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Linear and non-linear analyses of convection in a micropolar fluid occupying a porous medium
Authors:P G Siddheshwar  C V Sri Krishna  
Institution:

a Department of Mathematics, Bangalore University, Central College Campus, Bangalore 560 001, India

b Department of Mathematics, Sir M. Visvesvaraya Institute of Technology, Bangalore 562 157, India

Abstract:Linear and weakly non-linear analyses of convection in a micropolar fluid occupying a high-porosity medium are performed. The Brinkman–Eringen momentum equation is considered. The linear and non-linear analyses are, respectively, based on the normal mode technique and truncated representation of Fourier series. The linear theory for a two-phase system reiterates that the preferred mode of convection is stationary as in the case of a single-phase system. An autonomous system of differential equations representing cellular convection arising in the study is considered to analyse the critical points. The Nusselt number is obtained as a function of micropolar and porous medium parameters.
Keywords:Rayleigh-Benard convection  Micropolar fluids  Porous media  Double Fourier series  Linear and non-linear analyses
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