ISSN 0965-5425, Computational Mathematics and Mathematical Physics, 2014, Vol. 54, No. 12, pp. 1886–1902. © Pleiades Publishing, Ltd., 2014. 1886 1. INTRODUCTION In the recent years the peristaltic flows of Newtonian and non-Newtonian fluids have attracted the attention of number of researchers because of its applications in physiology and biomechanical systems. Since the pioneering work done by Latham (see [1]) a variety of analytical and numerical studies with dif- ferent flow geometries have been reported (see [2–7]). The study of peristaltic flow in an asymmetric channel have been first discussed by Eytan and Elad in [8] because of its application in intra uterine fluid flow in a non pregnant uterus. After Eytan and Elad (see [8]) number of researchers have discussed the peristaltic flow in an asymmetric channel. Recently, Elshehawey et al. in [9] have discussed the peristaltic transport in an asymmetric channel through a porous medium. The peristaltic mechanism of a Maxwell fluid in an asymmetric channel have been analyzed by Hayat et al. in [10]. Wang et al. in [11] have consid- ered the magnetohydrodynamic peristaltic motion of a Sisko fluid in a symmetric or asymmetric channel. The peristaltic motion of a Carreau fluid in an asymmetric channel have been studied by Ali and Hayat in [12]. Kothandapani and Srinivas have discussed the peristaltic transport of a Jeffrey fluid under the effects of magnetic field in an asymmetric channel (see [13]). The study of heat transfer analysis is another interesting area in connection with peristaltic motion, which has industrial applications like sanitary fluid transport, blood pumps in heart lungs machine and transport of corrosive fluids where the contact of fluid with the machinery parts are prohibited. Only a lim- ited attention have been focussed to the study of peristaltic flows with heat transfer (see [14, 16]). The peri- staltic transport in an asymmetric channel with heat transfer have been examined by Srinivas and Kothandapani in [17]. In the papers cited above, no slip has been used. There are few attempts in which non standards boundary conditions are used. Recently, Nadeem and Akram in [18, 19] have discussed the peristaltic flow of Newtonian and non-Newtonian fluids in an asymmetric channel with slip conditions. To the best of authors knowledge the peristaltic flow of non-Newtonian fluid in a vertical asymmetric channel with slip condition is still unexplored. Therefore, the purpose of the present investigation is to highlight the peristaltic flow of a Carreau fluid in a vertical asymmetric channel with slip condition. The problem is solved analytically under the assumptions of long wave length and low Reynolds number. Numerical computation are carried out to calculate the expression of pressure rise. The graphical results Effects of Slip and Heat Transfer on a Peristaltic Flow of a Carreau Fluid in a Vertical Asymmetric Channel 1 S. Akram Department of Basic Sciences, Military College of Signals, National University of Sciences and Technology, Islamabad 44000, Pakistan e-mail: drsafiaakram@gmail.com Received May 22, 2013 Abstract—In the present paper the results of numerical modeling of peristaltic flow of a Carreau fluid in a vertical asymmetric channel are presented. The effects of slip and heat transfer have been ana- lyzed. Using the approximation of long wavelength, low Reynolds number and with the suitable dimensionless variables, the reduced equations have been solved analytically by regular perturbation method. The expressions for velocity, stream function, temperature, pressure gradient and pressure rise have been computed which strongly depend on the physical parameters of the Carreau fluid. With the help of analytical results the expression for pressure rise has been computed using numerical inte- gration scheme. To reveal the tendency of the solutions, typical results for velocity, temperature, stream function, pressure gradient and pressure rise are presented for different values of controlling parameters. DOI: 10.1134/S0965542514080028 Keywords: peristaltic flow, carreau fluid, partial slip, vertical asymmetric channel, heat transfer. 1 The article is published in the original.