Convection with temperature dependent fluid properties

The instability of the thermal conduction solution when a layer of fluid is heated from below and convection cells form is treated extensively in this book. Up to this point we have mostly assumed the properties of the fluid are constant. It may, however, be argued that viscosity should always be treated as a function of temperature in the Bénard problem, since it is one of the fluid properties which does exhibit a considerable change with varying temperature. To appreciate this variation we simply look at values for mundane fluids. For example, (Rossby, 1969) quotes that the kinematic viscosity of water varies from 0.01008 cm2sec-1 at 20°C to 0.00896 cm2sec-1 at 25°C, this being approximately a 10% change. Over the same temperature range the thermal conductivity only exhibits a 1.5% change. (Rossby, 1969) also quotes values for the viscosity of a 20 cSt silicone oil, of 0.2137 cm2sec-1 at 20°C and 0.1904 cm2sec-1 at 25°C, i.e. approximately a 20% variation. Over this temperature range the thermal conductivity of the same silicone oil is constant. The viscosity values just quoted are for typical room temperatures over a range in which the Boussinesq approximation may be expected to hold. If the temperature range is greater the viscosity variation is also typically much larger. For example (Lide, 1991) states that the viscosity of olive oil varies from 138.0 centipoise at 10°C to 12.4 centipoise at 70°C.