This article examines the effects of entropy generation, heat transmission, and mass transfer on the flow of Jeffrey fluid under the influence of solar radiation in the presence of copper nanoparticles and gyrotactic microorganisms, with polyvinyl alcohol–water serving as the base fluid. The impact of source terms such as Joule heating, viscous dissipation, and the exponential heat source is analyzed via a nonlinear elongating surface of nonuniform thickness. The development of an efficient numerical model describing the flow and thermal characteristics of a parabolic trough solar collector (PTSC) installed on a solar plate is underway as the use of solar plates in various devices continues to increase. Governing PDEs are first converted into ODEs using a suitable similarity transformation. The resulting higher-order coupled ODEs are converted into a system of first-order ODEs and then solved using the RK 4th-order method with shooting technique. The remarkable impacts of pertinent parameters such as Deborah number, magnetic field parameter, electric field parameter, Grashof number, solutal Grashof number, Prandtl number, Eckert number, exponential heat source parameter, Lewis number, chemical reaction parameter, bioconvection Lewis number, and Peclet number associated with the flow properties are discussed graphically. The increase in the radiation parameter and volume fraction of the nanoparticles enhances the temperature profile. The Bejan number and entropy generation rate increase with the rise in diffusion parameter and bioconvection diffusion parameter. The novelty of the present work is analyzing the entropy generation and solar radiation effects in the presence of motile gyrotactic microorganisms and copper nanoparticles with polyvinyl alcohol–water as the base fluid under the influence of the source terms, such as viscous dissipation, Ohmic heating, exponential heat source, and chemical reaction of the electromagnetohydrodynamic (EMHD) Jeffrey fluid flow. The non-Newtonian nanofluids have proven their great potential for heat transfer processes, which have various applications in cooling microchips, solar energy systems, and thermal energy technologies.

A novel analysis of the electromagnetohydrodynamic (EMHD) non-Newtonian nanofluid blood flow incorporating CuO and Al${}_2$O${}_3$ nanoparticles through a permeable walled diseased artery having irregular stenosis and an aneurysm is analyzed in this paper. The non-Newtonian behavior of blood flow is addressed by the Casson fluid model. The effective viscosity and thermal conductivity of nanofluids are calculated using the Koo-Kleinstreuer-Li model, which takes into account the Brownian motion of nanoparticles. The mild stenosis approximation is employed to reduce the bi-directional flow of blood to uni-directional. The blood flow is influenced by an electric field along with a magnetic field perpendicular to the blood flow. The governing mathematical equations are solved using Crank-Nicolson finite difference approach. The model has been developed and validated by comparing the current results to previously published benchmarks that are peculiar to this study. The results are utilized to investigate the impact of physical factors on momentum diffusion and heat transfer. The Nusselt number escalates with increasing CuO nanoparticle diameter and diminishing the diameter of Al${}_2$O${}_3$ nanoparticles. The relative % variation in Nusselt number enhances with Magnetic number, whereas a declining trend is obtained for the electric field parameter. The present study’s findings may be helpful in the diagnosis of hemodynamic abnormalities and the fields of nano-hemodynamics, nano-pharmacology, drug delivery, tissue regeneration, wound healing, and blood purification systems.

In this study, the computational analysis of entropy generation optimization for synthetic cilia regulated ternary hybrid Jeffery nanofluid (Ag-Au-TiO₂/PVA) flow through a peristaltic vertical channel with swimming motile Gyrotactic microorganisms is investigated. Understanding the intricate interaction of multiple physical phenomena in biomedical applications is essential for optimizing entropy generation and advancing microfluidic systems. The characteristics of nanofluid are explored for the electroosmotic MHD fluid flow in the presence of thermophoresis and Brownian motion, viscous dissipation, Ohmic heating and chemical reaction. Using the appropriate transformations, a set of ordinary differential equations are created from the governing partial differential equations. The resulting ODEs are numerically solved using the shooting technique using BVP5C in MATLAB after applying the long-wavelength and low Reynolds number approximation. The velocity, temperature, concentration, electroosmosis, and microorganism density profiles are analyzed graphically for different emerging parameters. Graphical investigation of engineering interest quantities like heat transfer rate, mass transfer rate, skin friction coefficient, and entropy generation optimization are also presented. It is observed that the rate of mass transfer increases for increasing thermophoretic parameter, while reverse effect is noted for Brownian motion parameter, Schmidt number, and chemical reaction number. The outcomes of present study can be pertinent in studying Cilia properties of respiratory tract, reproductive system, and brain ventricles.

This paper examines two methods for solving the nonlinear fractional Phi-four problem with variable coefficients. One of the distinct states of the Klein–Gordon model yields the Phi-four equation. It is also used to simulate the kink and anti-kink solitary wave connections that have recently emerged in biological systems and nuclear particle physics. The approaches that are being suggested consist of the Yang transform, the homotopy perturbation approach, the decomposition approach, and the fractional derivative as stated by Caputo. The advantages of the proposed techniques are their capability of combining two dominant approaches for attaining precise and approximate solutions of nonlinear equations. It is important to keep in mind that the suggested methods can perform better in general as they need less computational effort than the alternative methods, while keeping a high level of numerical precision. The actual and estimated outcomes are demonstrated in graphs and tables to be quite similar, demonstrating the usefulness of the proposed approaches. Additionally, several simulations are used to show the physical behaviors of the found solutions with regard to fractional order. The article’s results possess complimentary properties that relate to the symmetry of partial differential equations.