Abstract
The mixed convection flow in a vertical duct is analysed under the assumption that e, the ratio of the duct width to the length over which the wall is heated, is small. It is assumed that a fully developed Poiseuille flow has already been set up in the duct before heat from the wall causes this to be changed by the action of the buoyancy forces, as measured by a buoyancy parameter α. An analytical solution is derived for the case when the Reynolds numberRe, based on the duct width, is of 0 (1). This is extended to the case whenRe is 0 (e−1) by numerical integrations of the governing equations for a range of values of α representing both aiding and opposing flows. The limiting cases, |α| ≫ 1 andR=eRe of 0 (1), andR and α both large, with α of 0 (R 1/3) are considered further. Finally, the free convection limit, α large with αR of 0 (1), is discussed.
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