scholarly journals Exact analysis of Effect of Non-uniform Temperature Gradient on Marangoni Convection with Free Slip Condition

2011 ◽  
Vol 10 (2) ◽  
pp. 1-10
Author(s):  
S.P. Suma ◽  
Y.H. Gangadharaiah
Keyword(s):  
Temperature Gradient ◽  
Marangoni Convection ◽  
Horizontal Layer ◽  
Temperature Profiles ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Expansion Procedure ◽  
Single Term ◽  
Basic Temperature ◽  
Good Agreement

The effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a horizontal layer with a free-slip bottom heated from below and cooled from above is considered. A linear stability analysis is performed to undertake a detail investigation. The eigenvalues are obtained for lower rigid isothermal and upper free adiabatic boundaries. The resulting eigenvalue problem is solved exactly and single-term Galerkin expansion procedure. The influence of various parameters on the onset of convection has been analyzed. Three non-uniform basic temperature profiles are considered and the results obtained from both the methods are compared and are found to be in good agreement. Some general conclusions about their destabilizing effects are presented.

scholarly journals Effects of Magnetic Field and Nonlinear Temperature Profile on Marangoni Convection in Micropolar Fluid

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
M. N. Mahmud ◽  
R. Idris ◽  
I. Hashim
Keyword(s):  
Magnetic Field ◽  
Temperature Profile ◽  
Micropolar Fluid ◽  
Marangoni Convection ◽  
Horizontal Layer ◽  
Critical Conditions ◽  
Closed Form Expression ◽  
Onset Of Convection ◽  
Single Term ◽  
Basic Temperature

The combined effects of a uniform vertical magnetic field and a nonuniform basic temperature profile on the onset of steady Marangoni convection in a horizontal layer of micropolar fluid are studied. The closed-form expression for the Marangoni numberMfor the onset of convection, valid for polynomial-type basic temperature profiles upto a third order, is obtained by the use of the single-term Galerkin technique. The critical conditions for the onset of convection have been presented graphically.

scholarly journals Effects of Controller and Nonuniform Temperature Profile on the Onset of Rayleigh-Bénard-Marangoni Electroconvection in a Micropolar Fluid

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
H. M. Azmi ◽  
R. Idris
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Micropolar Fluid ◽  
Marangoni Convection ◽  
Temperature Gradients ◽  
Temperature Profiles ◽  
Nonuniform Temperature ◽  
Onset Of Convection ◽  
Basic Temperature ◽  
Rayleigh Benard

Linear stability analysis is performed to study the effects of nonuniform basic temperature gradients on the onset of Rayleigh-Bénard-Marangoni electroconvection in a dielectric Eringen’s micropolar fluid by using the Galerkin technique. In the case of Rayleigh-Bénard-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.

scholarly journals Effects of Magnetic Field and Non-Uniform Basic Temperature Gradient

2002 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
S. Pranesh
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Conducting Fluid ◽  
Wave Number ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

The effects of a non-uniform temperature gradient and magnetic field on the onset of convection in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free/adiabatic boundary and a lower rigid/isothermal boundary have been considered. A linear stability analysis is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the Eigen values. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid without Suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

Effect of Solute Concentration Gradients on the Onset of Convection: Uniform and Nonuniform Initial Gradients

1986 ◽  
Vol 108 (4) ◽  
pp. 776-782 ◽  
Author(s):  
M. Kaviany ◽  
M. Vogel
Keyword(s):  
Temperature Gradient ◽  
Concentration Gradient ◽  
Fluid Layer ◽  
Onset Time ◽  
Solute Concentration ◽  
Concentration Gradients ◽  
Linear Amplification ◽  
Onset Of Convection ◽  
Gradient Layer ◽  
Good Agreement

The time of the onset of convection in a fluid layer, which is initially stably stratified and then heated from below in a transient manner, is determined experimentally and analytically. The initial stratification is due to the presence of a solute concentration gradient. In addition to initial linear solute concentration distributions two other specific initial solute concentration distributions are considered. In Case 1, a zero gradient layer is located underneath a nonzero and uniform gradient layer. In Case 2, the zero gradient layer is on the top. The linear amplification theory is applied to the prediction of the onset time. Interferometry is used as a means of determining the onset time experimentally. It is shown that since the adverse temperature gradient is concentrated near the bottom, any nonuniformity in the solute concentration gradient in this region reduces the effectiveness of the gradient in delaying the onset. Experimental and predicted results are in good agreement.

scholarly journals On competition between modes at the onset of Bénard-Marangoni convection in a layer of fluid

2002 ◽  
Vol 43 (3) ◽  
pp. 387-395
Author(s):  
Ishak Hashim
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Marangoni Convection ◽  
Horizontal Layer ◽  
Linear Stability Theory ◽  
Onset Of Convection ◽  
Relevant Case

AbstractIn this paper we use classical linear stability theory to analyse the onset of steady and oscillatory Bénard-Marangoni convection in a horizontal layer of fluid in the more physically-relevant case when both the non-dimensional Rayleigh and Marangoni numbers are linearly dependent. We present examples of situations in which there is competition between modes at the onset of convection when the layer is heated from below.

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