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.

Atherosclerosis, which causes the artery walls to thicken, the lumen to narrow, and the wall to thin in some places, is characterized by plaque accumulation in the arteries. These blood flow modifications can cause aneurysms and heart attacks if left unattended. Most of the arteries in the cardiovascular system are branched; therefore, a parent artery (main artery) with two daughter arteries (branched arteries) is considered in the present analysis. To examine the impact of various nanoparticle combinations on blood flow, four distinct nanoparticles, namely, gold (Au), graphene oxide (GO), copper (Cu), and tantalum (Ta), were injected into the blood to generate Au–GO–Cu–Ta/blood tetrahybrid nanofluid. In arteries with small diameters, blood behavior is regarded as non-Newtonian; therefore, blood behavior is governed by Jeffrey fluid in the present analysis. It has been investigated how Hall effects, Joule heating, radiation, and viscous dissipation affect blood flow through an artery that has an overlapping stenosis in the branches and a bell-shaped stenosis in the main artery. The approximation of mild stenosis is utilized to simplify and non-dimensionalize the governing equations. The Crank–Nicolson finite-difference scheme is used in MATLAB to solve the resulting equations. The results for velocity, temperature, wall shear stress, flow rate, and heat transfer rate are represented graphically. Furthermore, the entropy optimization has been performed for the specified problem. Enhancement in velocity with half of the bifurcation angle (η) can be observed from the velocity contours. The velocity of the tetrahybrid nanofluid increases with an increase in Jeffrey fluid parameter (λ1*) and shape parameter of the nanoparticles (n) as well. Introducing nanoparticles into the bloodstream can improve targeted drug delivery, allowing for more precise treatment at the cellular level. In addition, the tunable properties of nanoparticles offer possibilities for enhanced therapeutic and diagnostic treatments in a variety of medical disorders.

The current study is centered on the application of magnetically targeted drug delivery in a constricted vertical bifurcated artery utilizing Fe3O4 nanoparticles. The arterial stenosis is characterized by a bell-shaped narrowing in the parent artery and overlapping narrowing in the daughter artery. The blood is regarded as exhibiting the rheological behavior of a Casson fluid. The temperature-dependent nature of blood viscosity is postulated, and Reynold’s viscosity model describes it. This study examines the impact of electromagnetohydrodynamics (EMHD), body acceleration, Joule heating, and viscous dissipation. The assumption of a no-slip velocity condition is made at the walls of the artery. The governing equations are subjected to a process of non-dimensionalization and simplification, employing the mild-stenosis approximation. The resulting equations are subsequently solved in MATLAB by employing the finite-difference Crank–Nicolson technique. Entropy plays a significant role during any treatment or surgery; therefore, the present problem addresses entropy generation minimization. The results for velocity, temperature, wall shear stress, flow rate, impedance, heat transfer rate, entropy generation number, and Bejan number are represented graphically. The velocity contours illustrate that the flow velocity enhances with the Casson fluid and particle mass parameters. Furthermore, the number of trapped bolus also increases in the daughter artery. The nanofluid velocity and particle velocity decrease with an increase in the particle concentration parameter in the parent artery and the daughter artery. Entropy declines with the temperature difference parameter increment, whereas the Bejan number enhances. Magnetite (Fe3O4) nanoparticles have various applications owing to their biocompatibility, elevated magnetic susceptibility, chemical stability, non-toxic nature, and cost-effectiveness.