International Journal of Modern Physics B

Lubrication theory has attained attention lately due to its practical applications, such as the formation of thin films, adhesives, and lubrication of components of machines. Jeffrey’s nanofluid flow over the stagnation region past a power-law lubricated surface is presented in this study. Buongiorno’s model is employed to scrutinize the effects of thermophoresis and Brownian motion phenomena with constant wall and prescribed surface temperature (PST) and effects of heat source/sink, chemical reaction, and Joule heating. Due to the continuity of shear stress of fluid-lubricant and velocity at the interface, interfacial conditions are generated. By similarity conversions, ordinary differential equations are obtained and their solutions are computed numerically. For power-law index equaling $\frac{1}{2}$, local similarity solutions are calculated by adopting a finite difference scheme, viz. bvp4c in MATLAB. The energy profiles for constant and prescribed temperatures are monitored. The effects of pertinent parameters on the flow, thermal, and mass distributions are scrutinized and illustrated in graphs. Flow field decreases significantly by raising slip parameter as the aptitude of power-law lubricant to improve the velocity of the bulk fluid. The numerical comparison of wall stress and Nusselt number is also presented. The slip and Jeffrey’s material parameters raise the numerical outcomes of the wall shear stress. In addition, increment in Prandtl number enhances the numerical value of the Nusselt number; however, it reduces for relaxation-to-retardation times ratio.

We examine multiwave (MW), rogue wave (RW), periodic wave (PW), homoclinic breather (HB), breather lump wave (BLW), $M$-shaped rational solutions, lump soliton, kink cross-rational (KCR), periodic cross-kink rational (PCKR), periodic cross-rational (PCR) solutions for the Degasperis–Procesi (DP) equation in shallow water waves through appropriate polynomial function scheme. We also compute some interactions for stated model including interaction of $M$-shaped soliton with one kink, interactional solution with two kinks also lump soliton with kink one and kink two solutions. Furthermore, we made suitable 3D, 2D and contour profiles via appropriate parameters.

In this study, influence of non-Fourier’s heat flux in 2D Darcy Forchheimer flow of modified Eyring–Powell for a stretching sheet is discussed. Here, thermal conductivity of modified Eyring–Powell model depends upon temperature and porosity variable as well as Cattaneo–Christov heat-mass flux effects are also considered. By means of some suitable similarity transformations and simple BCs, coupled PDEs are transformed into a set of coupled ODEs. Resulting ODEs are solved by using bvp4c technique. The graphical results are obtained via MATLAB. The pictorial outcomes of some physical parameters are displayed. The acquired outcomes disclosed that temperature gradient decreases with the growing values of thermal relaxation parameter Prandtl number, while the concentration profile decreases for higher Lewis number.

In this study, generalized higher-order nonlinear Schrödinger equation is under consideration analytically. This equation is used in the field of slowly varying envelope of the electric field in the optical fiber with self-phase modulation, third-order dispersion, self-steepening and stimulated Raman scattering. For the sake of optical solitons and other solutions, we use two methods such as generalized exponential rational function (GERFM) and Sardar subequation method (SSEM). The solutions are gained in different forms such as bright, dark, singular, combo solitons, as well as hyperbolic, trigonometric and rational solutions. Some of the acquired wave solutions are characterized graphically in 3D, contour forms and 2D shapes to illustrate the dynamical behavior. A comparable analysis of this study with the available consequences in literature confirms the innovation and assortment of present accomplished wave solutions and hence enhances the great performance of the employed techniques. The offered method can be utilized to assist complicated models applicable to a wide variety of physical situations. We hope that a wide spectrum of engineering model professionals will find this study to be beneficial.

In this study, we experimentally study the dependence of the intensity of laser radiation incident on and transmitted through a layered InSe crystal. A picosecond YAG:Nd³⁺ laser with a parametric light generator was used as a light source, making it possible to generate light pulses with a duration of $\sim$30 ps, tunable in frequency within the range of 0.75–1.5 μm. Optical bistability in the region of exciton resonance was detected in an InSe crystal at room-temperature under the picosecond YAG:Nd laser. It is shown that the decrease in absorption in the exciton resonance region is associated with the process of exciton–exciton interaction, shielding of excitons, and the Mott transition.

