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In this paper, we introduce the Hermite wavelet method (HWM), a numerical method for the fractional-order Bagley–Torvik equation (BTE) solution. The recommended method is based on a polynomial called the Hermite polynomial. This method uses collocation points to turn the given differential equation into an algebraic equation system. We can find the values of the unknown constants after solving the system of equations using the Maple program. The required approximation of the answer was obtained by entering the numerical values of the unknown constants. The approximate solution for the given fractional-order differential equation is also shown graphically and numerically. The suggested method yields straightforward results that closely match the precise solution. The proposed methodology is computationally efficient and produces more accurate findings than earlier numerical approaches. [ABSTRACT FROM AUTHOR]

This study numerically investigated the entropy production in nanofluids' dissipative unsteady oscillatory flow characterized by variable electric conductivity and magnetic heating effects. The imposition of the non-isothermal boundary condition on the oscillatory stretching sheet plays a crucial role in establishing the self-similar solution in the presence of viscous heating. An external magnetic field (uniform in space and time) is imposed perpendicular to the plane of the oscillating stretched boundary. The energy equation, incorporating viscous dissipation effects and momentum equation, is reduced to nonlinear coupled partial differential equations and numerically solved using the Gear-generalized differential quadrature scheme.Additionally, to ensure the precision and reliability of the outcomes, the numerical code undergoes a thorough validation process that involves comparing its outputs to the findings of previous available studies. The Corcione model is implemented to describe the nanofluid's effective viscosity and thermal conductivity. Furthermore, expressions for entropy production and relative irreversibility parameter (Bejan number), considering variable electric conductivity, are derived and computed based on solutions obtained from momentum and energy equations. The impacts of parameters such as magnetic parameter, variable electric conductivity parameter, Eckert number, Strouhal number, Prandtl number and temperature difference parameters on flow, heat transfer, entropy generation, and Bejan number are systematically illustrated and examined. We observed that increasing the variable electric conductivity parameters reduces the velocity profiles while improving the thermal fields. Similar behavior is found when the strength of a magnetic field is increased. The skin friction coefficient exhibits an augmentation in response to the Eckert number, dimensionless time, Strouhal number, nanoparticle volume fraction, magnetic parameter, and variable thermal conductivity parameter. Conversely, the Nusselt number increases concerning the Strouhal number and nanoparticle volume fraction. At the same time, it declines in association with the magnetic parameter, dimensionless time, Eckert number, and variable electric conductivity parameter.This comprehensive investigation enhances our understanding of nanofluid dynamics and provides valuable insights for optimizing thermal management systems across various engineering disciplines. [ABSTRACT FROM AUTHOR]

In this article, we investigate a couple of nonlinear time-fractional evolution equations, namely the cubic-quintic-septic-nonic equation and the Davey–Stewartson (DS) equation, both of which have significant applications in complex physical phenomena such as fiber optical communication, optical signal processing, and nonlinear optics. Using a powerful technique named the extended generalized Kudryashov approach, we extract different rich structured soliton solutions to these models, including bell-shaped, cuspon, parabolic soliton, singular soliton, and squeezed bell-shaped soliton. We also study the impact of fractional-order derivatives on these solutions, providing new insights into the dynamics of nonlinear models. The results are compared with the existing literature, revealing novel and distinct solutions that offer a deeper understanding of these fractional models. The results show that the implemented approach is useful, reliable, and compatible for examining fractional nonlinear evolution equations in applied science and engineering. [ABSTRACT FROM AUTHOR]

The present study reviews the relevant research done on the fluid–structure interaction (FSI) in channels and vessels. The cases of FSI in channels with elastic plates, channels with variable geometry, flow airfoils, blood vessels, and heart valves are presented, using data from credible research articles. The review is carried out with a focus on the performance of the FSI method in solving engineering problems in channels, reporting its findings such as the effect of power-law exponent, the Nusselt number in different parts of a fluid, lift, and drag for a rigid cylinder and a plate in Newtonian fluids, the formation of eddy current, and the distribution of velocity and pressure in a fluid and on walls. The review is instrumental for researchers, engineers, and academics in providing comprehensive insight into methodologies and applications of fluid–structure interaction. [ABSTRACT FROM AUTHOR]

In this article, the peristaltic flow of blood‐based nanofluid is examined numerically by employing the generalized differential quadrature method. The Casson constitutive model is adopted to depict the flow characteristics in a uniform wavy tube. Besides, the non‐Newtonian nature and heat transfer feature of the nanofluidic medium are also scrutinized properly in the presence of platelet magnetite nanoparticles Fe3O4. After deriving the governing conservation equations, the resulting flow model is modeled successfully under the realistic assumptions of long wavelength and low Reynolds number. Also, the experimentally tested correlations related to the thermophysical properties of nanofluids are incorporated in the conservation equations to explore the effect of adding magnetite nanoparticles in the biofluidic medium. Mathematically, the obtained partial differential equations are transformed into the dimensionless form by utilizing feasible transformations. Furthermore, the impacts of sundry physical parameters on the trapping phenomena, pressure gradient, velocity, wall shear stress, and temperature are discussed thoroughly for the present MHD non‐Newtonian nanofluid flow model via various displays. [ABSTRACT FROM AUTHOR]