Effect of imposed time-periodic boundary temperature on on the onset of rayleigh-benard convection in a dielectric couple stress fluid (original) (raw)
Related papers
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.
Rayleigh-Benard Convection in a Dielectric Liquid: Imposed Time-Periodic Boundary Temperatures
2009
We discuss the thermal instability in a layer of dielectric fluid when the boundaries of the layer are subjected to synchronous/asynchronous time-periodic temperatures. Only infinitesimal disturbances are considered. Perturbation solution in powers of the amplitude of the applied temperature field is obtained. In the case when the Imposed Time-periodic Boundary Temperatures (ITBT) at the two walls are synchronized then for moderate values of frequency the role of the electric Rayleigh Number in inducing subcritical instabilities is delineated. A similar role is shown to be played by the Prandtl number. The dielectric parameters and Prandtl number have the opposite effect at large frequencies. The system is most stable when the ITBT is asynchronous. The problem has relevance in many dielectric fluid applications wherein regulation of thermal convection is called for.
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...
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.
Rayleigh-Benard convection in a dielectric liquid: time-periodic body force
PAMM, 2007
We discuss the thermal instability in a layer of dielectric fluid when the boundaries of the layer are subjected to synchronous/asynchronous time-periodic temperatures. Only infinitesimal disturbances are considered. Perturbation solution in powers of the amplitude of the applied temperature field is obtained. In the case when the Imposed Time-periodic Boundary Temperatures (ITBT) at the two walls are synchronized then for moderate values of frequency the role of the electric Rayleigh Number in inducing subcritical instabilities is delineated. A similar role is shown to be played by the Prandtl number. The dielectric parameters and Prandtl number have the opposite effect at large frequencies. The system is most stable when the ITBT is asynchronous. The problem has relevance in many dielectric fluid applications wherein regulation of thermal convection is called for.
Malaysian Journal of Mathematical Sciences
Convection heat transfer especially Rayleigh-Bénard convection plays a significant role either in nature or industry applications. Particularly, in industry, the instability of the Rayleigh-Bénard convection process is important to see whether the quality of final goods is excellent or not. Therefore, in this study linear stability theory has been performed to investigate the influence of cubic temperature gradient and cubic concentration gradient on the onset of convection in a double-diffusive micropolar fluid. By adopting the single-term Galerkin procedure, parameters N1,N3,N5 , and Rs have been analyzed to investigate their influence on the onset of convection. The results found that the coupling parameter N1 and micropolar heat conduction parameter N5 will put the system in stable conditions. Meanwhile, the couple stress parameter N3 and solutal Rayleigh number Rs will destabilize the system. The results also show that by increasing the value of the solutal Rayleigh number Rs ,...
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
2014
Linear stability analysis is performed to study the effects of nonuniform basic temperature gradients on the onset of Rayleigh-Benard-Marangoni electroconvection in a dielectric Eringen’s micropolar fluid by using the Galerkin technique. In the case of Rayleigh-Benard-Marangoni convection, the eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal boundaries. The influence of various parameters has been analysed. Three nonuniform basic temperature profiles are considered and their comparative influence on onset of convection is discussed. Different values of feedback control and electric number are added up to examine whether their presence will enhance or delay the onset of electroconvection.
Applied Mathematical Modelling, 2016
The combined effect of couple stresses and a uniform horizontal AC electric field on the stability of buoyancy-driven parallel shear flow of a vertical dielectric fluid between vertical surfaces maintained at constant but different temperatures is investigated. Applying linear stability theory, stability equations are derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number G c , the critical wave number a c and the critical wave speed c c are computed for wide ranges of couple stress parameter c , AC electric Rayleigh number R ea and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number even in the presence of couple stresses but increases significantly with increasing c. Moreover, the effect of increasing R ea is to instill instability, while the couple stress parameter shows destabilizing effect in the stationary mode but it exhibits a dual behavior if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.
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.