Study of single and two component convection in micropolar liquid /

Study of single and two component convection in micropolar liquid /

Mathematics

In this thesis, we study linear and non-linear analysis of RayleighBénard and double diffusive convection in a micropolar liquid. The effect of non-uniform basic temperature gradient, non-uniform basic concentration gradient, temperature modulation at the boundary and gravity modulation are studied.
The problem investigated in this thesis through a light on externally controlled internal convection in a micropolar liquid. The problems investigated in this thesis have possible application in geophysics, astrophysics, oceanography engineering and in space situations with gjitter connected with gravity stimulation study. With this motivation, we investigate in this thesis four problems and their summary is given below one by one.
(i) EFFECT OF GRAVITY MODULATION ON HEAT
TRANSFER BY RAYLEIGH-BÉNARD CONVECTION IN A
MICROPOLAR LIQUID 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 thesis. In this problem the effect of time-periodic body force or grtavity modulation on the onset of Rayleigh-Bénard convection in a micropolar liquid 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 Lorenzvii model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat transfer.
(ii) LINEAR AND WEAKLY NON- LINEAR STABILITY
ANALYSIS OF DOUBLE-DIFFUSIVE CONVECTION IN A
MICROPOLAR LIQUID The linear and non-linear stability analysis of double diffusive convection in a micropolar liquid layer heated and saluted 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 coupling parameter, micropolar heat conduction parameter and solutal Rayleigh number
increases the heat and mass transfer. (iii) THE EFFECT OF NON - UNIFORM TEMPERATURE / CONCENTRTION DISTRIBUTION ON THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN A MICROPOLAR LIQUID The effect of non-uniform temperature/concentration distribution on the onset of double diffusive convection in a micropolar liquid layer heated and soluted below and cooled from above between two parallel
plates of infinite extend separated by a thin layer is studied using linear stability analysis based on normal mode technique. The eigen value is obtained for free-free, rigid-free, rigid-rigid, velocity boundary conditions with isothermal temperature boundary conditions using Galerkian method. It is observed that by choosing the appropriate non-uniformviii temperature or concentration gradient it is possible to advance or delay
the onset of double diffusive convection. (iv) EFFECT OF TEMPERATURE MODULATION ON THE ONSET OF DOUBLE – DIFFUSIVE CONVECTION IN A MICROPOLAR LIQUID
The effect of temperature modulation on the onset of double-diffusive convection in a micropolar liquid is investigated by making a linear stability analysis. The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-periodic sinusoidal perturbation is applied to the wall temperatures. The Venezian approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitude
temperature.

N, Arun Kumar - 0944301

CHRIST (Deemed to be University)

2013

English

PhD