This work investigates the intricate dynamics of the (1+1)-dimensional Hodgkin–Huxley model with conformable derivatives in order to find new soliton solutions using the G'/G -expansion method. This research not only advances our understanding of complex systems but also opens up new avenues for novel applications in fields like neuroscience, optical fiber communications, and plasma physics. The anticipated outcomes could lead to new understandings of signal transmission, wave propagation in nonlinear media, and neuronal dynamics. This work shows that the G'/G -expansion method can be used to find new soliton solutions, providing a promising direction for future nonlinear science and its applications.

The energy and mass transference through ternary nanofluid (TNF) over a stretching spinning sheet is estimated in the present study. The TNF has been prepared by the distribution of magnesium oxide (MgO), titanium dioxide (TiO2), and cobalt ferrite (CoFe2O4) nanoparticles (NPs) in water. The study of the TNF over a rotating stretching sheet can be directly used in optimizing the performance of solar thermal collector, high-power electronics cooling, and aerospace heat shields. Such flow has a vital role in the optimization of lubrication processes and nuclear reactor cooling in which high thermal conductivity and centrifugal flow manipulation is needed. The TNF flow has been calculated under the consequence of mixed convection, thermal radiation, constant and exponential heat source/sink, magnetic field, and porous medium. The flow scenario is mathematically stated in the form of a nonlinear system of PDEs (partial differential equations). The set of PDEs is transfigured into the non-dimensional system of ODEs (ordinary differential equations), by means of the similarity variables. The results are obtained through the bvp4c code (Matlab built-in package). The percent error between present and published study at Pr=5.0 is 0.0034541%, which ensure the accuracy of the proposed model and applied methodology. The energy transfer rate drops by up to 20.4049%, 25.5465% and 32.4766% by varying the exponential heat source/sink factor from -1.0 t0 1.0 in case of nano, hybrid and ternary nanofluid respectively. The transfer rate enhances up to 52.7911% and 51.2236% by varying heat radiation and Dufour number from 1.0 to 3.0 and 1.5 to 3.5 in case of THNF, respectively.

The variable slip flow of a ternary hybrid nanofluid over an inclined rotating disk under a time-dependent magnetic field is thoroughly evaluated in this work. Copper, titanium dioxide, and aluminum oxide nanoparticles depressed in water make up the working fluid. This work is novel because it simultaneously incorporates thermal radiation, viscous dissipation, Joule heating, Hall and ion-slip currents, and a non-Fourier heat transport mechanism utilizing the C-C heat flux model in a rotating disk configuration with velocity slip. This combined framework enables a more realistic representation of anisotropic magnetohydrodynamic transport in trihybrid nanofluid, which has not been reported previously for inclined rotating systems. The transformed similarity system is solved numerically using a collocation approach for nonlinear boundary-value problems. Streamline and isotherm visualizations are employed to elucidate the flow structure and thermal behavior. The results indicate that increasing Hall and ion-slip parameters significantly modifies the components of tangential and radial velocity while reducing the Lorentz force resistance. Thermal radiation and viscous dissipation enhance the temperature distribution, whereas the Cattaneo-Christov model suppresses thermal overshoots and predictsa thermal boundary layer that is narrower than the traditional Fourier law. In comparison to traditional nanofluids, the ternary hybrid nanofluid exhibits better heat transfer performance, indicating its potential for sophisticated thermal control in spinning magnetohydrodynamic systems.

The key purpose of this research is to analyze the heat transfer in dovetail device wetted with quint nanofluid subject to different influential parameters like radiations, porosity, convective, conductive, heat generation and their contribution in the heat transfer. Further, to investigate the joint effects of linear and nonlinear heating sources. The model is designed for dovetail device associated to promising heat transfer parameters. The physical model is governed by second order problem with the influence of quint concentration. To investigate the heat transfer, an innovative idea of Response Surface Technique (RST) and ANOVA successfully implemented and achieved better responses of the model against the parameters and furnished the results. It is examined that the presence of linear and nonlinear heating sources are crucial for heat transfer applications. The nonlinear source is observed excellent for enhanced heat transfer while linear source is good to achieve the applications at low heat transport. Further, concentrations, radiations and heat generation enhanced the dovetail device performance while permeability and conduction drop the heat mechanism. This investigation provides promising heat transfer in dovetail device wetted with quint nanofluid which is unique combination not reported so far. By implementing the Response Surface Technique (RST) and ANOVA, the analysis exceptionally measures the interactive and individual role of the parameters. This unified approach offers a novel predictive paradigm for optimizing and designing of the device in advanced heat transfer applications.

