Digital computational techniques and the laminar flow of a fluid through a helical conduit - Manlapaz, Romeo L. (1968)
This thesis is a study of the feasibility of applying a numerical method of integrating the partial differential equations describing the laminar flow of an incompressible Newtonian fluid through a helical conduit with the aid of an IBM System/360 computer. The relevant partial differential equations are first developed in the appropriate variables and in the appropriate system of coordinates. The partial derivatives in these differential equations are then approximated by finite differences expressions developed from the Taylor series, and the error equations for correcting the assumed values of the dependent variables on the various grid points are set up.
The computational program for systematically correcting the assumed values of the dependent variables is then developed on the basis of two assumptions: 1). that in correcting the values on any grid point, the errors which need to be considered are those on the grid point itself and those on the grid points immediately adjacent to it; and 2). That the errors themselves are small enough in comparison with the values to permit a linearization of the error equations. Finally, the computational program is utilized to solve the laminar flow problem using several permutations of the Reynolds number and the reduced helical radius, and the results of these attempts at a solution are evaluated . The results obtained show that the computational program as developed and applied works only for a very limited range of Reynolds numbers, and fails to yield convergent results at higher Reynolds numbers.
Thesis (M.S. Chemical Engineering)--University of the Philippines Diliman.
Keywords: Laminar flow -- Mathematical models; Fluid dynamics -- Mathematical models; Fluid mechanics