Mathematical Modeling of Constrained Vapor Bubbles

2003 ◽  
Author(s):  
Vladimir S. Ajaev ◽  
G. M. Homsy
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Liquid Interface ◽  
Vapor Bubbles ◽  
Dimensional Model ◽  
Type Analysis ◽  
Steady Regime ◽  
Mass Fluxes ◽  
Steady State Solutions ◽  
Vapor Liquid

We develop a mathematical model of a long vapor bubble in a micro-channel with given temperature distributions on the walls. We assume that the shape of the bubble is dominated by capillary forces everywhere except near the walls of the channel and use a lubrication-type analysis to find the local vapor-liquid interface shapes and mass fluxes near the walls. Both two- and three-dimensional steady-state solutions are found such that evaporation near the heated bottom is balanced by condensation in colder areas of the vapor-liquid interface. The total length in this steady regime is found from the integral mass balance and investigated as a function of heating conditions. Steady-state conditions can no longer be satisfied when the intensity of heating is above a certain level. In this regime the bubble is expanding. We investigate such expansion in the framework of a two-dimensional model in the limit of small capillary number.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

SPATIAL DISORDER OF CNN — WITH ASYMMETRIC OUTPUT FUNCTION

2001 ◽  
Vol 11 (08) ◽  
pp. 2085-2095 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
KAI-PING CHIEN ◽  
SONG-SUN LIN ◽  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Steady State ◽  
Three Dimensional ◽  
Cellular Neural Networks ◽  
Output Function ◽  
One Dimensional ◽  
Spatial Entropy ◽  
The One ◽  
Steady State Solutions

This investigation will describe the spatial disorder of one-dimensional Cellular Neural Networks (CNN). The steady state solutions of the one-dimensional CNN can be replaced as an iteration map which is one dimensional under certain parameters. Then, the maps are chaotic and the spatial entropy of the steady state solutions is a three-dimensional devil-staircase like function.

A three-dimensional thermal study of a mercury discharge lamp with double envelope for different orientations

2014 ◽  
Vol 81 (2) ◽  
Author(s):  
Mohamed Bechir Ben Hamida ◽  
Kamel Charrada
Keyword(s):  
Steady State ◽  
Transport Phenomena ◽  
Three Dimensional ◽  
Convective Transport ◽  
Thermal Study ◽  
Mercury Lamp ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Discharge Lamp ◽  
Double Envelope

This paper is devoted to study the dynamics of a discharge lamp in different position. As an example of application, we chose the mercury lamp. For this, we realized a three-dimensional model, steady state. After the validation of this model, we used it to reproduce the influence of some parameters that have appeared on major transport phenomena of mass and energy in studying the lamp operating in different positions. Indeed, the pressure and the orientation of the lamp are modified. The effect of convective transport and the accumulation of mercury behind the electrodes are studied.

scholarly journals Ans, SProduction Inventory Controlled Self-Service Queuing System

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Anoop N. Nair ◽  
M. J. Jacob
Keyword(s):  
Steady State ◽  
Poisson Process ◽  
Three Dimensional ◽  
Queuing System ◽  
Analytic Method ◽  
Queuing Models ◽  
Production Inventory ◽  
Qbd Process ◽  
Self Service ◽  
Steady State Solutions

We consider a multiserver Markovian queuing system where each server provides service only to one customer. Arrival of customers is according to a Poisson process and whenever a customer leaves the system after getting service, that server is also removed from the system. Here the servers are considered as a standards, Sproduction inventory. Behavior of this system is studied using a three-dimensional QBD process. The condition for checking ergodicity and the steady state solutions are obtained using matrix analytic method. Unlike classical queuing models, the number of servers varies in this model according to an inventory policy.

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