Natural convection in a corrugated slot
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal
|Journal / Publication||Journal of Fluid Mechanics|
|Online published||23 Feb 2017|
|Publication status||Published - 25 Mar 2017|
|Link to Scopus||https://www.scopus.com/record/display.uri?eid=2-s2.0-85013627424&origin=recordpage|
Analysis of natural convection in a horizontal slot formed by two corrugated isothermal plates has been carried out. The analysis is limited to subcritical Rayleigh numbers Ra where no secondary motion takes place in the absence of corrugations. The corrugations have a sinusoidal form characterized by the wavenumber, the upper and lower amplitudes and the phase difference. The most intense convection occurs for corrugation wavelengths comparable to the slot height; it increases proportionally to Ra and proportionally to the corrugation height. Placement of corrugations on both plates may either significantly increase or decrease the convection depending on the phase difference between the upper and lower corrugations, with the strongest convection found for corrugations being in phase, i.e. a 'wavy' slot, and the weakest for corrugations being out of phase, i.e. a 'converging-diverging' slot. It is shown that the shear forces would always contribute to the corrugation build-up if erosion was allowed, while the role of pressure forces depends on the location of the corrugations as well as on the corrugation height and wavenumber, and the Rayleigh number. Placing corrugations on both plates results in the formation of a moment which attempts to change the relative position of the plates. There are two limiting positions, i.e. the 'wavy' slot and the 'converging-diverging' slot, with the latter being unstable. The system would end up in the 'wavy' slot configuration if relative movement of the two plates was allowed. The presence of corrugations affects the conductive heat flow and creates a convective heat flow. The conductive heat flow increases with the corrugation height as well as with the corrugation wavenumber; it is largest for short-wavelength corrugations. The convective heat flow is relevant only for wavenumbers of O(1), it increases proportionally to Ra3 and proportionally to the second power of the corrugation height. Convection is qualitatively similar for all Prandtl numbers Pr, with its intensity increasing for smaller Pr and with the heat transfer augmentation increasing for larger Pr.