Non-Newtonian Natural Convection Along a Vertical Plate with Uniform Surface Heat Fluxes

Natural convection of non-Newtonian fluids along a vertical flat plate with the heating condition of uniform surface heat flux was investigated using a modified power-law viscosity model. In this model, there are no physically unrealistic limits in the boundary-layer formulation for power-law non-Newtonian fluids. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge is removed; hence, the boundary-layer equations can be solved straightforwardly by marching from the leading edge downstream. Numerical results are presented for the case of shear-thinning as well as shear-thickening fluids for two limits. The numerical results demonstrate that a similarity solution for natural convection exists near the leading edge, where the shear rate is not large enough to trigger non-Newtonian effects. After the shear rate increases beyond a threshold value, non-Newtonian effects start to develop and a similarity solution no longer exists. This indicates that the length scale is introduced into the boundary-layer formulation by the classical power-law correlation.