Doctor of Philosophy
Mechanical and Materials Engineering
Dr. J. M. Floryan
Convection in an infinite horizontal slot subject to spatially distributed heating has been investigated for a wide range of Prandtl numbers. The primary flow response consists of convection in the form of rolls. When heating wave number alpha is sufficiently large the convection is found to be limited to a layer adjacent to lower wall and a uniform conductive layer emerges at upper section of the slot.
Conditions leading to the emergence of secondary convection have been identified using linear stability of the above primary convection. The secondary convection gives rise to longitudinal, or transverse, or oblique rolls; or to oscillatory mode at onset. Three mechanisms of instability have been identified. For small and moderate alpha parametric resonance leads to the pattern of instability that is locked-in with the pattern of heating. The second mechanism is associated with the formation of patterns of vertical temperature gradients and patterns of primary convection currents, operates approximately in the same range of alpha. The third mechanism operates for large alpha where instability is driven by uniform mean vertical temperature gradient created by primary convection and fluid response becoming similar to that found in the case of uniformly heated wall. A rapid stabilization of the oblique rolls is observed when alpha is reduced sufficiently, with the oscillatory mode taking the dominant role. As alpha becomes very small, secondary motions concentrate around the hot spots. When an external flow is introduced into the slot, the heating assists in reduction of the overall drag.
Hossain, Mohammad Zakir, "Convection Due to Spatially Distributed Heating" (2011). Electronic Thesis and Dissertation Repository. 312.