We examine the effect of the breaking of vorticity conservation by viscous dissipation on transport in the underlying fluid flow. The transport of interest is between regimes of different characteristic motion and is afforded by the splitting of separatrices. A base flow that is vorticity conserving is therefore assumed to have a separatrix that is either a homoclinic or heteroclinic orbit. The...

MHD viscous oscillating type blood flow through lumen in arteries and varicose veins motivating to the study of disordered vessels veins. The nervous system, like other micro respiratory system is modeled geometrically shape tapered curvy walls varying cross section which new approach this problem same has advantage compared geometrical channel shapes. Blood taken as viscoelastic optically thic...

Phase mixing was introduced by Heyvaerts and Priest (1983) as a mechanism for heating the plasma in the open magnetic field regions of coronal holes. Here the basic process is modified to include a stratified atmosphere in which the density decreases with height. We present an analytical solution in the case of zero dissipation and use a numerical code in the non-zero dissipation case to descri...

We develop and discuss global accretion solutions for viscous ADAF disks containing centrifugally supported isothermal shock waves. The fact that such shocks can exist at all in ADAF disks is a new result. Interestingly, we find that isothermal shocks can form even when the level of viscous dissipation is relatively high. In order to better understand this phenomenon, we explore all possible co...

Variational turbulence is among the few approaches providing rigorous results in turbulence. In addition, it addresses a question of direct practical interest, namely, the rate of energy dissipation. Unfortunately, only an upper bound is obtained as a larger functional space than the space of solutions to the Navier-Stokes equations is searched. Yet, in some cases, this upper bound is in good a...

In a weakly ionized plasma, the evolution of the magnetic field is described by a “generalized Ohm’s law” that includes the Hall effect and the ambipolar diffusion terms. These terms introduce additional spatial and time scales which play a decisive role in the cascading and the dissipation mechanisms in magnetohydrodynamic turbulence. We determine the Kolmogorov dissipation scales for the visc...

A non-isothermal formulation of the Poisson-Nernst-Planck with Navier-Stokes equations is used to study the influence of heating effects in the form of Joule heating and viscous dissipation and imposed temperature gradients on a microchannel/nanochannel system. The system is solved numerically under various cases in order to determine the influence of temperature-related effects on ion-selectiv...

The conditions defining a stationary fluid flow may lead to multiplicity of solutions. This circumstance is widely documented in the literature when mixed convection vertical channel or duct accompanied by an important effect viscous dissipation. Usually, there are double solutions with parallel velocity field which satisfy given temperature boundary and prescribed mass rate. However, internal ...