Influence of Wall Properties on the Peristaltic Flow of a Nanofluid in View of the Exact Solutions: Comparisons with Homotopy Analysis Method

No doubt, the exact solution of any physical system is considered optimal when it is available. Such exact solution is of great importance not only in validating the accuracy of the approximate solution obtained for the same problem but also to derive the correct physical interpretation of the involved physical phenomena. In this paper, the system of linear and nonlinear partial differential equations describing the peristaltic flow of a nanofluid in a channel with compliant walls has been solved exactly. These exact solutions have been implemented to explore the exact effects of Prandtl number Pr, thermophoresis parameter NT, Brownian motion parameter NB, and Eckert number Ec on the temperature, the nanoparticle concentration profiles, and the heat transfer coefficient Z(x). In addition, the exact results have been compared with a very recent work via the homotopy analysis method for the same problem. Although these comparisons showed that the published approximate results coincide with the current exact analysis, a few remarkable differences have been detected for the behaviour of the heat transfer coefficient.