Effect of modulation on onset of thermal convection of a second-grade fluid layer 

[[abstract]]This study examines the stability of a horizontally extended second-grade fluid layer heated from below, when a steady temperature difference between the walls is superimposed on sinusoidal temperature perturbations. A linear stability analysis proposed by Venezian (J. Fluid Mech. 35 (1969) 243) is employed to obtain the critical Rayleigh numbers for different types of temperature modulation. The free-free and isothermal boundary conditions are considered so as to allow analytic solutions. The stability characterized by the shift in critical Rayleigh number R-2c is calculated as a function of the modulation frequency omega, the Prandtl number Pr, and the viscoelastic parameter Q. It is found that the onset of convection can be delayed or advanced by these parameters. (C) 2004 Elsevier Ltd. All rights reserved.[[note]]SC