| An analysis of thermocapillary flow and temperature profiles in flattened, horizontally levitated, laser-heated thin glycerin disk is carried out. A model is based on the observed shape and the thickness is taken to be a minimum and much smaller at the center with a gentle parabolic profile at both the top and the bottom surfaces.; Considering boundary conditions on the surface where the surface stresses are balanced with the thermocapillary force corresponding to temperature gradient, general three-dimensional governing equations are averaged over the thickness of the disk-shaped drop and transformed into two-dimensional equations. To avoid difficulties with handling pressure terms, the momentum equation is formulated in terms of the vorticity and some additional terms due to a dimpled surface and the temperature gradient.; A numerical approach is used to solve the equations. The governing equations are discretized into finite difference equations by using central difference approximation. From the discretized equation, penta-diagonal coefficient matrices are constructed and solved in using Matlab program.; For the convective heat transfer on drop surfaces, acoustic streaming is studied when the fluid medium and the drop are in a small-amplitude high-frequency relative oscillatory motion along the symmetry axis of the flatten drop. The Biot numbers on each surface are used as its boundary conditions.; The modeling results are compared with experimental measurements of the isothermal lines by thermographic means and show good agreement. Therefore, the results obtained can be used for the thermal analysis of a levitated flatten drop. |
