Modern Physics Letters B

In this work, the Cattaneo–Christov double diffusion model is used to analyze the three-dimensional boundary layer flow of an upper-convected Maxwell fluid flowing over a bi-directional stretching surface. The model assumes that the fluid’s diffusivity is concentration-dependent, whereas dynamic viscosity and thermal conductivity are temperature-dependent; and the model takes into account the influence of the magnetic field of uniform strength. The problem is formulated using the conservation rules of mass, momentum, and energy as well as the boundary layer approximation. The resulting nonlinear system is then numerically solved using the bvp4c procedure in MATLAB. The obtained results are set forth graphically to illustrate the variations of different parameters. It is contemplated that the increase in thermal relaxation parameter results in a drop in fluid temperature while there is an enhancement in the concentration profile. Also, the temperature field has a direct relationship with the temperature-dependent viscosity. This research has proven its utility in industries where there is a need to analyze fluid flow over surfaces that can stretch in two directions.

The heat transfer characteristics of nanofluid play an important role in several industries to optimize their performance with the interaction of dissipative heat. However, in energy harvesting its application is vital. Therefore, the current heat transfer analysis was carried out based on the consequence of viscous and Joule dissipation in favour of the hybrid nanofluid flow over an elongating permeable curved convective thermal surface. Additionally, the external heat source and linear thermal radiation influence the flow phenomena whenever the velocity slip and nanoparticle shape effects associated with Hamilton–Crosser thermal conductivity model are significant. The designed equations relating to the flow phenomena are solved numerically using shooting-based Runge–Kutta fourth techniques followed by the similarity transformations used for the nondimensional form of the system of equations. The role of characterizing factors is deployed via graphs and described briefly. The correlation with the earlier investigation for the numerical outcomes of the rate of energy transport is also reported. The major outcomes of the study reveal that the enhanced curvature parameter along with the particle concentrations within their limit overshoots the velocity profiles further, the external heat source combined with thermal radiation also favors in enhancing fluid temperature.

The primary aim of this study was to examine the peristaltic flow of an unsteady non-Newtonian TiO₂ nanofluid through a uniformly symmetric channel under the influence of electro-osmosis. The fluid behavior was modeled by the Sutterby model. Furthermore, the flow took place through a porous medium, following a modified form of Darcy’s law. Additionally, the impacts of Dufour and Soret effects, chemical reaction, activation energy, viscous dissipation, heat generation, and thermal radiation were considered. A wave transformation was used to simplify the governing equations describing the velocity, temperature, and nanoparticle concentration. These simplified equations were then solved analytically using the homotopy perturbation method. Additionally, set figures were employed to illustrate and discuss the impact of the physical parameters involved in the problem on the obtained solutions. It is found that the presence of a modified Darcy’s medium in the Navier–Stokes equation results in a porous term that is dependent on the index of the Sutterby model. Furthermore, it is found that as the thermophoresis parameter increases, the nanoparticles are more concentrated, and their flow from the hot region to the cold region is more effective. Additionally, it is observed that in the presence of thermal radiation, the activation energy and the Brownian motion parameter have similar effects on the concentration profile.

This paper presents an analytical investigation into the propagation of a normal shock wave in Van der Waals gas flow, employing the Buongiorno model. It explores the dynamics of this flow type under a shock wave, considering modified Rankine–Hugoniot (RH) jump conditions within the Buongiorno model framework. By solving the RH conditions, this study provides a solution for gas flows with varying nanoparticle concentrations, facilitating an examination of parameter variations under discontinuity. The abstract further emphasizes the graphical representation of velocity coefficient and pressure in adiabatic gas flow during a shock wave, considering compressive and exponential waves. The analysis accounts for nanoparticle concentration and non-ideal parameters.

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of ${\mathrm{\text{TiO}}}_2$ and ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$ nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$ nanoparticles. The HNF $({\mathrm{\text{TiO}}}_2+{\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4∕{\mathrm{\text{H}}}_2\mathrm{\text{O}})$ exhibits 0.45–0.75% increase in heat transfer rate when compared to a nanofluid $({\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4∕{\mathrm{\text{H}}}_2\mathrm{\text{O}})$ for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement.

This study focuses on the dielectric responses of the ${\text{B}}_{36}$ nano-Borophene lattice, using Monte Carlo simulations. It explores the impact of various parameters, including temperature, the $J_{\mathrm{\text{SS}}}$ coupling interaction, the crystal field D, and the impact of the longitudinal electric field $E_{\mathrm{\text{Z}}}$, on the dielectric characteristics of nano-Borophene. Simulation study results show that these parameters significantly influence the blocking temperature $T_{\mathrm{\text{B}}}$ and modify the shape and area of the electrical hysteresis cycle. This research can make an important contribution to the understanding of dielectric phenomena, which is essential in fields such as high-temperature dielectric devices and other advanced technological applications.

