Effect of Non-Uniform Basic Temperature Gradient on the Onset of Rayleigh-Bénard-Marangoni Electro-Convectionin a Micropolar Fluid

Thadathil Varghese Joseph, Sree Ramaiah Manjunath, Subbarama Pranesh

Department of Mathematics, BNMIT, Bangalore, India.
Department of Mathematics, Christ University, Bangalore, India.

DOI: 10.4236/am.2013.48158                

Abstract

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.

Keywords

Rayleigh-Bénard-Marangoni; Non-Uniform Temperature Gradient; Electric Field; Micropolar Fluid; Galerkin Technique

Conflicts of Interest

The authors declare no conflicts of interest.

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