (GaAs)${}_{1-y-z}$(Ge${}_2{)}_y$(ZnSe)${}_z$ from the liquid phase of the tin solution-melt on GaAs (100) substrates were investigated. The conditions required for the formation of the solid solution of molecular substitution were revealed. A possible configuration of the crystal structure of the solid solution (GaAs)${}_{1-y-z}$(Ge${}_2{)}_y$(ZnSe)${}_z$ is presented. In the spectral photosensitivity of the $n$-GaAs–$p$-(GaAs)${}_{1-y-z}$(Ge${}_2{)}_y$(ZnSe)${}_z$ structures, peaks with maxima at photon energies of 1.37 eV and 2.62 eV were found. The band diagram of the solid solution (GaAs)${}_{1-y-z}$(Ge${}_2{)}_y$(ZnSe)${}_z$ was presented.

Heat transfer is an important phenomenon in the industrial sector. Thus, the simulation is made to compute the distribution of heat in a rectangular channel in this paper. A heated rod is inserted at the center of the rectangular channel. The fluid flowing in the rectangular channel is considered to be a viscous fluid. Navier–Stokes equations of motion for laminar flow are used. The medium for the fluid motion is considered to be a porous medium. Heat transfer is computed for nonlinear two-dimensional incompressible and unsteady flows. The Fourier’s law of heat conduction is used for the transmission of heat in the rectangular channel. The Finite Element Method (FEM) is applied to the solution of the problem. For different values of the permeability parameter, Prandtl number and Rayleigh number, the graphic solution for the velocity and temperature fields is shown.

This paper analyzes the employment of nanotechnology and FHD effect on the transportation of fluid within a container. Carrier fluid is a combination of H₂O and iron oxide and homogeneous model was incorporated to guess the features. The complex equations can be achieved by incorporating the source terms of Kelvin force and gravity term and in order to solve them, the control volume-based FEM approach was applied. To examine the accuracy, previous article of on FHD flow was examined and the achieved data showed nice accuracy. Laminar flow was analyzed and the influences of Kelvin and gravity forces were examined along with the role of the nano-sized particles. As Mn${}_F$ augments, impingement of fluid with wall enhances and bigger Nu was obtained. The effect of Ra on the characteristics of ferrofluid is same as Mn${}_F$. Disperse of nanosized material makes Nu to rise to about 12.8% owing to greater conductivity of ferrofluid. Given $\mathrm{\text{Ra}}=1$E4, the augment of Kelvin force causes Nu to intensify to about 27.09%.

In this modern era of research, fluid mechanics and particularly nanofluids flowing on the stretching surfaces are considered to be occurring more often due to their faster heat transfer mechanism. Mostly, the theoretical research related to nanofluids including this one contributed in studying the performance and reaction of nanomaterials against different physical constraints so that they have wide applications in several developed engineering industries like, atomic receptacles, transportation, microchip technology as well as biomedicine industry and food industry. Several fluids permeating in industrial and biological processes are pseudo-plastics. Their non-Newtonian behavior is usually related to structural reorganizations of the fluid molecules due to their flow. Keeping this in view, this study is an effort to investigate two-dimensional steady incompressible Cattaneo–Christov heat flux model of Carreau–Yasuda nanofluid in the presence of thermal radiation and velocity slip. The governed model is presented through partial differential equations which are transformed into ordinary differential equations by using similarity transformation. The final system of equations are solved numerically and the results are expressed through graphs and tables for fluid’s velocity temperature, concentration and physical quantities like heat and mass flux. It is observed that skin friction as well as local heat and mass flux decline with velocity slip parameter and heat transfer rises but mass flux at surface declines through increment in radiation parameter.

