A multi-layer integral model for locally-heated thin film flow

JOURNAL OF COMPUTATIONAL PHYSICS

卷:336

Article

Kay, E. D.¹  Hibberd, S.²  Power, H.³ 

[1] Norton Straw Consultants, Steam Engine House, Derby DE22 1DZ, England

[2] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

[3] Univ Nottingham, Dept Mech Mat & Mfg Engn, Nottingham NG7 2RD, England

关键词: Thin film flow;    Marangoni effect;    Layered model;    Integral model;    Moderate Reynolds number;   

DOI  :  10.1016/j.jcp.2017.01.066

来源: Elsevier

【 摘 要 】

Based on an approach used to model environmental flows such as rivers and estuaries, we develop a new multi-layered model for thin liquid film flow on a locally-heated inclined plane. The film is segmented into layers of equal thickness with the velocity and temperature of each governed by a momentum and energy equation integrated across each layer individually. Matching conditions applied between the layers ensure the continuity of down-plane velocity, temperature, stress and heat flux. Variation in surface tension of the liquid with temperature is considered so that local heating induces a surface shear stress which leads to variation in the film height profile (the Marangoni effect). Moderate inertia and heat convection effects are also included. In the absence of Marangoni effects, when the film height is uniform, we test the accuracy of the model by comparing it against a solution of the full heat equation using finite differences. The multi-layer model offers significant improvements over that of a single layer. Notably, with a sufficient number of layers, the solution does not exhibit local regions of negative temperature often predicted using a single-layer model. With Marangoni effects included the film height varies however we find heat convection can mitigate this variation by reducing the surface temperature gradient and hence the surface shear stress. Numerical results corresponding to the flow of water on a vertical plane show that very thin films are dominated by the Marangoni shear stress which can be sufficiently strong to overcome gravity leading to a recirculation in the velocity field. This effect reduces with increasing film thickness and the recirculation eventually disappears. In this case heating is confined entirely to the interior of the film leading to a uniform height profile. (C) 2017 Elsevier Inc. All rights reserved.

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