Dynamic Behavior of a Steady Flow in an Annular Tube With Porous Walls at Different Temperatures

Abstract

In this paper, the axisymmetric flow of a viscous fluid through a porous annular tube with walls kept at different temperatures is studied theoretically. The physical properties of the fluid remain constant, notably its specific mass, its dynamic viscosity and its thermal diffusivity. The nondimensional parameters which the solutions of the problem depend on are defined. A numerical integration using the shooting method is applied for solving the Navier–Stokes equations and the energy equation. Bifurcation diagrams are presented and enable to highlight significant properties of the flow. Some thermal behaviors corresponding to specific values of the parameters are performed. Asymmetric solutions of the steady flow are described and some results about velocity components are also analyzed.

Viscous flow and heat transfer through two coaxial porous cylinders

“…This involves the dominance of flow reversal in the annular tube which manifests itself as a parabolic behavior through the axial velocity. Comparing to previous studies where inertial terms are not neglected [15,21,25], it follows that the high fluid viscosity in the present work is favorable to flow reversal. However, there are some zones situated at the vicinity of the hot wall where the axial velocity per unit length exceeds it value at walls.…”

“…The variation of the dynamic viscosity while other properties of the fluid remain constant couples the Navier-Stokes equations to the energy equation. If the temperature difference between the walls of the annulus is not high enough to produce significant changes in the dynamic viscosity, the Navier-Stokes equations and the energy equation are in partial coupling [25]. In fact, this partial coupling is due to the correlation in terms of the stream function and thermal gradients through the energy equation.…”

Modeling gasodynamic vortex cooling

“…[32] did not employ the incompressible limit, but studied the problem without the outer cylinder. Several studies on convective heat transfer between concentric cylinders are reviewed in [38][39][40].…”