This research investigates the influence of the combined effect of the chemically reactive and thermal radiation on electrically conductive stagnation point flow of nanofluid flow in the presence of a stationary magnetic field. Furthermore, the effect of Newtonian heating, thermal dissipation, and activation energy are considered. The boundary layer theory developed the constitutive partial differential momentum, energy, and diffusion balance equations. The fundamental flow model is changed to a system of coupled ordinary differential equations (ODEs) via proper transformations. These nonlinear-coupled equations are addressed analytically by implementing an efficient analytical method, in which a Mathematica 11.0 programming code is developed for numerical simulation. For optimizing system accuracy, stability and convergence analyses are carried out. The consequences of dimensionless parameters on flow fields are investigated to gain insight into the physical parameters. The result of these physical constraints on momentum and thermal boundary layers, along with concentration profiles, are discussed and demonstrated via plotted graphs. The computational outcomes of skin friction coefficient, mass, and heat transfer rate under the influence of appropriate parameters are demonstrated graphically.

The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency.

The fractional regularized long wave equation and the fractional nonlinear shallow-water wave equation are the noteworthy models in the domains of fluid dynamics, ocean engineering, plasma physics, and microtubules in living cells. In this study, a reliable and efficient improved F-expansion technique, along with the fractional beta derivative, has been utilized to explore novel soliton solutions to the stated wave equations. Consequently, the study establishes a variety of reliable and novel soliton solutions involving trigonometric, hyperbolic, rational, and algebraic functions. By setting appropriate values for the parameters, we obtained peakons, anti-peakon, kink, bell, anti-bell, singular periodic, and flat kink solitons. The physical behavior of these solitons is demonstrated in detail through three-dimensional, two-dimensional, and contour representations. The impact of the fractional-order derivative on the wave profile is notable and is illustrated through two-dimensional graphs. It can be stated that the newly established solutions might be further useful for the aforementioned domains.

This research delves into the radial vibrations of dissipative poroelastic spherical shells, which are embedded within an elastic foundation and subjected to rotational dynamics. The analysis identifies that the inclusion of dissipative effects gives rise to a transcendental, complex-valued frequency equation. A numerical approach, specifically the bisection method, is employed in MATLAB for solution derivation. In instances where the argument is relatively small, the study leverages the asymptotic expansions of Bessel functions, facilitating the bifurcation of the frequency equation into two distinct real-valued equations. These equations are instrumental in computing the natural frequency as a function of the shell’s thickness. Furthermore, the research rigorously examines how rotational forces influence the natural frequency. The culmination of this study is presented through a series of graphical depictions, which succinctly illustrate the impact of rotational dynamics on the radial vibrations of thick-walled hollow structures situated in various elastic media. The overall findings contribute significantly to our understanding of the behavior of poroelastic materials in rotational environments, with implications for both theoretical and practical applications in material science and engineering. The results can benefit the theoretical development of orthopedic study projects connected to spherical poroelastic medium.

Diabetes is a chronic disease and a major public health concern all over the world, even when made feasible to learn about the root cause of the disease by awareness along with the methods of prevention. This study introduces a mathematical deterministic model that describes the progression of type 2 diabetes, integrating a component of awareness and a saturation treatment function named Holling type II. The presented work investigates and numerically analyzes the impact of various treatment strategies, such as consistent physical activity, a healthy diet, access to medical services, and the efficacy of treatments. The research findings indicate that the use of Holling type II treatment functions can prevent minor and major complications related to diabetes.