Unstable convection in vertical channels with heating from below, including effects of heat sources and frictional heating

Author / Creator

Ostrach, Simon, author

Available as

Online

Summary

The effects of heat sources and frictional heating on the laminar fully developed channel flow subject to a body force between two parallel plates oriented in the direction of the body force are an...

The effects of heat sources and frictional heating on the laminar fully developed channel flow subject to a body force between two parallel plates oriented in the direction of the body force are analyzed. Solutions are obtained for combined forced- and natural-convection flows for the cases in which the wall temperature variations are linear and (1) the wall temperatures are specified, (2) the walls are both insulated, and (3) the net mass flow in the channel is zero. These solutions depend on the Rayleigh number which was previously found to be the factor determining the stability and type of flow for horizontal and vertical layers of fluids heated from below but without heat sources or frictional heating. Similar stability characteristics are displayed in the present problem, and the heat sources affect the flows only in a quantitative manner.

When the effects of frictional heating are considered, two distinct solutions are obtained for each set of parametric values. Solutions neglecting frictional heating correspond to a different exact solution for values of the Rayleigh number smaller and larger than the critical. The related approximate and exact solutions are essentially coincident when the frictional-heating parameter is small but differ for unit order values of this parameter. The approximate solutions (id est, those neglecting fictional heating) are shown to be always invalid for Rayleigh numbers near critical.

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