Convective heat transfer in non-uniformly heated corrugated slots

An analysis of heat transfer in non-uniformly heated corrugated slots has been carried out. A sinusoidal corrugation is placed at the lower plate that is exposed to heating consisting of uniform and sinusoidal components, while the upper smooth plate is kept isothermal. The phase difference Ω_TL describes the shift between the heating and geometric non-uniformities. The analysis is limited to heating conditions that do not give rise to secondary motions. Depending on Ω_TL, the conductive heat flow is directed either upwards, or downwards, or is eliminated. Its magnitude is smallest for the long-wavelength systems and largest for the short-wavelength systems, and it increases proportionally to the corrugation amplitude and heating intensity. The same heating creates horizontal temperature gradients that give rise to convection whose form depends on Ω_TL. Convection consists of counter-rotating rolls with the size dictated by the system wavelength when the hot spots (points of maximum temperature) overlap either with the corrugation tips or with the corrugation bottoms. Thermal drift forms for all other values of Ω_TL. The convective heat flow is always directed upwards, and it is the largest in systems with wavelengths comparable to the slot height. The magnitude of the overall heat flow increases proportionally to the heating intensity when conductive effects dominate and proportionally to the second power of the heating intensity when convection dominates. It also increases proportionally to the corrugation amplitude. The system characteristics are dictated by convection when the relative position of the heating and corrugation patterns eliminates conduction. Addition of the uniform heating component amplifies the above processes, while uniform cooling reduces them. The processes described above are qualitatively similar for all Prandtl numbers of practical interest with the magnitude of the convective heat flow increasing with Pr.