In this paper, the generalized exponential (GExp) method has been employed to construct novel solitary wave solutions of the nonlinear fractional biological population (FBP) model. This model is used to demonstrate the relation of the population with deaths and births. Many novel traveling wave solutions have been formulated in distinct forms such as exponential, hyperbolic and trigonometric forms. These solutions have been explained in three different axes. The first axis is plotting them in their three optional (real, imaginary and absolute value), the second axis is handling these solutions for constructing the requested conditions for applying trigonometric quintic B-spline (TQBS) scheme. The second one determines the accuracy of the obtained analytical solutions by showing the error’s value between the analytical and numerical solutions. At the same time, the third one is comparing our analytical and numerical solutions, which have recently been published that explain the paper’s contribution and novelty.

The nonlinear second-harmonic generation (SHG) and third-harmonic generation (THG) in “12–6” tuned GaAs/GaAlAs double quantum wells (QWs) are calculated in the presence of applied electric field under the effective mass approximation. The influence of the structural parameter of the double QW is also considered, which is the main means to adjust its nonlinear optical properties. The eigenvalues and corresponding eigenfunctions of the double QWs system are obtained via the finite difference technique. The nonlinear SHG and THG are presented as a function of the photon energy, structural parameter, and applied electric field. It is shown that the SHG and THG are sensitive to both the applied electric field and the structure parameters, which can tune the nonlinear optical properties efficiently by adjusting the symmetry and confined potential of the double QWs.

Numerical simulation was offered for scrutinizing the freezing of water within the complex container. The container has elliptic left adiabatic wall while the right wall is sinusoidal wall and maintained at cold temperature. The drawback of water has been removed by adding alumina nanoparticles. For this modeling, different ranges of volume and shape factor of nanoparticles have been scrutinized by incorporating FEM. The configuration of grid alters with change of time and verification test has been presented which proved good accuracy. As bigger shape factor has been selected, the time of process decline less than 4% for cylinder shape and this percentage augments around 78.22% for blade shape. As nanoparticle fraction increases, the required time declines around 26.84%. The impact of blade shape in view of adding nanoparticles is 25.74% greater than that of cylinder shape.

In this paper, we will first present the TFMIADM with its adequate Dirichlet constraints. Right after that, we will review the formation of that model under the terms and assumptions of the RKHSM computational approach. The solutions and modeling of the utilized model will be discussed based on Caputo’s connotation of the partial time derivative. We will present the scores required to construct the appropriate spaces for the method and we will present several theories such as solutions representations, convergence restriction, and order of error. With the use of the Fourier functions expansion rule, the numeric–analytic solutions are expressed by collection sets of orthonormal functions system in $𝔄({\mathscr{H}})$ and $𝔅({\mathscr{H}})$ spaces. Right after that, we will solve this model in both time and space domains using the algorithms of the method used. Indeed, several drawings and tables that expound on the effectiveness and strength of the approach and its adaptation to the issue reviewed are utilized. In the end, some points of view and highlights are presented side by side with the most important modern references used.

In this research work, the two-dimensional (2D), incompressible fluid flow has been taken into consideration. The flow is supposed to be steady and laminar. By considering the water-based nanoparticles of SWCNTs and MWCNTs in the presence of thermal radiation, the rate of heat transferring and entropy generation effects in a regenerative cooling system of a rocket engine are evaluated. The effects of the length and radius of the nanomaterials on the problem are also considered. Solutions for temperature, velocity profile, irreversibility (entropy generation) and the Bejan number are discussed graphically, and the effects of various significant factors are considered on these profiles. The modeled physical problems in current exploration are dependent upon governing laws which appear in terms of PDEs. These PDEs are reformed into a system of nonlinear ODEs. We used numerical scheme known as (RK-4) in combination with the shooting iteration technique to obtain the solutions to transformed fluid flow equations, because the resultant ODEs are extremely nonlinear and finding the exact solution is very difficult. It is investigated that the Eckert number, nanoparticles volume fraction and radiation parameter upsurge the thermal field as well as the irreversibility of the system. Furthermore, the dual behavior of nanoparticles volume fraction and viscosity parameter on velocity profile is observed. Bejan number shows increasing effects in response to nanoparticles volume fraction and radiation parameter, whereas a reverse impact of Bejan number is noticed for the rising values of Eckert number.