Convective and Absolute Instabilities Induced by Viscous Dissipation in the Thermocapillary Convection with Through-Flow

2021 ◽  
Author(s):  
Eduardo V. M. dos Reis ◽  
Leonardo S. de B. Alves
Keyword(s):  
Viscous Dissipation ◽  
Shooting Method ◽  
Thermocapillary Convection ◽  
Thin Liquid Film ◽  
Internal Heating ◽  
Limited Region ◽  
Through Flow ◽  
Liquid Film Flow ◽  
Prandtl Numbers ◽  
Unstable Temperature

Abstract The mixed convection in a thin liquid film flow over a horizontal plate is investigated under finite Prandtl numbers. The gas-liquid interface is considered free, non-deformable and subject to surface tension gradients and convection, while gravity is assumed negligible. Therefore, Marangoni instead of buoyancy effects appear due to the unstable temperature stratification induced by the internal heating generated by viscous dissipation. A linear and modal stability analysis of this model is then performed to identify its convective/absolute nature. This is achieved by solving the resulting differential eigenvalue problem with a shooting method. Longitudinal rolls are the most unstable at the onset of instability for most parametric conditions. Otherwise, transverse rolls are the first to become convectively unstable. Finally, longitudinal rolls are absolutely stable. A transition to absolute instability occurs through transverse rolls, but only within a limited region in parametric space.

Analysis of Runback Water Flow on Anti-Icing Surface Using Volume-of-Fluid Method

2017 ◽  
Author(s):  
Mei Zheng ◽  
Wei Dong ◽  
Zhiqiang Guo ◽  
Guilin Lei
Keyword(s):  
Heat Transfer ◽  
Water Flow ◽  
Thin Liquid Film ◽  
Flow Characteristics ◽  
Volume Of Fluid ◽  
Complex Model ◽  
Two Phase ◽  
Flow And Heat Transfer ◽  
Liquid Film Flow ◽  
The Mathematical Model

The runback water flow and heat transfer on the surface of aircraft components has an important influence on the design of anti-icing system. The aim of this paper is to investigate the water flow characteristics on anti-icing surface using numerical method. The runback water flow on the anti-icing surface, which is caused by the impinging supercooled droplets from the clouds, is driven by the aerodynamic shear forces and the pressure gradient around the components. This is a complex model of flow and heat transfer that considers flow field, super-cooled droplets impingement and runback water flow simultaneously. In this case of gas-liquid two phase flow, the Volume-of-Fluid (VOF) method is very suitable for the solution of thin liquid film flow so that it is applied to simulate the runback water flow on anti-icing surfaces in this paper. Meanwhile, the heat and mass transfer of the runback water flow are considered in the calculation using the User-Defined Functions (UDFs) in ANASYS FLUENT. The verification is conducted by the comparison with the results of the experimental measurement and the mathematical model calculation. The effect of the airflow velocity and contact angle on the water flow are also considered in the numerical simulation.

Surface instabilities of thin liquid film flow on a rotating disk

1999 ◽  
Vol 26 (1-2) ◽  
pp. 75-85 ◽  
Author(s):  
G. Leneweit ◽  
K. G. Roesner ◽  
R. Koehler
Keyword(s):  
Liquid Film ◽  
Film Flow ◽  
Thin Liquid Film ◽  
Rotating Disk ◽  
Liquid Film Flow

scholarly journals Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Shooting Method ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Stagnation Point Flow ◽  
Stretching Surfaces

Abstract In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.

Marangoni convection of a viscous fluid over a vibrating plate

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190214
Author(s):  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Viscous Dissipation ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Plane Waves ◽  
Internal Heat ◽  
Runge Kutta Method ◽  
Insight Into ◽  
Unstable Temperature ◽  
Upper Boundary ◽  
Vibrating Plate

This research presents a new insight into Marangoni convection through investigating, both numerically and analytically, the surface tension driven instability activated by a coupled effect of a vibrating plate and viscous dissipation. A horizontal, thin fluid layer is bounded from below by an impermeable, adiabatic plate that vibrates in the horizontal direction. The upper boundary is modelled by a free surface subject to a thermal boundary condition of the third kind (Robin). The internal heat generation due to viscous dissipation yields a vertical, potentially unstable temperature gradient. The linear stability analysis of the stationary terms of the basic state is performed. The perturbed flow, in the form of plane waves, is superimposed onto the basic state. The obtained system of ordinary differential equations is solved numerically by means of the Runge–Kutta method coupled with the shooting method. For the two limiting cases, the isothermal upper boundary and adiabatic upper boundary, the analytical solutions of the eigenvalue problem are obtained. The values of the critical parameter, which identifies the threshold for the onset of Marangoni convection, are presented.

Spectral Analysis of Fronts in a Marangoni-Driven Thin Liquid Film Flow Down a Slope

2020 ◽  
Vol 80 (1) ◽  
pp. 95-118
Author(s):  
Anna Ghazaryan ◽  
Stephane Lafortune ◽  
Vahagn Manukian
Keyword(s):  
Spectral Analysis ◽  
Liquid Film ◽  
Film Flow ◽  
Thin Liquid Film ◽  
Liquid Film Flow

Lie group analysis of chemical reaction effects on MHD free convection dissipative fluid flow past an inclined porous surface

2015 ◽  
Vol 25 (7) ◽  
pp. 1557-1573 ◽  
Author(s):  
G. Venkata Ramana Reddy ◽  
Ali J Chamkha
Keyword(s):  
Free Convection ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Shooting Method ◽  
Porous Plate ◽  
Group Analysis ◽  
Convection Flow ◽  
Governing Equations ◽  
Content Type ◽  
The Magnetic Field

Purpose – The purpose of this paper is to study chemical reaction and heat and mass transfer effects on steady free convection flow in an inclined porous plate in the presence of MHD and viscous dissipation through the application of scaling group of transformation and numerical method. Design/methodology/approach – The fourth-order Runge-Kutta along with the shooting method is employed in the numerical solution of the governing equations. Findings – The magnetic field parameter, the permeability of porous medium and the viscous dissipation are demonstrated to exert a more significant effect on the flow field and, thus, on the heat transfer from the plate to the fluid. Originality/value – The problem is relatively original.

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