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

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.

Effects of Gravity Modulation and Internal Heat Generation on the onset of Rayleigh-Benard convection in a Micropolar Fluid

“…The perturbations equations ( 13)-( 17) are non-dimensionalised using the following definitions Using equation (17) in equation ( 14) and operating curl twice on the resulting equation, operating curl once on equation ( 15) and non-dimensionalizing the two resulting equations and equation ( 16), using equation ( 18), we get…”

“…A detailed survey of the theory of micropolar fluid and its applications are considered in the books of Erigen [5,6], Lukasazewicz [7] and Power [8], which has become an important field of research especially in many industrially important fluids like paints, polymeric suspensions, colloidal fluids, and also in physiological fluids such as normal human blood and synovial fluids. The theory of thermomicropolar convection was studied by many authors Datta and Sastry [9], Ahmadi [10], Rama Rao [11], Bhattacharya and Jena [12], Siddheshwar and Pranesh [13,14], Pranesh and Kiran [15], Pranesh and Riya [16], Joseph et al [17] and Pranesh [18].…”

Linear and non-linear analyses of double-diffusive-Chandrasekhar convection coupled with cross-diffusion in micropolar fluid over saturated porous medium

“…The importance of such fluids are found in blood, pharmaceuticals, fibre production, polymeric fluids, grease, etc. Siddeshwar and Pranesh (1983, 1999, 2001; Joseph et al (2013) and Pranesh and Baby (2014) have made a significant contribution in the field of micropolar fluids.…”