The variable thermal conductivity highly affects the heat performance of nanolubricant which has vibrant applications in chemical and mechanical engineering. Hence, this work explores the thermal feature of ZnO/SAE50 under thermal radiations, inconsistent heat source and viscous dissipation. The problem is formulated for transient case and obtained fourth order system including aforementioned physical effects. The model treated through bvp4c scheme and the results for different parameters are furnished and provided deep discussion. It is scrutinized that the movement of ZnO/SAE50 reduces for ϕ while S_q enhances it. The temperature performance is directly related to the inconsistent source parameters A and B and optimum changes are noticed about η =0.0 which indicates the middle region of the channel. The use of dissipation effects is observed favorable for the fluidic system efficiency and variable thermal conductivity number ϵ and S_q controlled heating of the system. The magnitude of skin friction improves from 1.05355 to 1.52862, and 1.18888 to 1.20392 for nanoparticles concentration and S_q , respectively. The prominent enhancement in the heat transfer due to R_d (4.99067 to 6.41030) and Ec (2.18116 to 4.89323) is examined. However, the non-uniform sources observed as heat controlling parameters. The squeezed effects help to regulate the heat transfer rate from 0.55644 to 2.89876 under S_q variations from 0.2 to 0.8.

This study investigates the heat mechanism in a porous fin using penta nanofluid due to its exciting applications in chemical engineering, thermal technologies, cooling devices, and in renewable energy. The novelty of this research falls in the use of penta nanoparticles with extended Tiwari and Das model, which modifies beyond the traditional models and it provides enrich heat transfer characteristics and efficiency control. The governing problem reduced into appropriate form by incorporating porosity, conductive heating, heat source and effective properties of modified Tiwari and Das model and then analyzed through MATLAB bvp4c algorithm. The problem results shown that the heat mechanism, efficiency and heatlines substantially improves with heat, thermal radiations and convective parameters. However, the porosity drops the heat from the fin due to enhanced medium resistance. Moreover, the use of penta nanofluid improve the cooling efficiency in the presence of model parameters. Thus, the proposed model with extended Tiwari and Das correlation offers a better energy management strategy for energy systems, and thermal engineering where precise heat transport and diminished heat losses are essential.

This study explores soliton phenomena in nonlinear systems governed by Fractional Schr & ouml;dinger Equations (FSEs) using Caputo fractional derivatives. The Schr & ouml;dinger Equation is a fundamental paradigm for understanding complex nonlinear systems, including hydrodynamics, quantum condensates, nonlinear optics, and shallow-water waves. We employ the innovative (r + G '/ G )-expansion technique to tackle the FSE system. By applying a wave transformation, we reduce the FSE system to a set of Nonlinear Ordinary Differential Equations (NODEs). We then convert these NODEs into nonlinear algebraic equations using a series solution ansatz. Solving the algebraic system using Maple, we obtain multiple families of soliton solutions for the targeted system. Select solutions are visualized in 3D, 2D, and contour graphical representations, demonstrating the precision and efficacy of our approach. These visualizations reveal intriguing wave profiles, including kink, damped, and periodic patterns, which provide valuable insights into the system's behavior. This research contributes to the understanding of soliton phenomena in nonlinear fractional systems, paving the way for further explorations in quantum mechanics, optics, and related fields.

We study the propagation of optical solitons in nonlinear media using a nonlinear Schrödinger equation with higher-order terms. We achieve accurate solutions as brilliant and dark solitons using the Extended Direct Algebraic Method (EDAM). The approach enables us to efficiently manage the dispersive and higher-order nonlinear factors. The impact of the coefficients on the soliton solutions is also investigated. Visual insights into the behaviour of the solitons are provided by the graphic analysis of the generated solutions using 2D and 3D plots. Furthermore, contour plots are created to show how the solutions vary depending on the different parameters, exposing complex structures and patterns. A greater comprehension of the physical phenomena that the equation describes is made possible by these graphical representations.

Buoyancy-driven viscous fluid flow across a curved surface is investigated numerically in this work using the coupled Maxwell and Navier-Stokes equations, with variable fluid characteristics represented as nonlinear functions of temperature. Realistic magneto-hydrodynamic effects are captured by including the Lorentz force and the influence of a fluctuating magnetic field in curvilinear coordinates. The governing partial differential equations are solved using the parametric continuation method (PCM) after being converted into a system of ordinary differential equations by similarity transformations. Results demonstrate excellent agreement when compared to previously published data using MATLAB's PCM solver to confirm correctness. According to the parametric study, buoyancy () improves fluid motion by around 15%, whereas greater curvature factors , Stuart numbers , and Prandtl numbers result in a 12%-16% drop in radial and arc-length velocities. The temperature profile falls by more than 23% as and increase, indicating the significance of thermal diffusivity in preventing heat buildup. It increases by 25% with higher magnetic interaction (, ). The induced magnetic field is strengthened by 6%-7% with a little increase in the magnetic interaction parameter , whereas the magnetic field intensity is reduced by about 25% with a larger . Skin friction falls by almost 10% with greater at moderate , but increases by 4% under larger Lorentz forces (, ). Overall, the results show that velocity, temperature, magnetic field distribution and surface forces are strongly influenced by buoyancy, curvature and electromagnetic parameters. The findings shed light on efficient energy optimisation, thermal control, and electromagnetic regulation of MHD flows over curved geometries.

