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.
Highlights
The dynamic response of forced convection in porous media to imposed disturbances is of high practical significance
The analyses presented aim to evaluate the linearity of the relation between the fluctuations in Nusselt number on different flow obstacles and those of the inlet flow
The dynamic response of forced convection in porous media to imposed oscillations on the inlet flow velocity was investigated through conduction of a pore-scale analysis
Summary
The dynamic response of forced convection in porous media to imposed disturbances is of high practical significance. Many natural and manmade systems involve forced convection within porous media in which the inlet flows are time dependent. The most conventional way of characterising the response of any physical system to input temporal disturbances is by working out the frequency response or transfer function [5]. This provides a strong means of predicting the system response to any arbitrary temporal disturbance with minimal computational effort. In this approach the response of system to harmonic inputs are measured/computed for a range of frequencies. Since transfer function provides the response of the system to each of those harmonics, the total response can be readily devised through superposition
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