Developing laminar flow characteristics in elliptic ducts using Mathieu functions

The study of flow through elliptic ducts is important in view of its application in compact heat exchangers. The governing differential equations in the entrance region of elliptic ducts are solved using Langhaar's linearization technique and the developing velocity solutions are expressed in terms of Fourier and Bessel product type Mathieu functions. Based on these solutions, the details of the entrance region such as developing velocity and pressure fields are mapped for four aspect ratios.