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International Heat Transfer Conference 13

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

MODELLING OF HEAT TRANSFER IN STABLE WAVY FILM FLOW BASED ON EFFECTIVE THERMAL DIFFUSIVITY

Georg Dietze
Institute of Heat and Mass Transfer, RWTH Aachen University, Aachen, Germany

Viatcheslav Vladimirovich Lel'
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Russia

Reinhold Kneer
Institute of Heat and Mass Transfer, RWTH Aachen University, Augustinerbach 6, 52062 Aachen, Germany

DOI: 10.1615/IHTC13.p25.130
12 pages

Résumé

A model for the prediction of the temperature field in the liquid phase of stable wavy film flows down a heated vertical wall was developed. The model consists of a 2-dimensional boundary value problem defining a spatial and temporal map of the temperature field in the wavy film. The governing model equation has the form of the steady state energy equation for a 2-dimensional problem whereby all wave-induced effects on the mapped temperature field are modelled with an effective diffusive term orthogonal to the wall. The corresponding flux is formulated with a Fourier-type constitutive equation introducing an effective thermal diffusivity as the main model parameter. Based on data from the 2-dimensional, transient numerical simulation of the film flow for a set of regimes (Re=20, 50; Pr=56, 80, 100) the field of the effective thermal diffusivity was determined using the equation error method and parameterised in the crosswise and stream wise coordinates. The boundary value problem constituting the model was then solved numerically using the parameterised distribution for the effective thermal diffusivity, a comparison of the resulting temperature field with data from the transient simulation yielding good agreement. The results represent a basis for the determination of a closure condition for the model. A closed formulation of the presented model constitutes an efficient tool for the design of technical systems.

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