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A COMPARISON OF METHODS FOR RAPID CALCULATION OF FRICTIONAL PRESSURE DROP AND HEAT TRANSFER COEFFICIENT FOR FLOW OF NON- NEWTONIAN FLUIDS IN DUCTS WITH NON-CIRCULAR CROSS SECTIONS

The paper presents a comparison of exact and approximate methods for calculating the frictional pressure drop with flow of purely viscous nonNewtonian fluids in passages with non-circular cross-sectional geometry. While comparing existing approximate methods for calculating the fully developed friction factor for power-law fluids, special emphasis is given to the widely used methods of Kozicki, Chou and Tiu (1966), Miller (1972) and the recent procedure by Delplace and Leuliet (1995). For some cross-sections consisting of doubly connected regions, values of geometrical parameters necessary to apply the methods cited above, are reported. For narrow passages, similar to those, encountered e.g. in CHE, analytical approximations of fully developed friction factors, and Nusselt number are reported. INTRODUCTION For stabilised laminar flow of Newtonian fluids, the exact solution for the frictional pressure drop and heat transfer coefficients with a noncircular geometry of the cross-section consists essentially in solving the momentum and energy equations in the corresponding cross-sectional geometry. Most complete source of results in this respect is available e.g. in Shah and London (1978). For laminar flow of purely viscous fluids, the momentum equation becomes non-linear and, therefore, integration is generally possible using numerical procedure only. Consequently, for most engineering purposes, rapid and reliable approximate procedures become important. For laminar flow of a Newtonian fluid in a circular tube the frictional pressure drop is related to the Reynolds number with the familiar hydraulic characteristic relation f = 16 Re , (1) where the Fanning friction factor and Reynolds number are given as f De p u L = ∆ 2 2 ρ , (2)