Abstract
An increasing number of technologies require prediction of unsteady forced convection in porous media when the inlet flow is unsteady. To gain further insight into this problem, the unsteady equations of continuity, Navier Stokes and energy are solved within the pores formed by several cylindrical flow obstacles. The system is modulated by sine waves superimposed on the inlet flow velocity, and the spatio-temporal responses of the flow and temperature fields are calculated. The results are then utilised to assess the linearity of the thermal response represented by the Nusselt number on the obstacles. It is shown that for linear cases, a transfer function can be devised for predicting the dynamic response of the Nusselt number. It is further argued that such a transfer function can be approximated by a classic low-pass filter which resembles the average response of the individual obstacles. This indicates that there exists a frequency threshold above which the thermal system is essentially insensitive to flow modulations. The results also show that changes in Reynolds number and porosity of the medium can push the dynamic response of the system towards non-linearity. Yet, there appears to be no monotonic change in the linearity of the response with respect to the Reynolds number and porosity. In general, it is found that for low Reynolds numbers, the dynamics of heat convection can be predicted decently by taking a transfer function approach. The findings of this study can enable further understanding of unsteady forced convection in porous media subject to time-varying inlet flows.
Highlights
The use of porous media in emerging technologies [1,2,3,4,5], including electrochemical systems [6,7] combustion of carbonneutral and renewable fuels [8,9], and micro chemical reactors [10,11], requires an understating of their dynamic responses
The focus is on identifying the conditions for which the nonlinear response can be safely ignored and the dynamics of heat transfer can be predicted by the straightforward transfer function approach
It drops down again when the Reynolds number increases to 250. This is an important result, as there is often a notion that lower Reynolds numbers render linear response and higher Reynolds numbers contribute to nonlinearity. Such an expectation stems from the macroscopic models of fluid flow in Unsteady forced convection in porous media can occur in systems subject to time-varying inlet flows
Summary
The use of porous media in emerging technologies [1,2,3,4,5], including electrochemical systems [6,7] combustion of carbonneutral and renewable fuels [8,9], and micro chemical reactors [10,11], requires an understating of their dynamic responses. This is because in these applications the inlet fluid flow rate can become strongly time dependant [12]. To evaluate the status of steady and unsteady pore-scale modelling, here a concise review of the literature on microscopic studies in porous media is put forward
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