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.

The effect of magnetic field on Marangoni convection in a nanofluid layer with internal heat source

2017 ◽  
Author(s):  
Izzati Khalidah Khalid ◽  
Nor Fadzillah Mohd Mokhtar ◽  
Zailan Siri ◽  
Zarina Bibi Ibrahim ◽  
Siti Salwa Abd Gani
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Marangoni Convection ◽  
Internal Heat ◽  
Internal Heat Source

Convection in Magnetic Fluids With Internal Heat Generation

1991 ◽  
Vol 113 (1) ◽  
pp. 122-127 ◽  
Author(s):  
N. Rudraiah ◽  
G. N. Sekhar
Keyword(s):  
Heat Source ◽  
Uniform Distribution ◽  
Heat Generation ◽  
Magnetic Fluid ◽  
Fluid Layer ◽  
Internal Heat ◽  
Magnetic Fluids ◽  
Internal Heat Generation ◽  
Stationary Convection ◽  
Expansion Technique

The effect of a uniform distribution of heat source on the onset of stationary convection in a horizontal Boussinesq magnetic fluid layer bounded by isothermal nonmagnetic boundaries is investigated. Solutions are obtained using a higher order Galerkin expansion technique, considering different isothermal boundary combinations (rigid-rigid, rigid-free, and free-free). It is found that the effect of internal magnetic number, due to a heat source, is to make the system more unstable. The results obtained, in the limiting cases, compare well with the existing literature.

The Effect of Spatially Nonuniform Internal Heating on the Onset of Convection in a Horizontal Fluid Layer

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
A. V. Kuznetsov ◽  
D. A. Nield
Keyword(s):  
Fluid Layer ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Source Strength ◽  
Linear Quadratic ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Special Cases ◽  
Basic Temperature ◽  
Horizontal Fluid Layer

In this paper, we investigated the onset of natural convection in a horizontal fluid layer due to nonuniform internal heat generation, which is relevant to a number of geophysical situations. We investigated a number of special cases, which we believe are paradigmatic. Those include linear, quadratic, concentrated, and exponential source strength distributions. Our results show that those situations that lead to a reduction/increase in the size of the region in which the basic temperature gradient is destabilizing lead to an increase/decrease in stability.

Fundamentals of Microwave-Material Interactions and Sintering

1988 ◽  
Vol 124 ◽  
Author(s):  
Wayne R. Tinga
Keyword(s):  
Strong Dependence ◽  
Internal Heat ◽  
Temperature Limit ◽  
Small Samples ◽  
Material Transport ◽  
Material Particle ◽  
Heating Uniformity ◽  
Materials Used ◽  
Insight Into ◽  
Process Material

ABSTRACTBasic interaction mechanisms are shown to depend strongly on the dielectric and magnetic properties of a process material. This causes a strong dependence of power absorption on frequency, material particle size, shape, temperature, and density. Sintering dynamics cause the microstructure of the treated material to change resulting in a change in microwave (1W) heating uniformity and rate. The concept of dielectric mixtures is introduced to predict the dielectric and heating properties of a host material with its inclusions in the form of shells, ellipsoids, spheres, disks and needles. Simplified models are described to give a process designer some insight into the behavior of MW sintering. Microwave power, by its very nature, gives better heating control and efficiency and provides internal heat to aid the material transport during sintering. No inherent temperature limit exists for MW sintering although refractory materials used to contain the process material create an artificial upper limit. It is shown that very high (1500–2000°C) temperatures in small samples can be readily achieved using commercial microwave ovens if appropriate MW transparent sample holders are used.

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.

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