Numerical solutions for laminar forced convection and fluid flow in pipes
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AbstractThe phenomenological equations of continuity, momentum and energy for laminar flow in a tube are solved using a fully implicit finite difference technique. A novel "four point staggered grid" system is developed in which the primary variables of axial and radial velocity, pressure and temperature are positioned at different places in each grid block. Furthermore, nodal points are located in the regions of highest velocity and temperature gradients, i.e. at the entrance and wall. A mass balance error of 0.05% is obtained with five radial blocks under Poiseuillian flow conditions. A similar uneven distribution for time is applied to unsteady state problems. Numerical results for the Graetz constant property problem, Szymanski start-up problem and Boussinesq entrance region problem for Newtonian fluids are in excellent agreement with analytical and experimental results. Subsequently, non-Newtonian steady and unsteady flow in the entrance region of tubes as well as laminar forced convection for variable viscosity fluids using three viscosity-temperature models are examined. Comparisons are made to resolve some of the differences between the existing correlations for friction factor and Nusselt number in the developed as well as developing regions. Pressure discontinuities in the entrance region are reported and transient phenomena in this region are described for both Newtonian and nonNewtonian fluids.
Bibliography: p. 73-75.
CitationPatience, G. S. (1987). Numerical solutions for laminar forced convection and fluid flow in pipes (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/23131
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