simulation of heat transfer on the peristaltic flow of a jeffrey-six constant fluid in a diverging tube

peristaltic flow of a jeffrey-six constant fluid in a nonuniform tube is investigated under the assumption of long wavelength and low reynolds number approximations. the dimensionless quantities are used to simplify momentum and energy equations assuming that fluid physical/rheological properties remain constant. regular perturbation method is invoked to find an analytical solution for the velocity and temperature field.