Experimental study of double-diffusive cellular convection due to a uniform lateral heat flux

Abstract

A uniform, lateral heat flux applied to a body of fluid with a vertical solute gradient, causes the horizontal growth of cellular convection. This paper deals with a series of experimental studies of the phenomenon, which yielded the following results. (1) The third non-dimensional parameter besides the Prandtl number and the diffusivity ratio, τ, in this particular double-diffusive convection was found to be π3 = − α(q/k)/β(dS/dz) in which q, k, −(dS/dz) are the lateral heat flux, the thermal conductivity of the fluid and the initial solute gradient respectively, and where α = −ρ−1(∂ρ/∂ T), and β = ρ−1(∂ρ/∂ S), ρ being the density. The existence of a critical value of π3 above which cellular convection occurs has been confirmed in this study. (2) When the solute used was varied (i.e. with τ different), the corresponding shift in the critical value of π3 was also observed indicating that the critical values of π3 are 0·13 for CuSO4 (τ = 3·5 × 10−3), 0·28 for common salt (τ = 9 × 10−3) and 0·76 for HCl (τ = 24 × 10−3). (3) The measured vertical height of a cell, h, when normalized with respect to a characteristic length L(= [vk/gα(q/k)]1/4 where v and k are the kinematic viscosity and the thermal diffusivity, respectively), increased steadily with π3, and for a given value of π3, h/L decreased with an increase in τ. (4) Studies of the shadowgraph pictures indicated that the initially developed roll cells quickly merge to form layers of outward-growing convection cells.