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.

The present work deals with the impact of hybrid nanoparticles (Au-Al₂O₃) on the blood flow pattern through a porous cylindrical artery with a bell-shaped stenosis in the presence of an external magnetic field, Joule heating, and viscous dissipation by considering two-dimensional pulsatile blood flow. The temperature-dependent viscosity model is utilized in this study. The blood flow is assumed to be unsteady, laminar, viscous, and incompressible. The mild stenotic presumption normalizes and reduces the bi-directional flow to uni-directional. The Crank-Nicolson scheme is applied to solve the continuity, momentum, and energy equations with appropriate initial and boundary conditions. Transport characteristics are visualized graphically for key dimensionless parameters such as Magnetic number ([ ]), Darcy number ( Da), Grashof number ( Gr), viscosity parameter ( β₀), Reynolds number ( Re), Eckert Number ( Ec), Prandtl number ( Pr), different concentration of both the nanoparticles ( ϕ₁, ϕ₂), and pressure gradient parameter ( B₁). The velocity contours for different emerging parameters have also been drawn to assess the overall behaviour of blood flow patterns. The non-dimensional velocity profile is enhanced with increment in values of Da, implying that the medium permeability provides less resistance to the flow. Increasing viscous dissipation ( Ec) and Joule heating ([ ]) parameter simultaneously raise the nanofluid temperature. Hybrid nanoparticles (Au-Al₂O₃/blood) effectively reduce hemodynamic variables such as wall shear stress and resistance (impedance). The present work finds applications in nano-mediated treatment of atherosclerosis and other diseases.