Major Research Project on Study of Elecroconvection in a Microploar Fluid

Major Research Project on Study of Elecroconvection in a Microploar Fluid

 Dr Pranesh

Professor

Department of Mathematics

CHRIST (Deemed to be University)

Bangalore – 560029

 

Abstract:

 

In this project, we study linear and non-linear analysis of Rayleigh-Benard and double diffusive electro convection in a micropolar fluid. The effect of non-uniform basic temperature gradient, suction-injection combination, temperature modulation at the boundary and gravity modulation are studied.

The problem investigated in this project throw a light on externally controlled internal convection in a micropolar fluid in the presence of electric field. The problems investigated in this project have possible application in geophysics, astrophysics, oceanography engineering and in space situations with g-jitter connected with gravity stimulation study.

With this motivation, we investigate in this project five problems and their summary is given below one by one.

 

(i)  Linear and Weakly Non-Linear Stability Analyses of Double-Diffusive Electro-Convection in a  Micropolar Fluid.

 

The linear and weakly non-linear stability analyses of double diffusive electro-convention in a micropolar fluid layer heated and saluted from below and cooled from above is studied. The linear and non-linear analyses are, respectively based on normal mode technique and truncated representation of Fourier series. The influence of various parameters on the onset of convection has been analyzed in the linear case. The resulting autonomous Lorenz model obtained in non-linear analysis is solved numerically to quantify the heat and mass transforms through Nusselt and Sherwood number. It is observed that the increase in concentration of suspended particles, electric field and electric Rayleigh number increases the heat and mass transfer.

 

(ii) The Effect of Imposed Time-Periodic Boundary Temperature and Electric Field on the Onset of Rayleigh-Bénard Convection in a Micropolar Fluid.

 

The effect of imposed time periodic temperature of small amplitude and AC electric field on the onset of Rayleigh-Bénard convection in a micropolar fluid is investigated using linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number that throws light on the possibility of subcritical motions. The Venezian approach is adopted for obtaining eigen value of the problem.  Three cases of oscillating temperature field are examined: (a) symmetric, so that the wall temperatures are modulated in-phase, (b) asymmetric, corresponding to out-of-phase modulation and (c) only the lower wall is modulated. It is observed that the system is most stable when the boundary temperatures are modulated out-of-phase. This problem is an example of external control of the internal convection.

(Iii)Linear and Non-Linear Analyses of Gravity  Modulation and Electric Field on the Onset of Rayleigh-Bénard Convection in a Micropolar Fluid

 

The vertical oscillation, or g-jitter or gravity modulation, is known to appear in the situation of the satellite. In the laboratory, Rayleigh-Bénard system subjected to time-periodic vertical oscillations may be useful in regulating the onset of convection and heat transfer. This aspect is also in focus in the project. In this problem the effect of time-periodic body force or gravity modulation on the onset of Rayleigh-Bénard convection in a micropolar fluid is investigated. The linear and non-linear analyses are performed. The linear theory is based on normal mode analysis and perturbation method. The expression for correction Rayleigh number is obtained as a function of frequency of modulation and other micropolar liquid parameters. The non-linear analysis is based on the truncated Fourier series representation. The resulting non-autonomous Lorenz model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat transfer.

 

(iv) Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh-Bénard Electro Convection in a Micropolar Fluid

 

The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Bénard convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for free–free, rigid–free and rigid–rigid velocity boundary combinations and for isothermal and /or adiabatic temperature boundaries.  The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analyzed. One linear and five non-uniform temperature profiles are considered and their comparative influence on onset is discussed.  It is found that by taking appropriate non-uniform temperature profiles it is possible to control the convection with electric field in a micropolar fluid.

 

(v)  Effects of Suction – Injection – Combination (Sic) on the Onset of Rayleigh –                   Bénard Electroconvection in a Micropolar Fluid.

 

The effect of Suction – injection combination on the onset of Rayleigh–Bénard electroconvection micropolar fluid is investigated by making a linear stability analysis. The Rayleigh-Ritz technique is used to obtain the eigenvalues for different velocity and temperature boundary combinations. The influence of various parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles.
 

Year of Publication: June 2013

ISBN:   978-93-82305-29-3

Major Research Project : Vol 2 

Pages :   x, 133

Price: available on request

Funded by Centre for Research-Projects-CHRIST (Deemed to be University)

Published by Centre for Publications, CHRIST (Deemed to be University)