Nonhomogeneous Lagging Response in Porous Media

Abstract

Heat transport in discrete media could display a different type of lagging due to the finite times required for the solid and gaseous phases to reach thermal equilibrium and the wavy conducting path that energy carriers have to follow along the solid phase. The microscopic two-step model is extended in this chapter to describe thermal lagging in sands, due to its easy access for reproducing the results, with emphasis on identifying the microstructural parameters dominating the delayed response between the heat flux vector and the temperature gradient. The dual-phase-lag model is compared with the experimental results to reveal the nonhomogeneous variation of the phase lags from near to far fields of the heater. For medium-sized blasting sand, both phase lags are of the order of seconds. In transition from the near (discrete) to the far (continuum) field, the lagging response displays a vivid pattern of precedence switch, from the gradient-to the flux-precedence type of heat flow, resulting from the accumulated effect of thermal lagging in the gradually expanded sample size.From the experimental results described in Chapters 4 and 5, it is clear that the success of the dual-phase-lag model lies in its unique way of describing the microscale interaction effect in space by the resulting delayed response in time. For heat propagation in superfluid liquid helium, Chapter 4, the time delay between the heat flux vector and the temperature gradient is caused by the finite time required for activating the molecules at a low temperature to an energy level appropriate for efficient heat conduction. For the short-pulse laser heating on metal films discussed in Chapter 5, alternately, the delayed response in metals is caused by the finite time required for the energy exchange between phonons and electrons. The physical mechanisms are different, but the philosophy of trading the microstructural interaction effect in space with the fast-transient effect in time is the same.This chapter generalizes the phonon-electron interaction (microscopic two-step) model to account for the lagging response caused by the energy exchange between different types of substances in the conductor. In ways parallel to the energy exchange between phonons and electrons, which are equivalent to two different substances in general, energy exchange between interstitial gas (gaseous phase) and medium-sized blasting sand (solid phase) are examined to extract the lagging behavior. Sand beds are used due to their easy access and