Band 19, Heft 1 -

In this paper, we explore the von-Kármán infinite disk problem for the situation where ferrofluid resides in the space above the rotating disk. Furthermore, flow field is influenced by axial magnetic field. In this study, we treat water as the base fluid which consists of homogeneous suspensions of Fe3O4${\rm{F}}{{\rm{e}}_{\rm{3}}}{{\rm{O}}_{\rm{4}}}$ ferromagnetic particles. The main motivation here is to resolve heat transfer problem in the existence of non-linear radiative heat transfer. With the aid of von-Kármán relations, the equations of fluid motion and heat transfer are changed into a set of self-similar differential equations. These equations are dealt by an implicit finite-difference method with high precision. The results reveal that wall heat transfer rate can be improved by increasing solid volume fraction of ferromagnetic particles. Drag coefficient at the disk and heat transfer rate are increased as the strength of Lorentz force is enhanced. Viscous dissipation effect has an important part in improving heart transfer process which is vital in some applications. The results demonstrate that cooling capability of magnetite–water nanofluid is much superior to the conventional coolants. An excellent correlation of present results with the previous published articles is found in the all the cases.

This article presents the effect of convective heating and velocity slip on flow generation of an incompressible micropolar fluid through a porous channel. The flow is induced by a constant axial pressure gradient applied in the flow direction. The non-linear governing equations are linearized using the quasilinearization technique and then solved by Chebyshev spectral collocation method. The numerical values of the velocity, microrotation and temperature are used to derive the corresponding entropy generation number and Bejan number within the porous channel. The influences of pertinent parameters on velocity, microrotation, temperature, entropy generation and Bejan number are discussed through graphs. It is observed that the convective heating tends to increase the entropy generation within the channel.

Understanding event-by-event correlations and fluctuations is crucial for the comprehension of the dynamics of heavy ion collisions. Relativistic hydrodynamics is an elegant tool for modelling these phenomena; however, such simulations are time-consuming, and conventional CPU calculations are not suitable for event-by-event calculations. This work presents a feasibility study of a new hydrodynamic code that employs graphics processing units together with a general MUSTA-FORCE algorithm (Multi-Stage Riemann Algorithm – First-Order Centred Scheme) to deliver a high-performance yet universal tool for event-by-event hydrodynamic simulations. We also investigate the performance of selected slope limiters that reduce the amount of numeric oscillations and diffusion in the presence of strong discontinuities and shock waves. The numerical results are compared to the exact solutions to assess the code’s accuracy.

Two numerical procedures are developed to approximate the solution of one-dimensional parabolic equations using extrapolated collocation method. By defining two different end conditions and forcing cubic spline to satisfy the interpolation conditions along with one of the end conditions, we obtain fourth- (CBS4) and sixth-order (CBS6) approximations to the solution in spatial direction. Also in time direction, a weighted finite-difference discretization is used to approximate the solution at each time level. The convergence analysis of the methods is discussed in detail and some error bounds are obtained theoretically. Finally, some different examples of Burgers’ equations with applications in fluid mechanics as well as convection–diffusion problems with applications in transport problems are solved to show the applicability and good performance of the procedures.

This work is related to dynamics of a second-order rational difference equation. We investigate the parametric conditions for local asymptotic stability of equilibria. Center manifold theorem and bifurcation theory are implemented to discuss the parametric conditions for existence and direction of period-doubling bifurcation and pitchfork bifurcation at trivial equilibrium point. Moreover, the parametric conditions for existence and direction of Neimark–Sacker bifurcation at positive steady state are investigated with the help of bifurcation theory. The chaos control in the system is discussed through implementation of OGY feedback control method. In particular, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control. Finally, numerical simulations are provided to illustrate theoretical results. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the system.

We consider the fractional retarded evolution equations CDtqu(t)+Au(t)=f(t,ut,∫0tw(t,s,us)ds),t∈[0,a],$$^{C}D_{t}^{q}u(t)+Au(t)=f\Big(t,u_t,\int_{0}^{t}w(t,s,u_s)ds\Big),\quad t\in[0,a],$$ where CDtq$^{C}D_{t}^{q}$, q∈(0,1]$q\in(0,1]$, is the fractional derivative in the Caputo sense, −A$-A$ is the infinitesimal generator of a C0$C_0$-semigroup of uniformly bounded linear operators T(t)$T(t)$(t≥0)$(t\geq0)$ on a Banach space X$X$ and the nonlinear operators f$f$ and w$w$ are given functions satisfying some assumptions, subjected to a general mixed nonlocal plus local initial condition of the form u(t)=g(u)(t)+ϕ(t)$u(t)=g(u)(t)+\phi(t)$, t∈[−h,0]$t\in[-h,0]$. Under more general conditions, the existence of mild solutions and positive mild solutions are obtained by means of fractional calculus and fixed point theory for condensing maps. Moreover, we present an example to illustrate the application of abstract results.

In this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrödinger equations on the half-line. Suppose that the solution {q1(x,t),q2(x,t)}$\{q_1(x,t),q_2(x,t)\}$ exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameter λ$\lambda$.