LAUSR

Abstract Heat convection response of a porous medium to the harmonic disturbances in the inlet flow is investigated in a configuration consisting of several obstacles. Navier Stokes and energy equations are solved computationally and the average Nusselt number around the obstacles is favourably compared against the existing empirical data. The Nusselt number fluctuations are then examined, revealing that the dynamical relations between the inlet flow fluctuations as the input and those of Nusselt number as the output, can be nonlinear. The extent of encountered nonlinearity is determined quantitatively through introduction of a measure of nonlinearity. It is shown that increases in the pore-scale Reynolds number can strengthen the nonlinearity. However, this is not a global trend and further increases in Reynolds number may push the system dynamics back to linear. Application of the concept of transfer function to the identified linear cases reveals that the frequency response of the Nusselt number closely resembles a classical low-pass filter. Further, through a statistical analysis, it is shown that thermal response of the porous medium is strongly dominated by those of the first few obstacles. This highlights the importance of taking pore-scale approach in the dynamical problems that involve heat convection in porous media.