Behaviour of the Onset of Rayleigh-Bénard Convection in Double-Diffusive Micropolar Fluids Under the Influence of Cubic Temperature and Concentration Gradient (original) (raw)
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International journal of engineering science, 1998
The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Bénard-Marangoni convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal 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 analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed.
2013
Abstract: The effect of feedback control on the criterion for the onset of Rayleigh-Benard convection in a horizontal micropolar fluid layer is studied theoretically. The bounding surfaces of the liquid are considered to either rigid on the upper and lower boundaries or upper boundary free and lower boundary rigid. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is found that the onset of instability can be delayed through the use of feedback control. Key words: Rayleigh-Benard convection • micropolar fluid • feedback control
Applied Mathematics, 2012
The effect of non-uniform basic concentration gradient on the onset of double diffusive convection in a micropolar fluid layer heated and saluted from below and cooled from above has been studied. The linear stability analysis is performed. The eigen value of the problem is obtained using Galerkian method. The eigen values are obtained for 1) free-free; 2) rigid-free; 3) rigid-rigid velocity boundary combination with isothermal temperature condition on spin-vanishing permeable boundaries. The influence of various micropolar parameters on the onset of convection has been analyzed. One linear and five non linear concentration profiles are considered and their comparative influence on onset is discussed and results are depicted graphically. It is observed that fluid layer with suspended particles heated and soluted from below is more stable compare to the classical fluid without suspended particles.
The main objective of this paper is the determination in the parameter space of the neutral hypersurface which separates the domain of stability from the instability domain in a problem of stationary convection in a micropolar fluid [1]. The influence of each of the micropolar parameters on the eigenparameter represented by the Rayleigh number is investigated using a spectral-Galerkin method based on expansion functions proved to assure an exponential convergence and small computational time expenses.
JOURNAL OF ADVANCES IN MATHEMATICS
The effect of gravity modulation (time periodic body force or g-jitter) on the onset of Rayleigh-Bénard convection in a micropolar fluid with internal heat generation is investigated by making a linear stability analysis. The stability of a horizontal layer of fluid heated from below is examined by assuming time periodic body force in the presence of internal heat source. A regular perturbation method is used to arrive at an expression to compute the critical Rayleigh number for small amplitude of modulation and dimensionless internal heat source. The Venezian approach is adopted to obtain the eigen value of the problem. The results obtained during the analysis have been presented graphically.
2019
The effect of internal heat generation and electric field on the onset of Rayleigh-Bénard convection in a micropolar fluid are studied by performing a linear stability analysis. The eigenvalue of the problem are obtained for rigid-rigid, rigidfree, and free-free velocity boundary combinations with isothermal and adiabatic temperature boundaries using the Galerkin technique. The microrotation is assumed to vanish at the boundaries. The impact of various micropolar fluid parameters, electric Rayleigh number, and the internal Rayleigh number on the onset of convection is analyzed. The linear theory is based on normal mode analysis. The expression of Rayleigh number is obtained as a function of the electric Rayleigh number, internal Rayleigh number, and other micropolar fluid parameters. It is observed that the increasing internal Rayleigh number destabilizes the system upon an infinitesimal disturbance on it. The control of the onset of electroconvection is possible with the help of th...
Effects of control on the onset of Bénard–Marangoni convection in a micropolar fluid
International Communications in Heat and Mass Transfer, 2010
A linear stability analysis was conducted to assess the feasibility of using a feedback control strategy on the onset of Bénard-Marangoni convection in a micropolar fluid. The single-term Galerkin technique was used to obtain the closed-form solution for the Marangoni number M for the onset of convection, satisfying three different non-uniform basic state temperature profiles. It is demonstrated that the controller gain parameter can successfully increase the critical Marangoni number.
International Journal of Engineering Research and Technology (IJERT), 2013
https://www.ijert.org/the-effect-of-imposed-time-periodic-boundary-temperature-and-electric-field-on-the-onset-of-rayleigh-bnard-convection-in-a-micropolar-fluid https://www.ijert.org/research/the-effect-of-imposed-time-periodic-boundary-temperature-and-electric-field-on-the-onset-of-rayleigh-bnard-convection-in-a-micropolar-fluid-IJERTV2IS70350.pdf 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.
Double-diffusive and Soret-induced convection in a micropolar fluid layer
Computers & Fluids, 2012
This paper reports an investigation of the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel. Asymmetric temperature and concentration boundary conditions are applied to the walls of the channel. The cases of double diffusion and Soret-induced convection are both considered. The governing parameters for the problem are the buoyancy ratio and the various material parameters of the micropolar fluid. The resulting non-dimensional boundary value problem is solved analytically in closed form using MAPLE software. A numerical solution of the time dependent governing equations is demonstrated to be in good agreement with the analytical model. The influence of the governing parameters on the fluid flow as well as heat and solute transfers is demonstrated to be significant.