Fluid Flow and Heat Transfer in Rotating Porous Media

The introduction chapter introduces the topic, its theoretical significance, as well as its applications in engineering and geophysics. Then a conceptual introduction of the porous media, its definitions and the continuum approach adopted in this book follows.

Modeling of flow and heat transfer in rotating porous media is introduced in this chapter. The governing equations are presented and transformed into dimensionless form in order, among others, to identifying conditions for neglecting terms in these equations. The classification of different types of rotating flows in porous media concludes the chapter.

Isothermal flow in roating porous media is shown to apply for conditions when the permeability of the porous medium is not constant, hence representing heterogeneous porous media. The demonstration of the possible existence of Taylor-Proudman columns in rotating porous media follows. Examples of secondary flows in a cross section perpendicular to the main flow direction are presented for a heterogeneous porous medium in a rotating square channel.

Natural convection in rotating porous media due to thermal buoyancy created by the centrifugal body force is presented. The distinction between the cases where the temperature gradients are aligned with the direction of the centrifugal body force or perpendicular to the latter are discussed separately. In the second case stability conditions have to be established, i.e. the convection does not occur unconditionally. A spectral system is then used to analyze the nonlinear effects leading to a system of ordinary differential equations for the amplitudes of convection. They predict a transition to chaotic solutions (weak turbulence) at certain values of the parameters.

The effect of the Coriolis acceleration on natural convection is presented in this chapter. When the imposed thermal gradient is perpendicular to the direction of the centrifugal body force unconditional natural convection occurs. Then the Coriolis effect is reflected in creation of secondary flows in a cross section perpendicular to the direction of the main convection. When the natural convection occurs due to gravitational buoyancy and the thermal gradient is parallel to the direction of the gravity body force natural convection occurs conditionally. Stability analysis is then required and presented for stationary or possibly oscillatory convection. Weak nonlinear solutions identify then the direction of the bifurcations for different values of the controlling parameters.

Combined gravity and centrifugal buoyancy due to thermal gradients are introduced in this chapter, followed by onset of convection in a binary mixture saturating the rotating porous layer. Effects of lack of local thermal equilibrium or local thermal non-equilibrium are then discussed. The case when the porous medium is anisotropic and the resulting effects on convection are then introduced. Applications of rotating porous media to nanofluids and solidification of binary alloys conclude this chapter.