Non-linear stability analysis of film flow down a heated or cooled inclined plane with viscosity variation

Chi-Chuan Hwang; Cheng I. Weng

doi:10.1016/0017-9310(88)90192-5

Non-linear stability analysis of film flow down a heated or cooled inclined plane with viscosity variation

Chi-Chuan Hwang, Cheng I. Weng

Department of Engineering Science

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

Non-linear kinematic equations for film thickness which takes into account the effect of viscosity variation governed by the Arrhenius-type relation are used to investigate the non-linear stability of film flows. The results show that cooling (heating) from the wall will stabilize (destabilize) the film flows both linearly and nonlinearly. The supercritical stability and subcritical instability both prove possible here with higher heating tending to reduce the threshold amplitude in the subcritical unstable region and increase the amplitude of supercritical waves. Stability is also influenced by the Prandtl number in the way that stability increases (decreases) as the Prandtl number increases when cooling (heating).

Original language	English
Pages (from-to)	1775-1784
Number of pages	10
Journal	International Journal of Heat and Mass Transfer
Volume	31
Issue number	9
DOIs	https://doi.org/10.1016/0017-9310(88)90192-5
Publication status	Published - 1988 Jan 1

All Science Journal Classification (ASJC) codes

Condensed Matter Physics
Mechanical Engineering
Fluid Flow and Transfer Processes

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abstract = "Non-linear kinematic equations for film thickness which takes into account the effect of viscosity variation governed by the Arrhenius-type relation are used to investigate the non-linear stability of film flows. The results show that cooling (heating) from the wall will stabilize (destabilize) the film flows both linearly and nonlinearly. The supercritical stability and subcritical instability both prove possible here with higher heating tending to reduce the threshold amplitude in the subcritical unstable region and increase the amplitude of supercritical waves. Stability is also influenced by the Prandtl number in the way that stability increases (decreases) as the Prandtl number increases when cooling (heating).",

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N2 - Non-linear kinematic equations for film thickness which takes into account the effect of viscosity variation governed by the Arrhenius-type relation are used to investigate the non-linear stability of film flows. The results show that cooling (heating) from the wall will stabilize (destabilize) the film flows both linearly and nonlinearly. The supercritical stability and subcritical instability both prove possible here with higher heating tending to reduce the threshold amplitude in the subcritical unstable region and increase the amplitude of supercritical waves. Stability is also influenced by the Prandtl number in the way that stability increases (decreases) as the Prandtl number increases when cooling (heating).

AB - Non-linear kinematic equations for film thickness which takes into account the effect of viscosity variation governed by the Arrhenius-type relation are used to investigate the non-linear stability of film flows. The results show that cooling (heating) from the wall will stabilize (destabilize) the film flows both linearly and nonlinearly. The supercritical stability and subcritical instability both prove possible here with higher heating tending to reduce the threshold amplitude in the subcritical unstable region and increase the amplitude of supercritical waves. Stability is also influenced by the Prandtl number in the way that stability increases (decreases) as the Prandtl number increases when cooling (heating).

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Non-linear stability analysis of film flow down a heated or cooled inclined plane with viscosity variation

Abstract

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