In this study, two-phase asymmetric peristaltic Carreau-Yasuda nanofluid flow in a vertical and tapered wavy channel is demonstrated and the mixed heat transfer analysis is considered for it. For the modeling, two-phase method is considered to be able to study the nanoparticles concentration as a separate phase. Also it is assumed that peristaltic waves travel along X-axis at a constant speed, c. Furthermore, constant temperatures and constant nanoparticle concentrations are considered for both, left and right walls. This study aims at an analytical solution of the problem by means of least square method (LSM) using the Maple 15.0 mathematical software. Numerical outcomes will be compared. Finally, the effects of most important parameters (Weissenberg number, Prandtl number, Brownian motion parameter, thermophoresis parameter, local temperature and nanoparticle Grashof numbers) on the velocities, temperature and nanoparticles concentration functions are presented. As an important outcome, on the left side of the channel, increasing the Grashof numbers leads to a reduction in velocity profiles, while on the right side, it is the other way around.

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