Poiseuille flow with variable physical properties — a simulation approach

Abstract

This paper investigates two computational approaches to the solution of a particular nonequilibrium fluid problem of Poiseuille flow. In the problem formula tion considered, the viscosity μ and the thermal con ductivity k are taken to be functions of temperature. By incorporating certain assumptions, the fundamental partial differential equations describing the phys ical situation can be simplified to a pair of non linear ordinary differential equations. The problem solution, however, is embedded in a two-point boundary value problem whose solution is complicated by an ill-behaved region at one end of the solution trajectory. Solutions to the problem are obtained using both an analog/hybrid computer and the S/360 CSMP package. The mechanisms provided in both these computational environments for handling logic signals provides the means for coping with the ill-behaved feature inher ent in the solution trajectory. The results obtained in both approaches compare favorably with previously reported results based on the Picard method. Each of the two approaches has its inherent advan tages and disadvantages in the context of the prob lem considered. With little doubt, the high "inter activity" of the analog/hybrid approach represented its most noteworthy asset, while the relative ease with which the basic problem dynamics could be pro grammed was the most advantageous feature of the CSMP approach. However, the relative difficulty in handling the two-point boundary value problem in the CSMP approach complicated the total programming effort required.