Asymptotic Solution for Thermocapillary Flow at High and Low Prandtl Numbers Due to Concentrated Surface Heating

[+] Author and Article Information
C. L. Chan, M. M. Chen, J. Mazumder

Laser Aided Materials Processing Laboratory, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801

J. Heat Transfer 110(1), 140-146 (Feb 01, 1988) (7 pages) doi:10.1115/1.3250444 History: Received September 19, 1985; Online October 20, 2009


Thermocapillary convection due to nonuniform surface heating is the dominant form of fluid motion in many materials processing operations. The velocity and temperature distributions for the region adjacent to the area of peak surface heating are analyzed for the limiting cases of large and small Prandtl numbers. For a melt pool whose depth and width are large relative to the thermal and viscous boundary layers, it is shown that the most important parameter is the curvature (i.e., ∇2 q ) of the surface heat flux distribution. The solutions of the temperature and stream functions are presented, some of which are in closed form. Simple, explicit expressions for the velocity and maximum temperature are presented. These results are found to be quite accurate for realistic Prandtl number ranges, in comparison with exact solutions for finite Prandtl numbers. Besides being more concise than exact results, the asymptotic results also display the Prandtl number dependence more clearly in the respective ranges.

Copyright © 1988 by ASME
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