This paper describes a new model for obtaining analytical solutions to the problem of non-Newtonian fluid flow through eccentric annuli. A discussion on non-Newtonian rheology is presented, followed by the development and solution of applicable differential equations using the Ostwald de Waele power-law model and a nonrectangular slot. Results indicate that velocity values are reduced greatly in the reduced region of the eccentric annulus. This is important in directional drilling where the drillpipe tends to lie against the hole. Design of mud flow for cuttings transport on the basis of the nominal average velocity could lead to serious problems associated with cuttings buildup in the low-velocity region of the annulus. Other practical ap-plications of this work include the determination of velocity distribution in chemical processes involving fluid flow through eccentric annuli – e.g., heat exchangers and extruders – and more accurate velocity profiles inside journal bearings, particularly for small diameter ratios. The main advantage in the new approach is that iterative finite difference methods used by previous investigators are avoided. Previous work along present lines used a linearized model and resulted in velocity profiles of unacceptable accuracy. This study improves both the accuracy and the solution technique.
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Iyoho et al. (1981) studied this question.