The Riga plate is a magnetized surface that influences fluid motion and boundary layer properties. It plays an important role in heat transfer, industrial processes, and aerodynamics. This study investigates the unsteady flow of a micropolar hybrid nanofluid (MHNF) over a Riga plate. The base-fluid sodium alginate (SA) has been used in the preparation of a hybrid nanofluid (HNF) consisting of CeO2 (cerium oxide) and Al2O3 (aluminum oxide) nanoparticles (NPs). The modeled equations are transformed into a dimensionless form via similarity transformations, and the resulting equations are then numerically solved using the PCM (parametric continuation method). The influence of numerous parameters on velocity, microrotation, energy, and fluid concentration profiles is demonstrated and explained using tables and figures. Results for skin friction, energy, and mass transmission rate are also provided. Comparisons to the published data corroborate the method’s accuracy. The skin friction reduces by up to 95.1263

The behavior of solitons in multimode fibers is investigated using the Connected Higher-Order Nonlinear Schrödinger Equations (CHNSE). A sophisticated algebraic technique is employed to analyze the CHNSE, yielding a variety of exact solutions, including bright and dark solitons, Weierstrass elliptic function solutions, periodic singular solutions, and hyperbolic and Jacobi elliptic solutions. These solutions are graphically represented using density and three-dimensional graphics to illustrate their physical characteristics. The CHNSE model provides deeper understanding of nonlinear optical processes in multimode fibers, essential for high-speed communication systems. The findings contribute to the development of new optical communication technologies.

[This corrects the article DOI: 10.1371/journal.pone.0319095.].

In this work, the unsteady flow and heat transfer properties of a hybrid nanofluid consisting of Ti O 2 - CoF e 2 O 4 nanoparticles dispersed in water over a rotating disk, that is, stretching radially are investigated. The combined effects of thermal radiation, slip boundary conditions, an applied magnetic field, and different nanoparticle shape are highlighted. This issue is crucial for enhancing heat transfer in complex thermal management systems, where conventional fluids usually perform poorly. Unlike previous studies, this work investigates in a novel manner the effects of different nanoparticle shapes (sphere, column, and lamina) at constant volume fraction under realistic operating conditions on flow resistance and thermal performance. The governing Navier-Stokes and energy equations were numerically solved using MATLAB's BVP4C solver and the Von K & aacute;rm & aacute;n similarity transformations. The results show that increasing the radiation parameter improves the temperature profile and makes cooling more efficient, but increasing the Prandtl number makes it less efficient. The Lorentz force causes higher magnetic fields to boost fluid temperatures and lower axial, tangential, and radial velocities. As the slip parameter increases, the fluid speeds decrease and the temperature of the wall increases. These findings demonstrate that spinning disc systems can flow and transfer heat more effectively by selecting the appropriate boundary slip and nanoparticle shape. Effective cooling systems and heat exchangers depend on this. The fluid rotating in front of the disk rotates more slowly when the unsteadiness parameter alpha <^> has a lower value.

An extended direct algebraic method is used in this work to examine the soliton solutions of the fractional Hirota-Satsuma coupled Korteweg-de Vries equation. Understanding the dynamic behaviour of solitons in nonlinear systems using analytical solutions is our goal. To obtain precise soliton solutions, we utilise a logistic technique. These solutions are then shown graphically in three dimensions, two dimensions, and contours. Soliton interactions' complex dynamics and stability in fractional nonlinear systems are demonstrated by the results. This study clarifies the underlying dynamics and possible uses of soliton behaviour in complex systems, advancing our understanding of this phenomenon.

