New concept about existence of Hartmann boundary layer in peristalsis through curved channel-asymptotic solution N. Ali . K. Javid . M. Sajid . T. Hayat Received: 24 May 2015 / Accepted: 10 December 2015 Ó Springer Science+Business Media Dordrecht 2015 Abstract The main objective of this paper is to investigate boundary layer character of the velocity in peristaltic flow of a Sisko fluid in a curved channel under the influence of strong imposed radial magnetic field. The Sisko fluid model falls in the category of generalized Newtonian fluid models. The constitutive equation of Sisko model is described in terms of three material constants namely; power-law index (n), infinite shear rate viscosity (a) and consistency index (b). This model is capable of predicting shear-thinning and shear-thickening effects for n \ 1 and n [ 1, respectively. The equation governing the flow is first derived under the assumptions of long wavelength and low Reynolds number, and then made dimensionless by defining appropriate parameters. In dimensionless form it contains three dimensionless parameters namely; generalized ratio of infinite-shear rate viscos- ity to consistency index, power-law index and Hart- mann number characterizing strength of the imposed magnetic field. It is found that the governing equation of flow becomes singular for large values of Hartmann number. Asymptotic solutions representing flow velocity at large values of Hartmann number are reported for two specific values of power-law index (namely n = 1 and n = 1/2) using singular perturba- tion technique. The flow velocity in either case exhibits qualitatively similar behavior. In fact, it exhibits boundary layer character i.e., it varies sharply in thin layer near the walls and varies linearly over rest of the cross-sections. This is contrary to what that is observed for flow velocity in straight channel (where except in thin layer near the channel walls the velocity over rest of the cross-section is uniform). The estimates of boundary layer thickness at upper and lower walls in either case are different. Moreover, the boundary layer thickness in either case is found to be inversely proportional to the Hartmann number. Keywords Curved channel  Peristalsis  Boundary layer  Radial magnetic field  Asymptotic solutions 1 Introduction The magnetohydrodynamic (MHD) flows of rheolog- ical materials have indispensable significance in the N. Ali  K. Javid (&) Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan e-mail: khurram_javid1985@yahoo.com M. Sajid Theoretical Physics Division, PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan T. Hayat Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan T. Hayat Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21598, Saudi Arabia 123 Meccanica DOI 10.1007/s11012-015-0346-2