Linear stability analysis for the onset of convection during microwave heating of oil confined within horizontal plates

This work performs linear stability analysis to investigate the onset of convection due to microwave incidences in a horizontal oil layer. The probability of onset has been characterized in terms of critical Rayleigh number (Ra-c), while the microwave power required to initiate convection has been quantified in terms of modified Rayleigh number ((Ra-c) over bar). The associated convection cell size has been illustrated by critical wave number (k(c)). These critical numbers (Ra-c, (Ra-c) over bar, and k(c) ) have been determined for the entire spectrum of oil thicknesses ranging from thin to thick samples and various possible microwave source configurations starting from one sided to distributed incidences. It has been shown that the critical numbers oscillate with oil thickness in intermediate regime indicating preferential onset for specific oil thicknesses. It has also been shown that microwave source configuration plays an important role in controlling the onset of convection. Finally, the variations of Ra-c and k(c) have been correlated to the spatial patterns of absorbed microwave power within oil, while modified Rayleigh numbers are shown to follow the qualitative trends of Delta T-s, where Delta T-s is the base state temperature difference between top and bottom plate. The results are useful not only for forecasting the onset but also for controlling onset of convection by selecting suitable experimental parameters. (c) 2009 American Institute of Physics. [DOI: 10.1063/1.3066236]