The purpose of this paper is to discuss the use of topological indices (TIs) to anticipate the physical and biological aspects of innovative drugs used in the treatment of Alzheimer’s disease. Degree-based topological indices are generated using edge partitioning to assess the drugs Tacrine, Donepezil, Ravistigmine, Butein, Licochalcone-A and Flavokqwain-A. Furthermore, using linear regression, a quantitative structure–property relationship (QSPR) model is developed to predict the characteristics such as boiling point (BP), flash point (FP), molar volume (MV), molecular weight, complexity and polarizability. The findings show that topological indices have the potential to be used as a tool for drugs discovery and design in the field of Alzheimer’s disease treatment.

We investigate the rational solitons of the Kraenkel–Manna–Merle (KMM) system in ferrites via symbolic computation with the ansatz functions technique and logarithmic transformation. The KMM system describes the propagations of the ferromagnetic particles in ferrite materials. Multiwave solitons are reported by using the three-wave technique. Homocentric breathers (HBs) approach is also applied to build new forms of exact solutions. We construct M-shaped solitons and their dynamics are shown via the appropriate values of parameters. Two types of interactions for rational soliton with kink wave are investigated. Additionally, kink cross-rational solitons (KCRSs) and periodic cross-rational solitons (PCRSs) are examined via suitable transformation.

In this paper, we examine a novel generalized $(2+1)$-dimensional Bogoyavlensky–Konopelchenko (gBK) model analytically via application of five mathematical methods, namely called Extended Simple Equation (ESE) method, Modified Extended Auxiliary equation mapping (MEAEM) method, $(G^{\prime }/G)$-expansion method, $\mathrm{\text{Exp}}(-\mathrm{\Psi }(\varphi ))$-expansion method and modified F-expansion method, respectively, to obtain different types solitary wave solutions in the form of trigonometric, hyperbolic, rational and exponential functions as compared to solutions exist in [S. T. Chen and W. X. Ma, Math. China 13 (2018) 525; A. Sonia, A. Jamshad, S.-U. Rehman and A. Ali, Int. J. Appl. Comput. Math. 9 (2023)]. The research focuses on physical systems, physiology, mathematical applications, engineering fields, and the chemical processes of species in the porous nanoparticles, examining the impact of various parameters on the nonlinear model. The graphs of some solutions are plotted in the form of two-dimensional and three-dimensional by assigning the particular values to the paraments with the assistance of mathematica software which illustrated the physical behavior of the concern model. The derived solution has numerous applications in fluid dynamics and the interaction of Riemann waves and long waves.

This study purposes to extract some fractional analytical solutions of the Peyrard-Bishop-Deoxyribo-Nucleic-Acid ($\beta$-PBDNA) dynamic model with the beta-derivative by the unified Riccati equation expansion method (UREEM). Furthermore, we examine the role of various parameters of the fractional model on the soliton dynamic. The research focuses on computational biophysics and materials science, examining the impact of various parameters on the fractional model. This paper contributes to understanding soliton solutions and the $\beta$-PBDNA dynamic model, demonstrating the applicability of the UREEM method to various fractional models. Some soliton solutions of the model are successfully generated by applying the UREEM. Implementing the UREEM, we take a fractional wave transformation to convert the model into a nonlinear ordinary differential equation. So, a linear equation system is generated. After the system is solved, the soliton solutions are gained for the appropriate solution sets. Finally, 3D, 2D and contour graphs of diverse solutions are depicted at suitable values of parameters. In addition, this paper presents 3D, 2D and contour graphs of various solutions with suitable parameter values. The results are beneficial for interpreting the model in future work and confirm that UREEM is effectively applicable to diverse fractional models, coupled with a comprehensive graphical analysis of how different parameters influence these solutions.

In this study, the nonlinear two-dimensional Kadomtsev–Petviashvili-modified equal width (KP-MEW) equation is under investigation, which is described as a nonlinear wave model in weakly restoring forces and shallow water waves in the way of ferromagnetic, solitary waves in two dimensions with short amplitude and long wavelength and are also helpful in the investigation of various behaviors in nonlinear sciences. We successfully found the interesting and novel solitary wave results in bright solitons, kink solitons, dark solitons, anti-kink solitons, periodic singular solitons for nonlinear two-dimensional KP-MEW equation on the base of extension of simple equation technique under symbolic computational software Mathematica. The created solitons play an important role in nonlinear engineering and physics such as nonlinear optics, nonlinear dynamics, soliton wave theory, optical fiber and communication system. We are sure that these constructed results are novel and interesting which does not exist in the previous literature works. The graphical representation of constructed results is shown by 2D, 3D and contour graphs. The investigated research work proved that utilized technique is more concise, straightaway and efficient for study of other nonlinear partial differential equations.

We show how the quantum hydrodynamical formulation of quantum mechanics converts the nonlocality in the standard wave-like description of quantum systems by an instability of the quantum system, which opens the door to a new way for studying quantum systems based on known methodologies for studying the stability of fluids. As a second result, we show how the Madelung equations describe quantized energies without any external quantization conditions.