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This research concerns examining the non-Newtonian blood flow behavior through an artery of elliptic cross-section, affected by several stenoses. The Rabinowitsch fluid model is used to investigate the non-Newtonian behavior of the blood for uniform and nonuniform shapes of stenosis. The mathematical equations have been converted into a dimensionless form, and their nonlinearity is reduced by applying the assumptions of mild stenosis. The resulting differential equations are solved by using analytical techniques. A new polynomial of degree eight is introduced to complete the solutions of mathematical equations. The entropy generation is studied mathematically to analyze the irreversibility effects. The detailed graphical examination delineates the physical aspects of mathematical results. The flow velocity is higher for uniform shape than for nonuniform stenosis. The rising percentage of stenosis significantly enhances the flow velocity of the stenotic region. The entropy is enormous near the stenotic wall and has small values near the centerline, which assures the smooth flow in this region. Further, the streamlines are plotted to find the position of stenosis and assess the flow nature for the growing height of stenosis and rising flow rate. [ABSTRACT FROM AUTHOR]

This novel study unfolds the heat and mass transfer investigation of Williamson nanofluid (WNF) through a porous medium past a stretching plate, along with considering heat generation/absorption. Nanoparticles hold significant significance in thermal engineering, industrial operations, and biomedical advancements, contributing to enhanced heat transfer, cooling mechanisms, thermal extrusion processes, and applications in cancer treatment, particularly in addressing brain tumors. The coupled ordinary differential equations (ODEs) are gained from governing partial differential equations (PDEs) by applying sufficient transformations. Then the ODEs of a nonlinear nature, along with boundary conditions, are solved through bvp4c, a built-in MATLAB program. A good agreement has been found in comparing the present study with already published papers. Numerical values for skin friction, mass transfer, and heat transfer are shown through a table against involved physical parameters, especially for both injection (S < 0) and suction (S > 0) cases, by varying the values of unsteadiness parameter A and Weissenberg number W e . The effects of the physical parameters on velocity, temperature, and mass profile are graphically depicted and illustrated minutely. It is noted that both the magnetic and Williamson parameters cause the thickness of the boundary layer to be reduced. It can be deduced from these findings that the rate of heat transfer over the surface of the plate decreases as the unsteadiness parameter increases. Furthermore, it is observed that an increase in the parameters of thermophoresis and Brownian motion leads to a higher temperature of the nanofluid. [ABSTRACT FROM AUTHOR]

This paper introduces a groundbreaking method, Homotopy-based Fourier transform, integrating Fourier transform and Homotopy perturbation for refined nonlinear problem-solving. The modification enhances solution technique efficiency, notably accelerating convergence, particularly in solving the Korteweg–de Vries equation. Demonstrating versatility, the method effectively addresses ordinary and partial differential equations, showcasing its applicability across diverse mathematical scenarios. Moreover, the approach is extended to nonlinear dynamical systems, illustrating its robustness in handling complex dynamic behaviors. This method proves especially suitable for highly nonlinear differential equations, offering an efficient and effective tool for scientists and engineers dealing with intricate mathematical models. By significantly improving convergence rates, the Homotopy-based Fourier transform stands out as a valuable asset in unraveling the complexities of nonlinear systems across various scientific and engineering applications. [ABSTRACT FROM AUTHOR]

The perturbed nonlinear Schrödinger equation is employed to characterize the dynamics of optical wave propagation when confronted with dissipation (or gain) and nonlinear dispersion that vary with both time and space. This equation serves as a fundamental model for investigating pulse dynamics within optical fibers and has application to nanofiber applications. This study successfully discovers optical solitons within this framework using the unified solver, Jacobi elliptic function, and simplest equation methods. We extract solutions using hyperbolic, trigonometric, and rational functions, including multi-solitons, dark, singular, bright, and periodic singular solitons. This study thoroughly compares our results with existing literature to provide novelty and significance of our findings. We have incorporated a detailed comparison between the methods employed in our study, which highlights their importance and strength. We have derived soliton solutions for the examined equations and generated 3D contour and 2D visual representations of the resulting solution functions. Alongside obtaining the soliton solutions, we offer a graphical exploration of how the parameters in the considered equations influence the system. [ABSTRACT FROM AUTHOR]