Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Viscous Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Incompressible Viscous Fluid ◽  
Temperature Fields ◽  
Partial Slip ◽  
Shear Stresses ◽  
Rotating Disk Flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

Exact Solutions Corresponding to the Viscous Incompressible and Conducting Fluid Flow Due to a Porous Rotating Disk

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Flow Field ◽  
Exact Solutions ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Conducting Fluid ◽  
Shear Stresses ◽  
Adiabatic Wall ◽  
Navier Stokes Equation

A study is pursued in this paper for the evaluation of the exact solution of the steady Navier–Stokes equation, governing the incompressible viscous Newtonian, electrically conducting fluid flow motion over a porous disk, rotating at a constant angular speed. The three-dimensional equations of motion are treated analytically yielding to the derivation of exact solutions. The effects of the magnetic pressure number on the permeable flow field are better conceived from the exact velocity and induced magnetic field obtained. Making use of this solution, analytical formulas for the angular velocity and current density components, as well as for the magnetic wall shear stresses, are extracted. Interaction of the resolved flow field with the surrounding temperature is then analyzed via energy equation. The temperature field is shown to accord with the convection, viscous dissipation, and Joule heating. As a result, exact formulas are obtained for the temperature field, which takes different forms, depending on whether isothermal and adiabatic wall conditions or suction and blowing are considered.

scholarly journals IV. On the second approximation to the "oseen” solution the motion of a viscous fluid

1928 ◽  
Vol 227 (647-658) ◽  
pp. 93-135 ◽  
Keyword(s):  
Viscous Fluid ◽  
Radial Flow ◽  
Equations Of Motion ◽  
Incompressible Viscous Fluid ◽  
Large Radius ◽  
Sufficient Distance ◽  
Uniform Stream

In a recent paper the author obtained expressions for the forces on a stationary cylinder in a steady stream of incompressible viscous fluid and showed that the force transverse to the stream follows the well-known Kutta-Joukowski law, whereas the force in the direction of the stream itself is given by a similar law, involving, instead of the circulation, an outward radial flow, compensated by an intake along a “tail” behind the cylinder. These results were obtained by considering the motion at a distance from the cylinder, and assuming that the velocities of disturbance from the uniform stream were so small that, at a sufficient distance, their squares and products could be neglected both in the equations of motion and in the integrals round a circle of large radius, in terms of which the forces on the cylinder were expressed.

scholarly journals CENTRIFUGAL DESTABILIZATION AND RESTABILIZATION OF PLANE SHEAR FLOWS

1996 ◽  
Vol 06 (02) ◽  
pp. 409-413
Author(s):  
A. J. CONLEY
Keyword(s):  
Viscous Fluid ◽  
Linear Stability ◽  
Stokes Equations ◽  
Path Following ◽  
Incompressible Viscous Fluid ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Plane Shear ◽  
Navier Stokes Equations ◽  
Spectral Techniques

The flow of an incompressible viscous fluid between parallel plates becomes unstable when the plates are tumbled. As the tumbling rate increases, the flow restabilizes. This phenomenon is elucidated by path-following techniques. The solution of the Navier-Stokes equations is approximated by spectral techniques. The linear stability of these solutions is studied.

scholarly journals Steady Flow over a Rotating Disk in Porous Medium with Heat Transfer

2009 ◽  
Vol 14 (1) ◽  
pp. 21-26 ◽  
Author(s):  
H. A. Attia
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Energy Transfer ◽  
Viscous Fluid ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Rotating Disk ◽  
Incompressible Viscous Fluid ◽  
Governing Equations ◽  
Temperature Distributions

The steady flow of an incompressible viscous fluid above an infinite rotating disk in a porous medium is studied with heat transfer. Numerical solutions of the nonlinear governing equations which govern the hydrodynamics and energy transfer are obtained. The effect of the porosity of the medium on the velocity and temperature distributions is considered.

Heat and Mass Transfer on the Unsteady Magnetohydrodynamic Flow Due to a Porous Rotating Disk Subject to a Uniform Outer Radial Flow

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Heat Transfer ◽  
Radial Flow ◽  
Magnetic Interaction ◽  
Rotating Disk ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Shear Stresses ◽  
Surface Shear ◽  
Entire Family ◽  
Integration Algorithm

An unsteady flow and heat transfer of an incompressible electrically conducting fluid over a porous rotating infinite disk impulsively set into motion are studied in the present paper. The disk finds itself subjected to a uniform normal magnetic field. The particular interest lies in searching for the effects of an imposed uniform outer radial flow far above the disk on the behavior of the physical flow. The governing Navier–Stokes and Maxwell equations of the hydromagnetic fluid, together with the energy equation, are converted into self-similar forms using suitable similarity transformations. A compact, unconditionally stable, and highly accurate implicit spectral numerical integration algorithm is then employed in order to resolve the transient behavior of the velocity and temperature fields. The time evolution and steady state case of some parameters of fundamental physical significance such as the surface shear stresses in the radial and tangential directions and the heat transfer rate are also fully examined for the entire family of magnetic interaction, radial flow, and suction/blowing parameters.

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