### Abstract

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. , INV TR S **2q) 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.

Original language | English (US) |
---|---|

Pages (from-to) | 140-146 |

Number of pages | 7 |

Journal | Journal of Heat Transfer |

Volume | 110 |

Issue number | 1 |

State | Published - Feb 1988 |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Physical and Theoretical Chemistry
- Mechanical Engineering

### Cite this

*Journal of Heat Transfer*,

*110*(1), 140-146.

**ASYMPTOTIC SOLUTION FOR THERMOCAPILLARY FLOW AT HIGH AND LOW PRANDTL NUMBERS DUE TO CONCENTRATED SURFACE HEATING.** / Chan, Cholik; Chen, M. M.; Mazumder, J.

Research output: Contribution to journal › Article

*Journal of Heat Transfer*, vol. 110, no. 1, pp. 140-146.

}

TY - JOUR

T1 - ASYMPTOTIC SOLUTION FOR THERMOCAPILLARY FLOW AT HIGH AND LOW PRANDTL NUMBERS DUE TO CONCENTRATED SURFACE HEATING.

AU - Chan, Cholik

AU - Chen, M. M.

AU - Mazumder, J.

PY - 1988/2

Y1 - 1988/2

N2 - 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. , INV TR S **2q) 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.

AB - 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. , INV TR S **2q) 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.

UR - http://www.scopus.com/inward/record.url?scp=0023965868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023965868&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0023965868

VL - 110

SP - 140

EP - 146

JO - Journal of Heat Transfer

JF - Journal of Heat Transfer

SN - 0022-1481

IS - 1

ER -