The purpose of this study is to construct diverse forms of exact soliton solutions and conduct a comprehensive qualitative analysis. For this aim, we use the Gross-Pitaevskii system, which belongs to the family of nonlinear Schr & ouml;dinger equations. This model is considered to be iconic and significant because it has potential applications in applied sciences, such as in physics, where it is used to exemplify quantum systems like Bose-Einstein condensates and illustrate the propagation of waves in optical fibers. Employing analytical techniques, the modified sine-cosine/sinh-cosh and extended rational sinh-Gordon expansion methods, we extract several waves from solutions in the shape of trigonometric, hyperbolic, and rational forms. To further deepen our insights related to the system's behavior, we execute a detailed dynamical analysis, including sensitivity, bifurcation, and chaos, using the corresponding Hamiltonian structure. We also derive the instability modulation using linear stability theory. Using Mathematica, we systematically simulate and verify all constructed results and present some solutions for appropriate parameter values using 2D, 3D, and contour plots. The outcomes provide fruitful insights relevant to multiple scientific domains, including optical fiber technology, plasma, and condensed matter physics. This work contributes to the ongoing study of nonlinear models by applying novel solution techniques and offering a broader perspective on the complex behavior of such systems. The novelty of this study lies in the fact that the proposed model has not been previously explored using the aforementioned advanced methods and comprehensive dynamical analyses.

An effective technique for analytically resolving fractional partial differential equations (FPDEs) is the analytic Fractional Characteristic Method (FCM). In this work, we examine the applicability of the FCM to several FPDEs and demonstrate their efficacy in solving them accurately. We go over the key components of the FCM and its advantages over other numerical and analytical techniques. According to our research, the FCM is a dependable and efficient technique for solving FPDEs, and it has the potential to be used in a variety of technological and scientific fields. Researchers and practitioners interested in using the FCM to find precise solutions to FPDEs can refer to the work’s outcomes, accurate soliton solutions for many applications, which are essential to engineering, optical communications, and nonlinear optics.

In this study, the high-resolution numerical simulation of the three-dimensional radiative rotating flow of polyalphaolefins (PAOs)-based nanolubricant with synergistic dispersion of molybdenum disulfide (MoS 2 ) and silicon dioxide (SiO 2 ) hybrid nanoparticles over a permeable surface expansion is presented. Motile bioconvection microorganisms are incorporated in the hybrid nanofluid to maximize the convective thermal performance and to stabilize the matrix of the multiphase solutions. The computational fluid dynamics framework considers the multiphysical coupled effects of the Darcy–Forchheimer porous medium, thermal radiation, heat sources and convective Biot boundary conditions with an aligned magnetic angle. The numerical approach, BVP4c is used to solve the transformed nonlinear equations of the boundary layer, and response surface methodology is applied to the surface topologies for the statistical mapping of the interactive limits of the parameters. It is found from the quantitative evaluations that the dominance of the porosity parameter is that it exactly gives a 67.4012% increase in the secondary skin friction as the porosity factor increases from 0.5 to 2.5. Moreover, the effect of an aligned magnetic field improves the energy transfer rate by 77.47%. The results of a rigorous grid independence matrix test show that when the number of discrete grid nodes is increased beyond ( N = 320), all boundary layer fluxes are asymptotically stabilized to within six decimal places. Consequently, absolute convergence results show that the absolute error residuals are always kept within a stable micro-band until 10 −8 , demonstrating the unprecedented numerical accuracy, stability and reliability of the present simulation for advanced microfluidic thermal management systems.

Fluidized bed reactors are widely applied in process industries due to their strong heat and mass transfer performance; however, their efficiency is often limited by gas bypassing, bubble coalescence, and non-uniform particle mixing. Although wall-mounted ribs are known to improve hydrodynamics, the combined influence of static bed height and rib geometry on reactor performance remains insufficiently understood. In this study, a combined experimental and numerical investigation was carried out on a vertical cylindrical fluidized bed (105 mm diameter) operating with fused alumina particles of mean diameter 177 µm. Experimental measurements were used to validate a transient Eulerian–Eulerian two-fluid CFD model implemented in ANSYS Fluent. The effects of three static bed heights (60, 70, and 80 mm) and three rib angles (135°, 150°, and 165°) were systematically examined. Key parameters, including solid volume fraction, particle velocity, pressure drop, hydrodynamic stability, and surface heat transfer coefficient, were analyzed using a phase-coupled SIMPLE algorithm. The results show that ribbed configurations significantly enhance gas–solid interaction compared to a smooth-walled bed by suppressing gas channeling and improving particle circulation. Among the tested geometries, the 150° rib angle provides the most stable hydrodynamic behavior, yielding a controlled 10–20% increase in particle velocity without excessive pressure loss. The best thermal performance was achieved with the 150° rib configuration at a 70 mm bed height, where the heat transfer coefficient reached approximately 550 W/m²·K, corresponding to a 57% improvement over the smooth bed. This enhancement was obtained with a negligible pressure drop penalty (<1%), ensuring energy-efficient operation. Overall, the study identifies the combination of a 150° rib angle and a static bed height of 70–80 mm as an optimal design for industrial fluidized bed reactors used in applications such as catalytic processing, combustion, and gasification, contributing to more efficient and sustainable thermal systems at low energy cost.