On the use of complex variables in the analysis of flows of an elastic fluid (Q1066737)

This interesting theoretical paper aims to demonstrate the usefulness of complex variables in investigating low Reynolds number flows of incompressible Newtonian and non-Newtonian fluids. It considers the extension of a complex differential equation describing plane creeping flow of a Newtonian fluid, by including both inertial and non-Newtonian effects in succession. The modified equations so obtained have been used to consider (i) low Reynolds number Hamel flow of a Newtonian fluid, (ii) low Reynolds number flow of a co-rotational Maxwell fluid over a circular cylinder. Apart from the simplifications in the analysis of plane flows, and a systematic solution process, the present approach of complex variables also avoids the use of Oseen type approximation which seem to be unjustified for the constitutive equations of non-Newtonian fluids.