This study is carried out to scrutinize the gyrotactic bioconvection effects on modified second-grade nanofluid with motile microorganisms and Wu’s slip (second-order slip) features. The activation energy and thermal radiation are also incorporated. The suspended nanoparticles in a host fluid are practically utilized in numerous technological and industrial products such as metallic strips, energy enhancement, production processes, automobile engines, laptops, and accessories. Nanoparticles with high thermal characteristics and low volume fraction may improve the thermal performance of the base fluid. By employing the appropriate self-similar transformations, the governing set of partial differential equations (PDEs) are reduced into the ordinary differential equations (ODEs). A zero mass flux boundary condition is proposed for nanoparticle diffusion. Then, the transmuted set of ODEs is solved numerically with the help of the well-known shooting technique. The numerical and graphical illustrations are developed by using a collocation finite difference scheme and three-stage Lobatto III as the built-in function of the bvp4c solver via MATLAB. Behaviors of the different proficient physical parameters on the velocity field, temperature distribution, volumetric nanoparticles concentration profile, and the density of motile microorganism field are deliberated numerically as well as graphically.

This article examines magnetohydrodynamic 3D nanofluid flow due to a rotating disk subject to Arrhenius activation energy and heat generation/absorption. Flow is created due to a rotating disk. Velocity, temperature and concentration slips at the surface of the rotating disk are considered. Effects of thermophoresis and Brownian motion are also accounted. The nonlinear expressions have been deduced by transformation procedure. Shooting technique is used to construct the numerical solution of governing system. Plots are organized just to investigate how velocities, temperature and concentration are influenced by various emerging flow parameters. Skin-friction Local Nusselt and Sherwood numbers are also plotted and analyzed. In addition, a symmetry is noticed for both components of velocity when Hartman number enhances.

In this article, the Laplace distribution is employed in lieu of the well-known normal distribution for finding better scalar values of risk. Explicit formulas for value-at-risk (VaR) and conditional value-at-risk (CVaR) are studied and used to manage the risk involved in a stock movement by using the GARCH model. Numerical simulations are given for a variety of stocks in equity markets to uphold the findings.

Nowadays, the problem of solar thermal absorption plays a vital role in energy storage in power plants, but within this phenomenon solar systems have a big challenge in storing and regulating energies at extreme temperatures. The solar energy absorber based on hybrid nanofluids tends to store thermal energy, and the hybrid nanofluids involve the stable scattering of different nano dimension particles in the conventional solvent at a suitable proportion to gain the desired thermophysical constraints. The authors focus on the behavior of the inclined plate absorber panel as the basic solution of water is replaced by a hybrid nanofluid, including $Cu$ (Copper) and $A{l}_2{O}_3$ (Aluminum Oxide), and water is utilized as a base surfactant in the current investigation. The inclined panel is integrated into a porous surface with the presence of solar radiations, Joule heating, and heat absorption. The fundamental equations of the flow and energy model are addressed with the similarity transformations. The homotopy analysis method (HAM) via Mathematica software is used to explore the solution to this problem. Furthermore, the important physical characteristics of the rate of heat transfer, omission and absorption of solar radiation, and its impact on the solar plant are observed.