Abstract
Aiding mixed convection flow resulting from the vertical flow of a uniform stream past a horizontal line source of heat is of importance in many practical situations such as hot-wire anemometry, etc. In this paper, the stability of such a flow to small disturbances is analyzed in terms of the linear stability theory. The analysis treats the presence of the free stream as a perturbation of a natural convection plume generated by the line source of heat. The base flow as well as the disturbance field are determined by means of a systematic perturbation expansion.
The results presented here extend the results of an earlier investigation [1], by considering second-order mixed convection effects. The results reveal that the free stream has a stabilizing effect. As expected, consideration of second-order mixed convection effects further enhances the stability of the flow. The reported results are valid at a large distance from the source where the flow field is dominated by buoyancy effects.
Résumé
Aidant la convection mixte d'un écoulement résultant d'un écoulement uniforme vertical, à l'arrière d'une source rectiligne horizontale de chaleur, est important en plusieurs situations pratiques, comme celui de l'anémomètre à fil chaud, etc. Dans cet article, la stabilité de ce genre d'écoulement aux pertubations est analysée par la théorie de la stabilité linéaire. L'analyse traits la présence de l'écoulement libre comme perturbation d'une convection naturelle du panache crée par la source rectiligne de chaleur. L'écoulement de base ainsi que le champ exposé aux perturbations sont déterminés au moyen d'une série de perturbations systématiques. L'analyse prend en considération la nature non-parallèle de l'écoulement de base.
Les résultats présentés ici, élargissent les résultats d'une étude précédente [1], en considérant le second ordre des effets de la convection mixte. La consideration du second ordre des effets de la convection mixte augmente la stabilité de l'écoulement. De même, l'effet de la convection mixte sur la courbe neutre semble différent de celle-ci pour une paroi limitée des écoulements.
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Krishnamurthy, R. A linear stability analysis of a mixed convection plume from a line source: higher order effects. Z. angew. Math. Phys. 43, 385–396 (1992). https://doi.org/10.1007/BF00946638
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DOI: https://doi.org/10.1007/BF00946638