Effect of rotation on Brinkman-Bénard convection of a Newtonian nanoliquid using local thermal non-equilibrium model

Abstract

Rayleigh-Bénard-Taylor convection in a Newtonian, nanoliquid-saturated high porous medium using the local thermal non-equilibrium model (LTNE) is studied analytically using the single term Galerkin technique. The Bousinessq approximation is considered to be valid and the exerted centrifugal force due to rotation is taken. A high porosity porous material glass reinforced fiber with porosity 0.88% is considered and hence the Brinkman model is adopted. The rate of rotation is quantified by the Taylor number and the stability of the system is controlled by thermal Rayleigh number. The expression for the critical eigenvalue (Rayleigh number) is obtained for both idealistic and realistic boundary conditions, that is, stress-free, isothermal and rigid-rigid, isothermal boundary conditions. The presumption of LTNE advances the inception of convection and increases the transport of heat in comparison with that of the local thermal equilibrium (LTE) assumption whereas the opposite phenomenon is seen with the effect of rotation. The effect of various non-dimensional parameters on the convection onset and on transport of heat is also investigated. The results of Rayleigh-Bénard-Taylor convection using the LTE assumption are obtained as limiting cases of the present study for infinite values of the ratio of thermal conductivities and the interphase heat transfer coefficient.