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

Abstract

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.

A Study of Soret-Dufour Effects on MHD Radiative Casson Nanofluid Flow Past an Inclined Surface with Chemical Reaction

“…Examples include heat exchangers, lubrication, electroplating, and the flow of fluid in connective tissue. Thin film flow analysis across a heated inclined plane was therefore proposed by Kay et al, [28] based on environmental model data. Srinivasulu and Bandari [29] deliberated the impact of non-linear thermal radiation and non-uniform heat source/sink on MHD boundary layer flow of Williamson nanofluid above an inclined stretching surface.…”

Radiative Heat Source Fluid Flow of MHD Casson Nanofluid over A Non-Linear Inclined Surface with Soret and Dufour Effects

“…Kay et al, [30] proposed the ecological model-based on thin film flow analysis over heated inclined plane. In order to solve the spreading thin fluid problem, Alharbi and Naire [31] developed the R-adaptive mesh method, which takes into account the surface tension at the free surface.…”