The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical± analytical solution of two-dimensional fully-developed laminar¯ow of non-Newtonian power-law¯uids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of powerlaw index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity pro®les computed by using this methodology are also compared with those calculated by approximated methods for power-law¯uids, within the range of governing parameters studied.

A hybrid analytical-numerical approach based on the Generalized Integral Transform Technique is employed to simulate the laminar forced convection (hydrodynamically fully developed and thermally developing laminar flow) of power-law non-Newtonian fluids inside ducts with arbitrary shaped cross-sections. The analysis is illustrated through consideration of both right angularly and isosceles triangular ducts subjected to constant wall temperature as thermal boundary condition. Reference results for quantities of practical interest such as dimensionless average temperature and Nusselt numbers within the thermal entry region were produced for different values of power-law index and apex angles. Finally, critical comparisons are performed with results available in the literature for direct numerical and approximate approaches.

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