The behavior of some peristaltic flow for some liquids in a vertical and horizontal cylindrical tube is studied before in non-closed form. In this paper, the nanoparticles AL_2 O_3/water flow is discussed in a peristaltic vertical cylindrical tube under the effect of gravity and the constant heat addition/absorption. The mass, Navier-Stokes, heat and volume flow rate equations represent the mathematical model for long wavelengths. The system of equations represents a closed form for the dependent parameters. The model is solved analytically in terms of nano temperature, velocity and pressure gradient distributions with existence of nanoparticles suspended in liquid. The stream function is obtained in the plane of fluid with nanoparticles

Various amplitude ratio and heating source parameter values have an impact on the nano temperature distribution in a peristaltic tube. The nano fluid velocity is increasing with the change of Grashof number values, rate of volume flow, heating source parameter and decreasing with void fraction of nano particles. The obtained results prove the validity of the current model