Combined forced and free flow of a power-law fluid in a vertical annular duct

An investigation of mixed convection and flow reversal in a vertical annular duct is presented with reference to laminar and fully-developed flow of a power-law fluid. The boundary surfaces are supposed to be isothermal, with unequal temperatures. The momentum balance and the energy balance equations as well as the viscous stress constitutive equation are solved analytically in order to obtain the velocity field, the viscous stress field and the temperature field. First, two special cases are analyzed: mixed convection of a Newtonian fluid; forced convection of a power-law fluid. Then, in the general case, the evaluation of the friction factors is employed to determine the conditions for the occurrence of flow reversal, for fixed values of the power-law index and of the ratio between the duct inner and outer radii.