Analytical and numerical solution for viscous dissipation effect on the heat transfer in a deformable channel

In this paper, shooting method and homotopy perturbation technique are applied for the flow analysis of temporal energy transport in a deformation channel with isothermal walls. An incompressible viscous fluid fills the space inside the channel. Analytical and numerical solutions are developed for the momentum and energy equations. The viscous dissipation effects are taken into account. Graphs for pertinent flow parameters are sketched and discussed. Comparison between the analytical and numerical solutions indicates an excellent agreement. It is noticed that behaviors of Prandtl and Eckert numbers on the temperature are qualitatively similar.