Flow and heat transfer analysis in a deformable channel

An analytical solution of the Navier–Stokes equations in a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls is presented to improve the existing analytical results and to provide a comparison with the exact numerical solutions. The analytical solution is obtained with the use of the homotopy analysis method (HAM) which provides a uniformly valid solution for a wide range of parameters and has a better accuracy. In addition, the heat transfer analysis is presented for the case where the channel walls are kept at a constant temperature. The analytical solution is obtained with the use of three different techniques, and a numerical solution is obtained by the shooting method. A detailed analysis and comparison of the results of all these methods is presented. Heat transfer analysis in a deformable channel has been carried out for the first time.