ABSTRACT
In this study, numerical simulations are conducted with the goal of exploring the impact of the direction of the moving wall, solute and thermal transport, and entropy production on doubly diffusive convection in a chamber occupied by a Casson liquid. Wall movement has a significant impact on convective flow, which, in turn, affects the rate of mass and heat transfer; this sparked our interest in conducting further analysis. The left and right (upright) walls are preserved with constant (but different) thermal and solutal distributions, while the horizontal boundaries are impermeable to mass transfer and insulated from heat transfer. Numerical solutions are acquired using the control volume technique. Outcomes under a variety of Casson fluid parameters, including Ri, Gr, buoyancy ratio, and direction of the moving wall(s), are explored, and the influences of entropy generation are comprehensively investigated. While the flow field consists of a single cell in case I, it is dual-cellular in case III for all values of the considered parameters. Comparing the three cases, the average heat and mass transport presented lower values in case III due to the movement of an isothermal (left) wall against the buoyant force, while these values are enhanced in case I. The obtained results are expected to be useful in thermal engineering, material, food, and chemical processing applications.
ABSTRACT
The study of rotating-disk heat-flow problems is relevant to computer storage devices, rotating machineries, heat-storage devices, MHD rotators, lubrication, and food-processing devices. Therefore, this study investigated the effects of a Hall current and motile microorganisms on nanofluid flow generated by the spinning of a disk under multiple slip and thermal radiation conditions. The Buongiorno model of a nonhomogeneous nanofluid under Brownian diffusion and thermophoresis was applied. Using the Taylor series, the effect of Resseland radiation was linearized and included in the energy equation. By implementing the appropriate transformations, the governing partial differential equations (PDEs) were simplified into a two-point ordinary boundary value problem. The classical Runge-Kutta dependent shooting method was used to find the numerical solutions, which were validated using the data available in the literature. The velocity, motile microorganism distribution, temperature, and concentration of nanoparticles were plotted and comprehensively analyzed. Moreover, the density number, Sherwood number, shear stresses, and Nusselt number were calculated. The radial and tangential velocity declined with varying values of magnetic numbers, while the concentration of nanoparticles, motile microorganism distribution, and temperature increased. There was a significant reduction in heat transfer, velocities, and motile microorganism distribution under the multiple slip conditions. The Hall current magnified the velocities and reduced the heat transfer. Thermal radiation improved the Nusselt number, while the thermal slip conditions reduced the Nusselt number.
ABSTRACT
In this paper, we propose and analyze a nonautonomous predator-prey model with disease in prey, and a discrete time delay for the incubation period in disease transmission. Employing the theory of differential inequalities, we find sufficient conditions for the permanence of the system. Further, we use Lyapunov's functional method to obtain sufficient conditions for global asymptotic stability of the system. We observe that the permanence of the system is unaffected due to presence of incubation delay. However, incubation delay affects the global stability of the positive periodic solution of the system. To reinforce the analytical results and to get more insight into the system's behavior, we perform some numerical simulations of the autonomous and nonautonomous systems with and without time delay. We observe that for the gradual increase in the magnitude of incubation delay, the autonomous system develops limit cycle oscillation through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasi-periodic oscillations. We apply basic tools of non-linear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system.
