document: Denier and Hewitt [12] have shown that bounded solutions to 9a, 9b and 9c subject to (10a) and (10b) exist only in the shear-thinning case for n>12. In the shear-thickening case they have shown that solutions become non-differentiable at some critical location ηc, and although it transpires that this singularity can be regularised entirely within the context of the power-law model, we will not consider such flows here. Thus in this study we will consider flows with power-law index in the range 12<n⩽1. They have also shown that for 12<n<1 to ensure the correct algebraic decay in the numerical solutions one must apply the Robin condition(11)(u¯′,v¯′)=nη(n-1)(u¯,v¯)asη→∞,at some suitably large value of η=η∞≫1. In the Newtonian case this relationship becomes singular, this is due to the fact that when n=1 the functions u¯ and v¯ decay exponentially. Cochran [13] showed that in this case(12)(u¯′,v¯′)=w¯∞(u¯,v¯)asη→∞,where w∞=-2∫0∞u¯dη.
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