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A b s t r a c tThe analysis of natural convection for moderate and high Prandtl numbers in a fluid saturated porous layer heated from below and subject to vibrations is presented with a twofold objective. First, it aims at investigating the significance of including a time derivative term in Darcy's equation when wave phenomena are being considered. Second it is dedicated to reporting results related to the route to chaos for moderate and high Prandtl number convection. The results present conclusive evidence indicating that the time derivative term in Darcy's equation cannot be neglected when wave phenomena are being considered even when the coefficient to this term is extremely small. The results also show occasional chaotic "bursts" at specific values (or small range of values) of R , exceeding some threshold. This behavior is quite distinct from the case without forced vibrations, when the chaotic solution occupies a wide range of R values, interrupted only by periodic "bursts". Periodic and chaotic solution alternate as the value of the scaled Rayleigh number varies.

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The investigation into possible applications of the thermal wave conduction theory to explain the spectacular enhancement of heat flux by a factor of between 1.4 to 2.5 in nanofluid suspensions is presented. While other possible explanations have been proposed to settle this discrepancy they were not investigated into sufficient detail for providing a definite answer and they all apply at the nano-scale level rather than bridging between the nano-scale effects and the macro-system investigated. The possible mechanisms proposed so far are Brownian motion, liquid layering at the liquid/particle interface, ballistic phonon effects, nanoparticle clustering as well as convection and wave effects. Furthermore, most available methods for measuring thermal conductivity assume and make use explicitly of the Fourier mechanism of heat transfer. If somehow the nano-level heat transfer effects impact profoundly on the resulting heat flux at the macro-level, possibly via wave phenomena, the whole concept behind the measurement device might be flawed. The present paper presents a possible way by which the transitions from nano-scale via the micro-scales towards the macro-scale occur, hence bridging the gap from nano devices to macro systems performance.