### Abstract

A generalized theory for thermocapillary flow and heat transfer in the stagnation region of a deep liquid layer under intense, non-uniform surface heating is developed for both plane two-dimensional and axisymmetric geometries. The theory approximates the surface heat flux distribution near the center by a parabola, and invokes the boundary layer approximation for the energy equation, but not for the momentum equation. The governing partial differential equations are transferred to a set of decoupled ordinary differential equations. Analytical solutions are found for some conditions. For other conditions numerical results are presented. The nature of the flow and heat transfer characteristics are presented and discussed. The results provide the basic scaling laws for thermocapillary convection in the deep fluid layer due to concentrated heating.

Original language | English (US) |
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Journal | American Society of Mechanical Engineers (Paper) |

State | Published - Jan 1 1985 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mechanical Engineering