Three dimensional numerical and asymptotic solutions for the peristaltic transport of a heat-conducting fluid

Abstract

Using the Oberbeck-Boussinesq (O-B) equations as a mathematical model, asymptotic solutions in closed form and numerical solutions are obtained for the peristaltic transport of a heat-conducting fluid in a three-dimensional flexible tube. The results show that the relation between mass flux and pressure drop remains almost linear and the efficiency of the transport depends mainly on the ratio of the wave amplitudeh and the average radius of the tubed. However, the 3-D flow is much different from the 2-D flow in the following ways: (i) The 3-D flow is much more sensitive to the change of the volume expansion coefficient α r ; (ii) Trapping and backflow are much more common in 3-D case; (iii) The longwave asymptotic approximation in 3-D case is not as good as in 2-D case, especially when α r is not small; (iv) The 3-D flow is more sensitive to Reynolds number change.