Combined free and forced laminar non-Newtonian convection in a vertical tube with constant wall temperature

Abstract

A theoretical and experimental investigation of combined free and forced, laminar, non-Newtonian convection has been carried out. The problem studied was heat transfer to a power law fluid with an initially fully developed velocity profile flowing upward through a constant wall temperature vertical, circular tube. Except for a linear variation of density with temperature in the body force term, all properties were assumed to be constants. The coupled system of governing equations was solved numerically. Typical developing velocity and temperature profiles are presented. Mean Nusselt numbers and dimensionless pressure drop as a function of dimensionless axial distance are presented for a range of the parameters: flow behavior index n, Prandtl number Pr, and Grashof over Reynolds number ratio Gr/Re. Results show that distortion of the velocity profile due to free convection can increase both the heat transfer and pressure drop significantly. Near the point of maximum velocity profile distortion, for sufficiently large values of Gr/Re, the local Nusselt number shows the unusual behavior of increasing with increasing axial distance. Experimental mean Nusselt numbers were obtained using 0·5 and 1·0 per cent aqueous solutions of Carbopol. With all properties evaluated at the wall temperature, the theoretical and experimental results agreed within ±15 per cent.