Flow in a Rectangular Channel with Double Orthogonal Collocation

Flow in a rectangular channel is a common problem encountered in the design of heat exchangers, monolithic reactors, and filters in combustion engines. This Demonstration shows the solution of the problem in a rectangular channel by means of a double-orthogonal collocation method.

A dimensionless mathematical model for flow in a rectangular channel is given in the following elliptic partial differential equation:

,

where is the velocity, and are positions in dimensionless units, with the boundary conditions , at and .

Reference: J. V. Villadsen and W. E. Stewart, "Solution of Boundary-Value Problems by Orthogonal Collocation," Chemical Engineering Science,22, 1967 pp. 3981–3996.