An Experimental Study on Combined Forced and Natural Convective Heat Transfer from Spheres to Power-Law Fluids

Abstract

Experiments have been carried out in the range of 1.0<N_pe<10³, 1.6×10^-6<N_Gr<0.44, 2.6×10⁴<N_pr, < 6.4×10⁵ and 0.24<N_Gr^{1/ (n+1)} N_pr'^{2n/ (3n+1)} <74, where N_pe is Péclet number, and N_Gr and N_pr are generalized Grashof and Prandtl number for power-law fluids as defined by Acrivos, respectively. A sphere, 46.03 mm in diameter, composed of eleven copper segments, and two brass spheres (19.03 and 9.534 mm in diameter) have been used. Test liquids used are 2.61 %MC (methylcellulose), 5.52 %CMC, 0.74 %SPA (sodium polyacrylate) and 1.48 %PEO aqueous solutions. The experimental data are summarized by the following relation :
Nu_m-2= [(0.866σ^2/3N_pe^1/3-0.553σ-0.341) ^3/2+ (0.44N_Gr^{1/ (2n+2)} N_pr'^{n/ (3n+1)} ) ^3/2] ^2/3 (K_b/K_s) ^{1/ (3n+1)}
where
σ=-2.475n³+6.738n²-7.868n+4.740
and K_b and K_s are the values of power-law model parameter K at the bulk liquid temperature t_b and the sphere surface temperature t_s, respectively. This equation has been shown to represent measured values of Nu_m, within an average deviation of 29.3 per cent.