Weak nonlinear analysis of Darcy-Brinkman convection in Oldroyd-B fluid saturated porous media under temperature modulation

Abstract

Abstract The analysis of chaotic convection of Oldroyd-B fluid in porous medium under temperature modulation is presented on the basis of Darcy-Brinkman model. A four-dimensional nonlinear system resulting from a truncated Galerkin expansion of the conservation and constitutive equations is set up to deal with the stability of convection with different Darcy number and Darcy-Rayleigh number. The chaotic behavior is controlled by Darcy-Rayleigh number while Darcy number has a great influence on the stability of system. With the lower boundary which is heated in a time-periodic manner, the system will change over to a state of periodic or chaotic motion from steady convection.