Flow and stability of a gravity-driven thin film over a locally heated porous wall
PHYSICS OF FLUIDS
Authors: Kumawat, Tara Chand; Tiwari, Naveen
Abstract
Stability analysis is performed for a gravity-driven thin liquid film flowing down a locally heated porous substrate. Using the lubrication approximation, the governing equations are simplified to derive the evolution equation for the free surface of the liquid film. The Beaver-Joseph condition is employed at the interface of the porous layer and the liquid film. The base profiles are mainly influenced by parameters that appear due to non-uniform heating. Linear stability analysis is performed and reported that both thermocapillary and rivulet instabilities are enhanced with increasing values of the Marangoni number, Biot number, and Beavers-Joseph coefficient and decreasing values of the Darcy number. Dependence of critical Darcy number on the porous layer thickness and the Beavers-Joseph coefficient is presented. It is also shown that the full Darcy model can be replaced with an approximated slip model. The growth rate from nonlinear computations is consistent with the linear stability analysis. Published under license by AIP Publishing.
Peak thermoelectric power factor of holey silicon films
JOURNAL OF APPLIED PHYSICS
Authors: Ma, Jun; Gelda, Dhruv; Valavala, Krishna V.; Sinha, Sanjiv
Abstract
The thermoelectric properties of nanostructured silicon are not fully understood despite their initial promise. While the anomalously low thermal conductivity has attracted much work, the impact of nanostructuring on the power factor has mostly escaped attention. While initial reports did not find any significant changes to the power factor compared to the bulk, subsequent detailed measurements on p-type silicon nanowires showed a stark reduction in the Seebeck coefficient when compared to similarly doped bulk. The reduction is consistent with the disappearance of the phonon drag contribution, due to phonon boundary scattering. Here, we report measurements on a different nanostructure, holey silicon films, to test if similar loss of phonon drag can be observed. By devising experiments where all properties are measured on the same sample, we show that though these films possess electrical conductivity close to that in the bulk at comparable doping, they exhibit considerably smaller thermopower. The data are consistent with loss of phonon drag. At neck distances between 120 and 230 nm, the power factor at optimal doping is similar to 50% that of the bulk. These insights are useful in the practical design of future thermoelectric devices based on nanostructured silicon. Published under license by AIP Publishing.