# Flow in a Rectangular Channel with Double Orthogonal Collocation

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.

Contributed by: Jorge Gamaliel Frade Chávez (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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.