Abstract
The convective circulation driven by a surface buoyancy flux in a dead-end open channel is analysed. On the assumption of similarity profiles for velocity and temperature, the governing partlial differential are reduced to two nonlinear ordinary differential equations by integrating over the flow depth. A closed-form solution of the differential equations is presented. The solution is a function of the Grashof number G and the modified Prandtl–Grashof number PmG½ defined ih (21). The velocity and temperature along the channel vary linearly as the distance and as the square of the distance respectively. Analytical expressions for the rate of total heat loss from the channel and the rateof flow in the channel are derived. The analytical results compare well with the available experimental data.
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