Laminar flow and heat transfer in power-law fluids flowing in arbitrary cross-sectional ducts

A numerical method capable of handling three-dimensional transport processes is devised to model the developing steady laminar flow and heat transfer to power-law fluids flowing in ducts of arbitrary but uniform cross section. The governing equations are the general momentum and energy equations parabolized in the axial direction and as such are applicable to flow systems with a predominant flow direction. An orthogonal body-fitted coordinate system is employed to handle complex cross-sectional geometries. The transformed equations are discretized in a finite-difference form, and the resulting algebraic equations are solved by line successive over-relaxation (SOR). For the purpose of testing the algorithms and the computer code, solutions are computed for the well-known case of a Newtonian fluid in a square duct. Excellent agreement with available numerical and experimental results is obtained. The versatility of the code is demonstrated by presentation of flow and heat transfer results for power-law fluids flowing in pentagonal and trapezoidal duets.