Non-Newtonian Natural Convection Along a Vertical Flat Plate With Uniform Surface Temperature

Abstract

Natural-convection boundary-layer flow of a non-Newtonian fluid along a heated semi-infinite vertical flat plate with uniform surface temperature has been investigated using a four-parameter modified power-law viscosity model. In this model, there are no physically unrealistic limits of zero or infinite viscosity that are encountered in the boundary-layer formulation for two-parameter Ostwald–de Waele power-law fluids. The leading-edge singularity is removed using a coordinate transformation. The boundary-layer equations are solved by an implicit finite-difference marching technique. Numerical results are presented for the case of a shear-thinning fluid. The results indicate that a similarity solution exists locally in a region near the leading edge of the plate, where the shear rate is not large enough to induce non-Newtonian effects; this similarity solution is identical to the similarity solution for a Newtonian fluid. The size of this region depends on the Prandtl number. Downstream of this region, the solution of the boundary-layer equations is nonsimilar. As the shear rate increases beyond a threshold value, the viscosity of the shear-thinning fluid is reduced. This leads to a decrease in the wall shear stress compared with that for a Newtonian fluid. The reduction in the viscosity accelerates the fluid in the region close to the wall, resulting in an increase in the local heat transfer rate compared with the case of a Newtonian fluid.