Mixed convection in a periodically heated channel

Mixed convection in a channel with flow driven by a pressure gradient and subject to spatially periodic heating along one of the walls has been studied. The pattern of the heating is characterized by the wavenumber alpha and its intensity is expressed in terms of the Rayleigh number Ra-p. The primary convection has the form of counter-rotating rolls with the wavevector parallel to the wavevector of the heating. The resulting net heat flow between the walls increases proportionally to Ra-p but the growth saturates when Ra-p = O(10(3)). The most effective heating pattern corresponds to alpha approximate to 1, as this leads to the most intense transverse motion. The primary convection is subject to transition to secondary states with the onset conditions depending on alpha. The conditions leading to transition between different forms of secondary motion have been determined using the linear stability theory. Three patterns of secondary motion may occur at small Reynolds numbers Re, i.e. longitudinal rolls, transverse rolls and oblique rolls, with the critical conditions varying significantly as a function of alpha. An increase of alpha leads to the elimination of the longitudinal rolls and, eventually, to the elimination of the oblique rolls, with the transverse rolls assuming the dominant role. For large ff, the transition is driven by the Rayleigh-Benard mechanism; while for alpha = O(1), the spatial parametric resonance dominates. The global flow characteristics are identical regardless of whether the heating is applied at the lower or the upper wall.