Analytical Study of Peristaltic Flow in a Doubly Connected Region with Heat Transfer Effects

An eccentric annular region is created by placing cylindrical tubes with a Z-axis as the axis is considered. The inner tube is assumed to be at a higher temperature than the outer tube. The outer wall is subjected to a peristaltic wave motion and the inner tube is rigid. The inner tube rotates with a fixed velocity due to which a small eccentricity is created. The study focuses on the effects of heat transfer and eccentricity on the flow. The coupled equations of motion are decoupled and solved by the regular perturbation method with eccentricity as the perturbation parameter. An approximate solution for temperature and velocity is obtained and graphically depicted. The flow rate is maintained constant and the effect of heat transfer on pressure gradient is analysed. As eccentricity increases pressure gradient and temperature increase thereby increasing velocity. An area of the cross-section decreases, and heat transfer gets accelerated. Velocity shows higher values in the presence of heat transfer. The above solutions are compared with closed-form solutions in the case of concentric cylinders. The rate of flow is more in the case of eccentric cylinders than concentric.