Closed Form Solution for Outflow Between Corotating Disks

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Closed Form ◽  
Stokes Equations ◽  
Closed Form Solution ◽  
Tangential Velocity ◽  
Form Solution ◽  
Navier Stokes ◽  
Published Data ◽  
Rotational Inertia ◽  
Viscous Losses ◽  
Present Solution

Mathematical expressions are derived for flow velocities and pressure distributions for a laminar flow in the gap between two rotating concentric disks. Fluid enters the gap between disks at the center and diverges to the outer periphery. The Navier–Stokes equations are linearized in order to get closed-form solution. The present solution is applicable to the flow between corotating as well as contrarotating disks. The present results are in agreement with the published data of other investigators. The tangential velocity is less for contrarotating disks than for corotating disks in core region of the radial channel. The flow is influenced by rotational inertia and convective inertia both. Dominance of rotational inertia over convective inertia causes backflow. Pressure depends on viscous losses, convective inertia, and rotational inertias. Effect of viscous losses on pressure is high at small throughflow Reynolds number. The convective and rotational inertia influence pressure significantly at high throughflow and rotational Reynolds numbers. Both favorable and unfavorable pressure gradients can be found simultaneously depending on a combination of parameters.

scholarly journals Closed-form solution for the edge vortex of a revolving plate

2017 ◽  
Vol 821 ◽  
pp. 200-218 ◽  
Author(s):  
Di Chen ◽  
Dmitry Kolomenskiy ◽  
Hao Liu
Keyword(s):  
Closed Form ◽  
Stokes Equations ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Leading Edge ◽  
Form Solution ◽  
Navier Stokes ◽  
Edge Vortex ◽  
Leading Edge Vortices

Flapping and revolving wings can produce attached leading-edge vortices when the angle of attack is large. In this work, a low-order model is proposed for the edge vortices that develop on a revolving plate at $90^{\circ }$ angle of attack, which is the simplest limiting case, yet shows remarkable similarity with the generally known leading-edge vortices. The problem is solved analytically, providing short closed-form expressions for the circulation and the position of the vortex. The good agreement with the numerical solution of the Navier–Stokes equations suggests that, for the conditions examined, the vorticity production at the sharp edge and its subsequent three-dimensional transport are the main effects that shape the edge vortex.

A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Elastic Field ◽  
Form Solution ◽  
Eshelby Tensor ◽  
Cylindrical Inclusion ◽  
Closed Form Expression ◽  
Equivalent Inclusion Method ◽  
Explicit Analytical Solution ◽  
Present Solution

From the analytical formulation developed by Ju and Sun [1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574], it is seen that the exterior point Eshelby tensor for an ellipsoid inclusion possesses a minor symmetry. The solution to an elliptic cylindrical inclusion may be obtained as a special case of Ju and Sun’s solution. It is noted that the closed-form expression for the exterior-point Eshelby tensor by Kim and Lee [2010, “Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion,” ASME Trans. J. Appl. Mech., 77, p. 024503] violates the minor symmetry. Due to the importance of the solution in micromechanics-based analysis and plane-elasticity-related problems, in this work, the explicit analytical solution is rederived. Furthermore, the exterior-point Eshelby tensor is used to derive the explicit closed-form solution for the elastic field outside the inclusion, as well as to quantify the elastic field discontinuity across the interface. A benchmark problem is used to demonstrate a valuable application of the present solution in implementing the equivalent inclusion method.

Viscous Flow with Second-Order Slip Velocity over a Stretching Sheet

2010 ◽  
Vol 65 (12) ◽  
pp. 1087-1092 ◽  
Author(s):  
Tiegang Fang ◽  
Abdul Aziz
Keyword(s):  
Viscous Flow ◽  
Slip Velocity ◽  
Stokes Equations ◽  
Closed Form Solution ◽  
Velocity Model ◽  
Form Solution ◽  
Second Order ◽  
Navier Stokes ◽  
Stretching Surface ◽  
Navier Stokes Equations

In this paper, viscous flow with a second-order slip condition over a permeable stretching surface is solved analytically. The current work differs from the previous studies in the application of a new second-order slip velocity model. The closed form solution reported is an exact solution of the full governing Navier-Stokes equations. The effects of slip and mass transfer parameters are discussed.

scholarly journals Theoretical study of an unsteady ciliary hemodynamic fluid flow subject to the Newton’s boundary conditions

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110404 ◽  
Author(s):  
Mubbashar Nazeer ◽  
Farooq Hussain ◽  
Fayyaz Ahmad ◽  
Sadia Iftikhar ◽  
Gener S Subia
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Biological Fluid ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Ciliary Motion ◽  
Hemodynamic Flow

This article addresses the hemodynamic flow of biological fluid through a symmetric channel. Methachronal waves induced by the ciliary motion of motile structures are the main source of Couple stress nanofluid flow. Darcy’s law is incorporated in Navier-Stokes equations to highlight the influence of the porous medium. Thermal transport by the microscopic collision of particles is governed by Fourier’s law while a separate expression is obtained for net diffusion of nanoparticles by using Fick’s law. A closed-form solution is achieved of nonlinear differential equations subject to Newton’s boundary conditions. Moreover, the current findings are compared with previous outcomes for the limiting case and found a complete coherence. Parametric study reveals that nanoflow is resisted by employing Newton’s boundary conditions. Thermal profile enhancement is contributed by the viscous dissipation parameter. Finally, one infers that hemodynamic flow of non-Newtonian fluid is an effective mode of heat and mass transfer especially, in medical sciences for the rapid transport of medicines in drug therapy.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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