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Fully-developed forced convection in rectangular ducts and illustrations of some general inequalities

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Abstract

New exact laminar convective temperature solutions for rectangular ducts with constant heat flux per unit length have been derived in uniform fashion for a variety of Dirichlet and Neumann boundary conditions. Those with null Dirichlet boundary conditions satisfy the hypothesis of a general inequality theorem. Consequences of the theorem are shown for the velocity and thermal fields of rectangular and elliptical ducts, which provide rigorous bounds for intermediate contours.

Résumé

Quelques solutions nouvelles exactes du problème de la convection laminaire de la chaleur dans les tuyaux de section rectangulaire ont été déduites d'une façon uniforme pour différentes conditions aux limites selon Dirichlet et Neumann. L'hypothèse d'un théorème général d'inégalité est satisfaite lorsque les conditions aux limites sont homogènes selon Dirichlet. Les conséquences de ce théorème sont montrées pour les champs de vitesse et de température dans les tuyaux rectangulaires et elliptiques, ce qui fournit des bornes précises pour des domaines intermédiaires.

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Authors and Affiliations

  1. Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland, USA

    Vivian O'Brien

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  1. Vivian O'Brien
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O'Brien, V. Fully-developed forced convection in rectangular ducts and illustrations of some general inequalities. Journal of Applied Mathematics and Physics (ZAMP) 30, 913–928 (1979). https://doi.org/10.1007/BF01590489

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  • DOI: https://doi.org/10.1007/BF01590489

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