Mixed convection with variable viscosity in a vertical annulus with uniform wall temperatures

The steady and laminar mixed convection with a temperature-dependent viscosity in a vertical annular duct with uniform wall temperatures is studied analytically. The flow is considered as purely axial and the fluid density is assumed to be a linear function of temperature. Analytical expressions of the dimensionless velocity distribution, of the dimensionless pressure drop and of the Fanning friction factors are determined. The importance of choosing the mean fluid temperature as the reference temperature in the definition of the difference between the pressure and the hydrostatic pressure is pointed out. The results show that the combined effects of buoyancy forces and of a variable fluid viscosity on the cross-section-averaged Fanning friction factor may be important, and that negative values of this quantity may occur.