In this research, the authors precisely focus on the analysis of the chaotic behavior in an Oldroyd-B fluid saturated anisotropic porous medium via a feedback control technique. A four-dimensional (4D) weakly nonlinear system emerging from a Galerkin method of the constitutive and preservation equations is developed to accord with a convective stabilization with various Darcy numbers (Da) and feedback control gain value $({\widehat{F}}_g)$. The chaotic dynamic convection is governed by the Darcy–Rayleigh number ($R_n$) and feedback control, while the Da has a significant impact on system stabilization. Their results reveal the effects of the feedback gain parameter $({\widehat{F}}_g)$, stress relaxation parameter ($\mathrm{\Gamma }$), strain retardation parameter ($\mathrm{\Lambda }$), Darcy number (Da), mechanical ($\zeta$) and thermal ($\chi$) anisotropy parameter on the stability and destabilization of thermal convection. Stabilization of thermal convection are important in cooling, nuclear power, and a range of technical, biological and engineering processes. In particular, feedback control gain values are discovered to be the preferred mode for the controlled onset of oscillatory convection. Finally, a graphical representation is presented to demonstrate that the feedback control approach is more effective in regulating the entire system when aperiodic external disturbances occur.

This paper studies the soliton solutions for Embedded soliton (ES) generating model with ${\chi }^2$ nonlinear susceptibility. The bright, rational, Jacobi elliptic, periodic, dark, Weierstrass, hyperbolic solitary wave solutions will be found with the aid of sub-ODE technique under certain conditions. The main objective behind the sub-ODE method is to find the wave solutions of a complex model with the help of simple and solvable ODEs called sub-ODEs. The resulting wave solutions are presented graphically for suitable values of different parameters.

In this research work, we investigate an unsteady flow over a rotating disk. We assign symbols to the selected dependent and independent quantities. Then all physical systems are modeled to mathematical form by applying physical laws for an ionized liquid flow over a rotating disk with nanoparticles from the set of Poisson Nernst–Planck model, Energy equation and Navier–Stokes equations. The set of partial differential equations along with the boundary conditions are transformed to a set of coupled ordinary differential equations for an electro-viscous flow of nanofluid over a rotating disk by using similarity transformations. The unknown physical quantities are investigated through Parametric Continuation Method (PCM). For physical purpose, physical quantities like flow behavior thermal properties, thermal variation, the distribution of ions in the fluid region, skin friction, are analyzed through graphical and tabulated results. As exact solutions are not possible for nonlinear ordinary differential equations (ODEs) system, therefore, such quantities are subjected to numerical calculation following Parametric Continuation Method (PCM) and validated the result through BVP4c package in Matlab.

Photoconductivity characteristic of undoped and gadolinium (Gd)/dysprosium (Dy) co-doped layered $p$-GaSe semiconductor has been experimentally investigated. A model is proposed to explain the obtained results. The creating possibility of multi-band photo-detectors with stable and reproducible parameters is shown and characteristics based on single crystals of $p$-GaSe are activated with mentioned rare-earth ions with concentration of $10^{-2}÷10^{-1}$ at.%.

In recent years, a novel technique for producing robust cementitious materials, called nanocomposites, has emerged. These materials are comprised of clay minerals and polymers. As a result, a vertical flat plate has been used to evaluate a clay-based cementitious nanofluid in this research. The impacts of first-order chemical reactions, heat generation/heat absorption, and the Jeffrey fluid model are taken into account for the study of flow. Newtonian heating and the conditions for slippage velocity have also been considered. The mathematical problem for the flow analysis has been established in relations of partially coupled partial differential equations and the model has been generalized using constant proportional Caputo (CPC) fractional derivative. The problem is solved using the Laplace transform technique to provide precise analytical solutions. On the concentration, temperature, and velocity fields, the physics of a number of crucial flow parameters have been examined graphically. The acquired results have been condensed to a very well-known published work to verify the validity of the current work. It is important to note here that the rate of heat transfer in the fluid decreases by 10.17% by adding clay nanoparticles, while the rate of mass transfer decrease by 1.31% when the value of $\varphi$ reaches 0.04.