A depth-averaged model for non-isothermal thin-film rimming flow

Kay, Edmund; Hibberd, S.; Power, H.

doi:10.1016/j.ijheatmasstransfer.2013.11.040

Cited by 18 publications

(31 citation statements)

References 24 publications

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“…The wall boundary conditions of no-slip velocity (18) and fixed temperature (20) set the values of a i,0 and b i,0 in the first layer (i = 1):…”

Section: Polynomial Velocity and Temperature Profilesmentioning

confidence: 99%

“…Further stability analysis of the inclined channel [6] and the effects of a surfactant at the interface [7] have been made. 20 The presence of a rigid upper boundary is found to have a strong effect on the stability of multilayer channels compared to those with a free upper surface. The presence of a free upper surface can lead to instability even in the limit of vanishing Reynolds number in contrast to the channel flow case [8].…”

Section: Introductionmentioning

confidence: 99%

“…Models based on the weighted-average technique with sixth-order polynomials for velocity [17] show improvements in stability predictions over the original quadratic model of Shkadov. Extensions to include thermal effects within IBL models have been provided 50 by [18] and [19] for a linear temperature profile and [20] for a quadratic temperature profile. A shortcoming of these models has been the prediction of areas of the film with unphysical negative temperatures when convection effects are significant.…”

Section: Introductionmentioning

confidence: 99%

“…Accurate resolution of the surface temperature gradient is important in order to capture the Marangoni effect correctly. It is noted that single-layer IBL models for these flows have reported unphysical negative temperatures on the film surface [18,20] leading to inaccuracy in the resulting film profile. Adaption of the multi-layer IBL approach to 85 this thin film application gives significant improvements in the local temperature fields and hence surface temperature gradient resolution.…”

mentioning

confidence: 99%

“…For the same reason the x−pressure gradient term in (5) is retained though it appears multiplied by . On similar grounds we retain the x-diffusion term in (6) though it appears multiplied by 2 since this can be significant in regions where the temperature field varies rapidly [20]. 7…”

mentioning

confidence: 99%

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

Kay¹,

Hibberd

Power

2017

Journal of Computational Physics

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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.

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“…The wall boundary conditions of no-slip velocity (18) and fixed temperature (20) set the values of a i,0 and b i,0 in the first layer (i = 1):…”

Section: Polynomial Velocity and Temperature Profilesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Kay¹,

Hibberd

Power

2017

Journal of Computational Physics

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Progress in understanding and modelling of annular two-phase flows with heat transfer

Anglart

2019

Nuclear Engineering and Design

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Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

2021

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A detailed analysis of steady coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the absence of surface-tension effects but in the presence of a non-uniform pressure distribution due to an irrotational airflow with circulation shows that the presence of the airflow can result in qualitatively different behaviour of the fluid film from that in classical coating flow. Full-film solutions corresponding to a continuous film of fluid covering the entire cylinder are possible only when the flux and mass of fluid do not exceed critical values, which are determined in terms of the non-dimensional parameters $F$ and $K$ representing the speed of the far-field airflow and the circulation of the airflow, respectively. The qualitative changes in the behaviour of the film thickness as $F$ and $K$ are varied are described. In particular, the film thickness can have as many as four stationary points and, in general, has neither top-to-bottom nor right-to-left symmetry. In addition, when the circulation of the airflow is in the same direction as the rotation of the cylinder the maximum mass of fluid that can be supported on the cylinder is always less than that in classical coating flow, whereas when the circulation is in the opposite direction the maximum mass of fluid can be greater than that in classical coating flow.

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A depth-averaged model for non-isothermal thin-film rimming flow

Cited by 18 publications

References 24 publications

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

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

Progress in understanding and modelling of annular two-phase flows with heat transfer

Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

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