Volume 16, Issue 5 -

This paper is concerned with the effects of body acceleration on an unsteady pulsatile flow of blood in a vessel. The non-Newtonian behavior of blood is modeled by the constitutive equation of an Oldroyd-B fluid. The behavior of the blood is assumed as an Oldroyd-B fluid in the core and a viscous fluid in the periphery. This new model predicts the relaxation and retardation phenomena in a pulsatile flow. Our interest lies in investigating the effects of stress relaxation and retardation in unsteady pulsatile flow of an Oldroyd-B fluid. The modeled equations are normalized and solved numerically using finite difference method. The results are graphically displayed and influence of the pertinent parameter on various physical quantities of interest is analyzed.

In this paper we study a prey–predator dynamical system suitable for species having no overlap between successive generations. Assuming that population evolves in discrete-time steps we investigate the prey refuge effect on prey–predator interactions. Stability analysis is applied in order to investigate the local stability properties of the fixed points of our modified model. Numerical simulation tools, such as parametric basins of attraction, phase plots, bifurcation and Lyapunov exponent diagrams are used in order to study further the complex dynamics of the system. It is shown that our modified prey–predator model exhibits a wider array of dynamics than its continuous counterpart. Adding an average refuge destabilizes the prey–predator interactions via a supercritical Neimark–Sacker bifurcation and several period-doubling bifurcations. Finally, the addition of a large refuge exhibits random-like dynamics leading to outbreaks in the prey population density. We show that reproduction in certain intervals is important and should be taken into account since it could help in the identification of insect pest population outbreaks.

This paper considers the unstable stratified turbulent flow in an open channel. A mathematical model of unstable stratified turbulent flow is introduced, which allows to assess the mean and fluctuation characteristics of the turbulent flow. The numerical algorithm is developed for solving this problem. A numerical method is based on the projection method, which divides the problem into three stages. At the first stage, it is assumed that the transfer of momentum occurs only by convection and diffusion. Intermediate velocity field is solved by fractional steps method. At the second stage, three-dimensional Poisson equation is solved by the Fourier method in combination with tridiagonal matrix method (Thomas algorithm). Finally, at the third stage, it is expected that the transfer is only due to the pressure gradient. The simulation results are in satisfactory agreement with the experimental data.

The paper presents a mathematical model of the thermal load on the aquatic environment under operational capacity 200 MW of thermal power plant. It is solved by the Navier–Stokes and temperature equations for an incompressible fluid in a stratified medium based on numerical method, the splitting method by physical parameters which approximated the finite volume method. The numerical solution of the equation system is divided into four stages. At the first step it is assumed that the momentum transfer is carried out only by convection and diffusion. Intermediate velocity field is solved by the five-step Runge–Kutta method. At the second stage, the pressure field is solved by the intermediate velocity field. Poisson equation for the pressure field is solved by Jacobi method. The third step is assumed that the transfer is carried out only by pressure gradient. The fourth step of the transport equation for temperature is also solved as momentum equations, with five-step Runge–Kutta method. The obtained numerical results of temperature distribution for operational capacity of 200 MW of three-dimensional stratified turbulent flow were compared with experimental data, which revealed qualitatively and quantitatively approximately the basic laws of hydrothermal processes occurring in the reservoir-cooler.

An approximate analytical solution of Richards’ equation (RE) in a semi-finite layer of porous medium is obtained in this article. The basic idea is constructing a function between the Boltzmann variable ϕ and the traveling wave solution of RE, introducing the function into RE and calculating the relevant parameters by differential transform method (DTM). In the end, three examples are prepared to show the accuracy of the presented approximate analytical solution.