Integral transform solution of internal flow problems based on Navier-Stokes equations and primitive variables formulation

The 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. Copyright q 2006 John Wiley & Sons, Ltd