Hartmann boundary layer in peristaltic flow for viscoelastic fluid: Existence

Abstract

This paper addresses the peristaltic flow phenomenon for non-Newtonian Jeffrey fluid inside an asymmetric channel subject to large magnetic field. The governing boundary value problem is approximated under the long wavelengths and small Reynolds number assumptions. Asymptotic approximation of the boundary value problem is made for large magnetic field. The resulting differential equation turns out to be singular boundary value problem which is solved for the velocity field using asymptotic analysis and higher order matching technique. The boundary layer regions are determined where the magnetic field dominates the viscous force. The main objective of this study is to discuss the different situations arising in analytical solutions calculated with the help of asymptotic analysis, under the effects of strong and weak magnetic field. The strong magnetic field gives rise to Hartmann boundary layer, which is investigated analytically to understand the role of magnetic field on the velocity filed in the boundary layer regions for peristalsis transport of rheological fluids in channels. It is noticed that the boundary layer velocity has inverse relation with the magnetic field parameter. Another significant consequence of this study is to reduce the boundary layer by employing strong magnetic field and that the velocity in the core of the channel due to peristalsis becomes uniform. The outcomes of magnetic field in peristaltic motion for Jeffrey fluid can be helpful in understanding the transport phenomena in human physiological systems.