Hydrodynamics and heat transfer of wavy thin film flow

doi:10.1016/S0017-9310(96)00016-6

International Journal of Heat and Mass Transfer

Volume 40, Issue 1, October 1996, Pages 179-190

https://doi.org/10.1016/S0017-9310(96)00016-6 Get rights and content

Abstract

The hydrodynamics and heat transfer of thin film flow with a wavy interface has been studied using computational fluid dynamics techniques. The velocity and temperature fields are obtained for periodic laminar flow with an assumed interface shape. The effect of sinusoidal and solitary waves on the heat transfer across the film is investigated. It is shown that the overall heat transfer coefficient is determined mainly by conduction through the film, rather than by the recirculation, if any, under the waves. However, the presence of interfacial waves still enhances the heat transfer coefficient due, mainly, to the effective thinning of the film. Copyright © 1996 Elsevier Science Ltd.

Section snippets

INTRODUCTION

The flow of a thin liquid film down a solid wall can often be observed in everyday life, as when rain water flows down a window pane. It is also a subject of industrial importance involving heat transfer and mass transfer, typical examples of which are film cooling of turbine blades and gas absorption in wetted-wall columns, respectively. There have been a number of studies of falling films over the past several decades. One of the earliest of these is that of Nusselt [1] dealing with steady

CALCULATION METHODOLOGY

Numerical simulation of fluid flow is increasingly being used to solve a wide variety of fundamental and practical fluid flow problems. Here, the set of equations governing the fluid flow (comprising normally mass and momentum conservation equations with appropriate boundary conditions) is solved using spectral or finite element or finite difference methods. The techniques have been developed to such an extent that normally they take the form of CFD codes, some of the well-known examples of

RESULTS

The results of the calculations for falling films without interfacial waves are shown first in Table 1. In these cases, a constant film thickness was assumed, and the motion of liquid under the action of gravity was calculated subject to a specified wall velocity. The average flow velocity, interface velocity and the heat transfer coefficient obtained from the calculation are listed in the table. The results, when converted into a stationary frame of reference, are independent of the wall

DISCUSSION AND CONCLUSION

We have studied the hydrodynamics and heat transfer characteristics of a wavy laminar flow of given interface shape. The wave velocity and the velocity field were obtained such that there was a balance between the wall shear stress and the gravitational force. Note that the shape of the interface is not predicted as part of the solution, but that the solution obtained (subject to the conditions of periodicity and no interfacial shear) corresponds to the case of falling film flow if the

NOMENCLATURE

g	acceleration due to gravity
k	thermal conductivity
L_t	length of tail section
L_f	length of wave front section
Pr	Prandtl number
Q	volumetric liquid flow rate per unit wetted perimeter
Re	film Reynolds number (U_aδ/ν)
T_i(x)	interface temperature at position x
T_w(x)	wall temperature at position x
u	velocity down film (x-direction)
u_a	average velocity in film
u_w	wave velocity
v	velocity normal to wall (y-direction)
x	distance down film.
Greek symbols
δ	liquid film thickness
λ	average heat transfer coefficient
λ(x)	local heat

Acknowledgements

S. Jayanti gratefully acknowledges the financial help he received from the Science and Engineering Research Council during the period of this study.

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^†: Now at the Indian Institute of Technology, Madras, India.

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Hydrodynamics and heat transfer of wavy thin film flow

Abstract

Section snippets

INTRODUCTION

CALCULATION METHODOLOGY

RESULTS

DISCUSSION AND CONCLUSION

NOMENCLATURE

Acknowledgements

Adv. Chem. Engng

Chem. Engng Sci.

Int. J. Mass Transfer

Int. J. Multiphase Flow

Int. J. Heat Mass Transfer

Int. J. Multiphase Flow

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Chem. Engng Sci.

Wave flow of thin viscous liquid films

Zhur. Exper. i. Teor. Fiz.

Wave formation in laminar flow down an inclined plane

J. Fluid Mech.

Initiation of roll waves

AIChE J.

Wavy flow in open channels

Trans. Am. Soc. Civil Engrs

Experiments on the onset of wave formation on a film of water flowing down a vertical plate

J. Fluid Mech.

Characteristics of flow in falling liquid films

Chem. Engng Progr.

The role of waves in two-phase flow: some new understanding, 1976 Award Lecture

Chem. Engng Educ.