Numerical study for bioconvection transport of micropolar nanofluid over a thin needle with thermal and exponential space-based heat source

Nanomaterials are the latest technique to upgrade thermal conduction of base liquids. The submerging of these nanomaterials in base liquid is known as nanofluid. In recent time the nanofluids are more useful in mechanical engineering, nanotechnology, bioscience, biotechnology and in many sectors. This analysis deals with the bio-convection transport of micropolar liquid containing nanomaterial's and gyrotactic motile microorganisms past a needle moving in parallel flow in occurrence of thermally radiation and activation-energy. Modeling of needle structure for bioconvection flow of micropolar nanofluid is developed. The behavior of temperature and exponential space-based heat source is considered. The boundary layer flow expressions for developed transport issue are represented by PDEs. Suitable similarity variables are used to change transport expressions in nondimensional nonlinear ordinary differential ones. The bvp4c algorithm has been used to numerically tackle dimensionless nonlinear differential equations (ODEs). All results are described by employing bvp4c tool in MATLAB. Impacts of active numbers on flow distributions are examined with sketches and tables. Temperature field and heat transfer rate are quite opposite for exponential space-based heat source sink parameter and heat sink/source parameter. The concentration of nanoparticles is reduced for larger amount of Brownian motion parameter while uplifts for thermophoresis parameter. Concentration is enriched for the growing magnitudes of thermophoresis number. Higher Peclet parameter decayed the microorganism's field

Global stability and modeling with a non-singular kernel for fractional order heroin epidemic model: Insights from different population studies

There has been a worldwide epidemic of heroin that has affected people, families, societies, and cultures across the world. Now, the heroin epidemic has transitioned from heroin abuse to the overuse of synthetic narcotics, which are widely accessible and inexpensively produced. In this work, a novel mathematical approach is applied to investigate the dynamics of the heroin epidemic model and its harmful effect on society with different population data. A heroin model has been constructed with the importance of a non-singular kernel in the sense of a generalized Mittag-Leffler kernel. The well-posedness of the proposed model is proven via fixed-point theory. To examine the heroin model, two equilibrium states have been determined. These equilibrium states are proven to be locally and globally asymptotically stable. To analyze the behavior of heroin, a basic reproduction number and sensitivity analysis are used to determine the impact of different parameters mathematically as well as through simulations. To find the approximate solution, we implement the Toufik–Atangana numerical method at different fractional order values. The sensitivity of the heroin model is carried out, and 3-D graphs show the significance of the parameter involved in the model. Finally, the numerical outcomes are presented with different values of fractional parameters