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Dimensionless versus Dimensional Analysis in CFD and Heat Transfer

H. Dillon[1], A.F. Emery[1], A. Mescher[1], and R.J. Cochran[2]
[1]University of Washington, Seattle, WA, USA
[2]Applied CHT, Seattle, WA, USA

Students in engineering and science are often exposed early in their studies to non dimensional analysis. When it comes to solving fluid flow/heat transfer problems, many solutions, particularly industrial ones, are based on finite element/finite volume using dimensioned quantities. In order to compare to reference information one would like to use codes like COMSOL Multiphysics to solve non dimensional problems. For example in convection a reference velocity can be expressed as n/L sqrt(Gr), n/L sqrt(Ra), n/L sqrt(Re), n/L, or a/L where n and a are the kinematic viscosity and thermal diffusivity and L is some length scale and Re, Gr and Ra are the Reynolds, Grashof and Rayleigh numbers. The different choices lead to different solution techniques, particularly for highly non linear problems and to different interpretations. The paper describes numerical experiments computing highly transient free convection flows, compares dimensionless and dimensional results, the solution techniques used, and discusses which and why specific choices of non dimensional groups are more appropriate to different flow situations.