Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure

doi:10.1016/S1004-9541(14)60040-9

Chin.J.Chem.Eng. ›› 2014, Vol. 22 ›› Issue (4): 365-369.DOI: 10.1016/S1004-9541(14)60040-9

• FLUID DYNAMICS AND TRANSPORT PHENOMENA • Next Articles

Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure

ZHANG Yan¹, ZHENG Liancun²

1 School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China;
2 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received:2012-12-08 Revised:2013-04-03 Online:2014-04-04 Published:2014-04-28
Supported by:
Supported by the National Natural Science Foundation of China (21206009), Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR201107123), and Program for Doctoral Fund in Beijing University of Civil Engineering and Architecture (101102307).

Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure

张艳¹, 郑连存²

1 School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China;
2 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

通讯作者: ZHANG Yan
基金资助:
Supported by the National Natural Science Foundation of China (21206009), Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR201107123), and Program for Doctoral Fund in Beijing University of Civil Engineering and Architecture (101102307).

Abstract

Abstract: This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximant technique. For the cases that buoyancy force is favorable or unfavorable to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.

Key words: Marangoni convection, similarity equations, asymptotic expansion, Padé, approximant, approximate solution

摘要： This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximant technique. For the cases that buoyancy force is favorable or unfavorable to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.

关键词: Marangoni convection, similarity equations, asymptotic expansion, Padé, approximant, approximate solution

ZHANG Yan, ZHENG Liancun. Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure[J]. Chin.J.Chem.Eng., 2014, 22(4): 365-369.

张艳, 郑连存. Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure[J]. Chinese Journal of Chemical Engineering, 2014, 22(4): 365-369.

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[2]	MAO Zaisha, LU Ping, ZHANG Guangji, YANG Chao. Numerical Simulation of the Marangoni Effect with Interphase Mass Transfer Between Two Planar Liquid Layers [J]. Chin.J.Chem.Eng., 2008, 16(2): 160-170.
[3]	SHI Ying, Kerstin Eckert. Orientation-dependent hydrodynamic instabilities from chemo-Marangoni cells to large scale interfacial deformations [J]. , 2007, 15(5): 748-753.

Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure

Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure

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