We develop a mathematical model for heat transfer and fluid flow near a contact line on a heated surface in the presence of thermocapillary flow and evaporation. The coupled heat transfer and flow problem is reduced to an equation for local thickness, which is then solved numerically. The steady-state results indicate that thermocapillary stresses act to reduce the rate of liquid flow towards the contact line and increase interfacial curvature there. We also discuss solutions than involve moving contact lines, applicable to studies of start-up and shut-down operations of heat pipes. The velocity of the contact line and the apparent contact angle are found as functions of the Marangoni number. Thermocapillary effect is shown to reduce contact line speed and increase the apparent contact angle. Finally, the local solution is incorporated into global solutions for curvature variations of an evaporating three-dimensional meniscus in a corner. This configuration is typically encountered in proposed designs of micro heat pipes. Interface curvature is found as a function of the axial coordinate for the case of linear axial temperature variation in the corner.

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