Marangoni-Benard convection in a low-aspect-ratio liquid layer

This paper presents the results of a study on the variation of the critical Marangoni number (Ma(sub c)) for the onset of Benard convection in a finite liquid layer bounded horizontally as well as from below. A direct-numerical-simulation procedure is devised to determine the Ma(sub c) for aspect ratios (Ar) ranging from 0.8 to 10. The results predict a strong increase of Ma(sub c) as Ar decreases to below 2. A dip of Ma(sub c) occurs between Ar = 1.45 and 1.3, which is accompanied by a pattern transition from a two-cell convection to a unicellular flow. For Ar above 4, the calculated Ma(sub c) shows little change and asymptotically approach a value of 116.15, with Biot number (Bi) equal to 1.