Publisher Summary This chapter presents the field of thermal convection in non-Newtonian fluids. The thermal convection in external flows of inelastic fluids is relatively well understood in the chapter. Thermal convection in viscoelastic fluids has been studied only in a restricted way. An approximate correlating equation for mixed convection in external flows on non-Newtonian fluids is presented. The chapter explores the theoretical indications to show that there are likely to be tremendous advantages in adding drag-reducing polymers to impart viscoelastic properties to materials undergoing the process of thermal convection under turbulent conditions. The problem of buoyancy-induced secondary flow in heated horizontal tubes appears to be most challenging from a theoretical viewpoint. There are certain equations that correlate heat transfer data empirically, but the situation is not wholly satisfactory. The possibilities of oscillatory convection in viscoelastic fluids appear to exist under certain circumstances. The chapter concludes that thermal convection experiments are difficult to conduct, therefore there appears to be a massive generation of data correlating overall heat transfer coefficients with process variables but practically very little information on the velocity and temperature fields.

Thermal Convection in Non-Newtonian Fluids*

The temperature dependence of the density of both pure and saline water, even to very high salinity and pressure levels, decreases at decreasing temperature toward an extremum. The nature of this variation precludes approximating the buoyancy-force density difference linearly with a temperature difference. This peculiar density variation of water has very significant effects, even at environmental temperature levels. A new equation has appeared which relates density to temperature, salinity and pressure with very high accuracy. Its form is especially suited to the analysis of convective motions. We consider here vertical boundary-layer flows. Analysis of flows arising from thermal buoyancy and from combined buoyancy effects shows the simplicity of the formulation. Relatively few new parameters arise. Extensive calculations for thermally buoyant flows show the large magnitude of the effects of the complicated density variation on transport. Buoyancy-force reversals and convective inversions are predicted. The latter are in close agreement with past experiments. A new Grashof number arises which is an accurate indication of the actual local flow vigour. The effects of specific temperature conditions are given in detail. The appreciable effect of the Prandtl number is calculated. Transport parameters are given for salinities and pressures up to 40 p.p.t. and 1000 bars, respectively.

Buoyancy-induced flows in water under conditions in which density extrema may arise

V.M. Soundalgekar

Papers

Laminar free convection flow of water at 4°C from a vertical plate with variable wall temperature

Unsteady free convection flow of an elastico-viscous fluid past an infinite plate with constant suction