On the competition between rotation and variable viscosity in a Darcy–Brinkman model

In this paper, the competing interplay between rotation and viscosity in the Darcy–Brinkman problem is analysed with industrial applications, including lubrication and heat transfer control. To the best of our knowledge, generally, a variable viscosity fluid saturating a porous medium does not produce any additional oscillating motions at the onset of convection. The absence of oscillating motions has been detected also in Capone &amp; Gentile (2000 Ricerche di Matematica 49 , 193–211), where the authors proved the validity of the principle of exchange of stabilities in a rotating porous medium. Here, it is shown numerically that the combined effect of rotation and variable viscosity may lead to the occurrence of oscillatory convection. Nonlinear analysis is performed via the energy method and sufficient condition for the stability of the basic solution is determined. Proximity of the results from the linear and nonlinear analyses is obtained thanks to numerical techniques, i.e. Chebyshev- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> </mml:math> method and golden section method.