Abstract
The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Benard-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.
Highlights
Convection due to variations of densities between two parallel plates caused by temperature difference and variations of temperature dependence surface tension in a horizontal fluid layer is of great importance because of its applications in science and engineering
The flow associated with Rayleigh-Bénard convection and Marangoni convection has been extensively reviewed in the literature
Marangoni convection is found to be of importance in crystal growth melts and nucleate boiling
Summary
Convection due to variations of densities between two parallel plates caused by temperature difference and variations of temperature dependence surface tension in a horizontal fluid layer is of great importance because of its applications in science and engineering. Such convection in literature is known as Rayleigh-Bénard and Bénard-Maangoni convection. The main objective of this paper is to provide the theoretical framework for studying the thermo capillary instabilities in the presence of buoyancy instability in earth laboratories for electrically conducting micropolar fluid layers under an AC electric field and non-uniform temperature gradients. Eigen value of the problem is obtained using single term Galerkin method
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