Mathematical Modelling Of Extraction Of The Underground Fluids: Application To Peristaltic Transportation Through A Vertical Conduit Occupied With Porous Material

Abstract

Abstract This paper gives a theoretical idea for extracting the underground fluids through peristalsis. Due to the similarity in aforesaid problem, peristaltic transportation of a viscous Newtonian fluid over a vertical porous conduit is studied by considering the impact of heat transfer. Presuming the long-wavelength approximation, explicit solutions are found as asymptotic expansions with reference to free convection and porosity parameters. Mathematical expressions for coefficient of heat transfer, temperature and mean flux are derived. It is experiential that for few precise values of dissimilar parameters under contemplation, the coefficient of heat transfer increases significantly as Grashof number and Eckert number increases. This narrates to optimization of heat transfer in some processes. Further, it has been observed that mean flow enhances with amplitude ratio, porosity in addition to pressure drop. This authorizes auxiliary research on the impacts of peristalsis on the flow features in vertical channels.