Effects of non-uniform nanoparticle concentration on entropy generation

The entropy generation analysis of a thermal process is capable of determining the efficiency of that process and is therefore helpful to optimize the thermal system operating under various conditions. There are several ingredients upon which the phenomenon of entropy generation can depend, such as the nature of flow and the fluid, the assumed conditions, and the material properties of the working fluid. However, the dependence of entropy generation phenomenon upon such properties has so far not been fully realized, in view of the existing literature. On the other hand, based upon the existing studies, it has been established that the non-uniform concentration of nanoparticles in the base fluid does cause to enhance the heat transfer rate. Therefore, it is logical to investigate the entropy production under the impact of non-homogenous distribution of nanoparticles. Based upon this fact the aim of current study is to explore a comprehensive detail about the influence of non-homogeneous nanoparticles concentration on entropy production phenomenon by considering a laminar viscous flow past a moving continuous flat plate. Non-uniform concentration is considered in the nanofluid modeling in which the Brownian and thermophoretic diffusions are considered which impart significant effects on velocity and temperature profiles. An exact self-similar solution to this problem is observed to be possible and is reported. The effects of various controlling physical parameters such as Brinkman number, Schmidt number, Prandtl number, diffusion parameter, and concentration parameter on both local as well as total entropy generation number and Bejan number are elaborated by several graphs and Tables. The obtained results reveal a significant impact of all aforementioned parameters on entropy generation characteristics. It is observed that by a 20% increase in nanoparticles concentration the total entropy generation is increased up to 67% for a set of fixed values of remaining parameters.

Magnetohydrodynamic Winds Driven by Line Force from the Standard Thin Disk around Supermassive Black Holes: II. A Possible Model for Ultra-fast Outflows in Radio-loud AGNs

In radio-loud active galactic nuclei (AGNs), ultra-fast outflows (UFOs) were detected at the inclination angle of ∼10°–70° away from jets. Except for the inclination angle of UFOs, the UFOs in radio-loud AGNs have similar properties to that in radio-quiet AGNs. The UFOs with such low inclination cannot be explained in the line-force mechanism. The magnetic-driving mechanism is suggested to explain the UFOs based on a self-similar solution with radiative transfer calculations. However, the energetics of self-similar solution need to be further confirmed based on numerical simulations. To understand the formation and acceleration of UFOs in radio-loud AGNs, this paper presents a model of the disk winds driven by both line force and magnetic field and implements numerical simulations. Initially, a magnetic field is set to 10 times stronger than the gas pressures at the disk surface. Simulation results imply that the disk winds driven by both line force and magnetic field could describe the properties of UFOs in radio-loud AGNs. Pure magnetohydrodynamics (MHDs) simulation is also implemented. When the initial conditions are the same, the hybrid models of magnetic fields and line force are more helpful to form UFOs than the pure MHD models. It is worth studying the case of a stronger magnetic field to confirm this result.

Mathematical model of wedge-shaped plain bearing considering the dependence of viscosity on pressure

This paper outlines a new approach for finding an asymptotic and exact self-similar solution for the zero and first (without taking into account the melt and considering the melt, respectively) approximation of the wedge-shaped plain bearing with a non-standard support profile of the slide and the low-melting metal coating of the surface. The given approach is based on the flow equation of a ferromagnetic fluid for a «thin layer», the continuity equation, as well as the equation describing the profile of the guide’s molten contour. The proposed method takes into account the dependence of the rheological properties of the lubricant and the melt that have ferromagnetic properties in the laminar flow on pressure. We have succeeded in obtaining accurate analytical dependences for the field of velocities and pressure at zero and first approximations and the ones for the profile of the guide’s molten surface. Besides, we have managed to determine the key performance properties for the slide–guide friction pair, including load-bearing capacity and friction force. Finally, we could assess how the bearing capacity and friction force are influenced by parameters caused by the coating melt adapted to the conditions of the support profile friction and a parameter that characterize the rheological properties of the lubricant.

Point-wise Self-similar Solution for Spiral Shocks in an Accretion Disk with Mass Outflow in a Binary

We examine the properties of spiral shocks from a steady, adiabatic, non-axisymmetric accretion disk around a compact star in a binary. We first incorporate all possible influences from a binary through adopting the Roche potential and Coriolis forces in the basic conservation equations. In this paper, we assume spiral shocks to be point-wise and self-similar, and that the flow is in vertical hydrostatic equilibrium to simplify the study. We also investigate mass outflow due to shock compression and apply it to an accreting white dwarf in a binary. We find that our model will be beneficial for overcoming the ad hoc assumption of an optically thick wind generally used in studies of the progenitors of supernovae Ia.

Far Field of a Three-Dimensional Laminar Wall Jet

We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

Convergence to diffusion waves for solutions of 1D Keller-Segel model

In this paper, we are concerned with the asymptotic behavior of solutions to the Cauchy problem (or initial-boundary value problem) of one-dimensional Keller-Segel model. For the Cauchy problem, we prove that the solutions time-asymptotically converge to the nonlinear diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which is derived by Darcy’s law, as in [11, 28]. For the initial-boundary value problem, we consider two cases: Dirichlet boundary condition and null-Neumann boundary condition on (u, ρ). In the case of Dirichlet boundary condition, similar to the Cauchy problem, the asymptotic profile is still the self similar solution of the corresponding parabolic equation, which is derived by Darcy’s law, thus we only need to deal with boundary effect. In the case of null-Neumann boundary condition, the global existence and asymptotic behavior of solutions near constant steady states are established. The proof is based on the elementary energy method and some delicate analysis of the corresponding asymptotic profiles.

Theory for the coalescence of viscous lenses

Drop coalescence occurs through the rapid growth of a liquid bridge that connects the two drops. At early times after contact, the bridge dynamics is typically self-similar, with details depending on the geometry and viscosity of the liquid. In this paper we analyse the coalescence of two-dimensional viscous drops that float on a quiescent deep pool; such drops are called liquid lenses. The analysis is based on the thin-sheet equations, which were recently shown to accurately capture experiments of liquid lens coalescence. It is found that the bridge dynamics follows a self-similar solution at leading order, but, depending on the large-scale boundary conditions on the drop, significant corrections may arise to this solution. This dynamics is studied in detail using numerical simulations and through matched asymptotics. We show that the liquid lens coalescence can involve a global translation of the drops, a feature that is confirmed experimentally.

Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

We consider the long-time behavior of solutions to a fourth-order nonlinear Schrödinger (NLS) equation with a derivative nonlinearity. By using the method of testing by wave packets, we construct an approximate solution and show that the solution for the fourth-order NLS has the same decay estimate for linear solutions. We prove that the self-similar solution is the leading part of the asymptotic behavior.

Larson–Penston Self-similar Gravitational Collapse

Using numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425–448, 1969) and Larson (Mon Not R Astr Soc 145:271–295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $$p=k\varrho $$ p = k ϱ , $$k>0$$ k > 0 , and subject to Newtonian gravity. We rigorously prove the existence of such a Larson–Penston solution.