Convection Driven by Surface Tension and Buoyancy in a Relatively Hotter or Cooler Layer of Liquid with Free slip Bottom

By : A.K. Gupta, D. Surya

Page No: 245-255

Abstract
Rayleigh-Bénard Marangoni convection in a relatively hotter or cooler layer of liquid is studied theoretically by means of modified linear stability theory. The upper surface of the layer is considered to be non-deformable free where surface tension gradients arise on account of variation of temperature and the lower boundary surface is also free, each subject to constant heat flux condition. The Galerkin technique is used to obtain the eigenvalue equation analytically which is then computed numerically. This analysis predicts that the onset of convection in a relatively hotter layer of liquid is more stable than a cooler one under identical conditions, irrespective of whether the two mechanisms causing instability act individually or simultaneously, and that the coupling between the two agencies causing instability remains perfect.

Authors :
A.K. Gupta : Department of Mathematics, Himachal Pradesh University Centre for Evening Studies, Shimla, India
D. Surya : Department of Mathematics & Statistics Himachal Pradesh University Summer Hill, Shimla, India