SUMMARYThe generalized integral transform technique (GITT) is employed in the solution of incompressible laminar channel flows as formulated by the steady-state Navier-Stokes and continuity equations under the primitive variables mathematical representation. A hybrid numerical-analytical solution is developed based on eigenfunction expansions in one space co-ordinate and error-controlled numerical solution of the resulting system of coupled ordinary differential equations in the remaining space direction. The approach is illustrated for developing flow between parallel-plates with uniform and irrotational inlet flow condition. The conventional Poisson-type equation for the pressure field with appropriate boundary conditions is also transformed and simultaneously solved with the momentum equation along the longitudinal direction, by considering eigenvalue problems for each of the two potentials, defined in the transversal direction. The transversal velocity component is then explicitly determined from the continuity equation. Numerical results of the longitudinal velocity component and friction factor fields are reported to illustrate the convergence behaviour and user prescribed error control inherent to the proposed hybrid approach. Critical comparisons with previous contributions on the same method that made use of the streamfunction-only formulation are also provided.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.