scholarly journals Hydromagnetic instability of a power-law liquid film flowing down a vertical cylinder using numerical approximation approach techniques

2009 ◽  
Vol 33 (4) ◽  
pp. 1904-1914 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Numerical Approximation ◽  
Vertical Cylinder ◽  
Approximation Approach ◽  
Hydromagnetic Instability

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

2006 ◽  
Vol 30 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
Film Interface

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Long-Wave Perturbation Method to Investigate Nonlinear Stability of the Thin Power Law Liquid Film Flowing Down on a Vertical Cylinder

2008 ◽  
Vol 24 (3) ◽  
pp. 241-252 ◽  
Author(s):  
P. -J. Cheng ◽  
K. -C. Liu
Keyword(s):  
Liquid Film ◽  
Perturbation Method ◽  
Power Law ◽  
Film Flow ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Wave Perturbation ◽  
Stability Diagrams ◽  
Long Wave

ABSTRACTThe influence of both the flow index and the cylinder size on the nonlinear hydrodynamic stability of a thin power law liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weakly nonlinear dynamics of the film flow for stability analysis. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained. The modeling results indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Finite-Amplitude Long-Wave Instability of a Thin Power-Law Liquid Film Flowing Down a Vertical Column in a Magnetic Field

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Po-Jen Cheng
Keyword(s):  
Magnetic Field ◽  
Liquid Film ◽  
Power Law ◽  
Vertical Cylinder ◽  
Finite Amplitude ◽  
Flow Index ◽  
Vertical Column ◽  
Electrically Conductive ◽  
Long Wave ◽  
The Stability

The long-wave perturbation method is employed to investigate the nonlinear hydromagnetic stability of a thin electrically conductive power-law liquid film flowing down a vertical cylinder. In contrast to most previous studies presented in literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The modeling results reveal that the stability of the film flow system is weakened as the radius of the cylinder is reduced. However, the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index.

Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface

1978 ◽  
Vol 45 (1) ◽  
pp. 19-24 ◽  
Author(s):  
V. Narayanamurthy ◽  
P. K. Sarma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Mathematical Formulation ◽  
Liquid Films ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Power Law Model ◽  
Falling Liquid Film ◽  
Falling Liquid Films ◽  
Special Case

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.

scholarly journals Free convection flow of power law fluid in a vertical cylinder of finite height

1995 ◽  
Vol 17 (2) ◽  
pp. 34-39
Author(s):  
Nguyen Van Que
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Power Law ◽  
Average Velocity ◽  
Vertical Cylinder ◽  
Convection Flow ◽  
Power Law Fluid ◽  
Free Convection Flow ◽  
Finite Height ◽  
Good Agreement

A numerical solution has been presented for free convection flow of power law fluid in a vertical cylinder of finite height. The average velocity along the channel and the heat transfer have been calculated. Graphs of velocities and temperature are shown. The results show good agreement with analytic one in the asymptotic case.

LES Simulation in a Thin Liquid Film Subjected to High Thermal Stresses

2003 ◽  
Author(s):  
M. V. Pham ◽  
F. Plourde ◽  
S. K. Doan
Keyword(s):  
Thermal Stress ◽  
Flow Field ◽  
Liquid Film ◽  
Power Law ◽  
Thermal Stresses ◽  
Thin Liquid Film ◽  
Strong Mixing ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Air Liquid Interface

Thermal transfers occurring in the vicinity of an air-liquid interface have been studied numerically through a Large Eddy Simulation technique. Results obtained clearly show the unsteady response of the liquid film submitted to such thermal stress. Structures are created at the interface in a very small layer and it has been found that turbulence acts strongly in that layer. Moreover, even if the configuration studied tends to weaken buoyancy, the dissipation was found to obey a −3 power law. This clearly indicates that the buoyancy pilots the way turbulence behaves on the flow field; the latter is mainly characterized by a strong mixing phenomenon taking place in the already identified layer at the interface.

Developing flow of a power-law liquid film on an inclined plane

2003 ◽  
Vol 15 (10) ◽  
pp. 2973 ◽  
Author(s):  
Steven J. Weinstein ◽  
Kenneth J. Ruschak ◽  
Kam C. Ng
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Inclined Plane ◽  
Developing Flow
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