Abstract
The qualitative effect of a non-uniform basic temperature gradient on the linear stability analysis of the Rayleigh–Benard convection in an Eringen's micropolar fluid is studied numerically using a single-term Galerkin technique. The eigenvalue is obtained for free–free, rigid–free, and rigid–rigid velocity boundary combinations with isothermal and adiabatic temperature conditions on the spin-vanishing boundaries. The eigenvalues are also obtained for lower rigid isothermal and upper free adiabatic boundaries with vanishing spin. The influence of various micropolar fluid parameters on the onset of stationary convection has been analysed. Six different basic temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the Rayleigh number obtained is lower than that of the corresponding Newtonian fluid problem. Some important mechanisms of advancing or delaying convection are discussed.
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