Heat transfer and horizontally averaged temperature of convection with large viscosity variations

Abstract

Experiments with fluids whose viscosity depends strongly on temperature are used to study the effect of viscosity variations in the range 10−10⁵ on the heat transfer and horizontally averaged temperature of a convecting layer between horizontal isothermal boundaries. At large viscosity variations (3 × 10³ and 10⁵) and Rayleigh numbers less than the critical value given by linear theory, the system can be either conductive or convective depending on whether the Rayleigh number is increased from an earlier conductive state or decreased from a preexisting convective state. At higher Rayleigh numbers and for the entire range of viscosity variation studied the heat transfer differs little (< 20%) from that of a uniform-viscosity fluid when the Rayleigh number is defined in terms of the viscosity corresponding to a temperature equal to the average of the boundary temperatures. The relationship between Nusselt number and supercriticality (R_a/R_c) is even more remarkable being independent of viscosity variation and indistinguishable from that of a uniform-viscosity fluid with appropriate Prandtl number. The horizontally averaged temperature becomes increasingly asymmetrical with increasing viscosity variation due to the relatively large temperature change across the cold, more-viscous boundary layer, and results in an isothermal interior temperature significantly hotter than the average of the boundary temperatures. The measured temperature and convective heat transfer as a function of depth show that for viscosity variations greater than about 100 most of the viscosity change occurs within a stagnant conductive layer that develops above the actively convecting part of the system.