In this paper, a mathematical model is proposed to study the influence of elasticity on peristaltic flow of nanofluid in a vertical tube with temperature dependent viscosity. The expressions for axial velocity, temperature, flux and pressure gradient are derived. The different nanofluids suspensions are consider to analyze the influence of elasticity on flux variation. Application of blood flow through veins is studied by expressing relationship between pressure gradient and volume flow rate in an elastic tube. The effect of different pertinent parameters on the flow characteristics of nano fluid in an elastic tube with peristalsis is analyzed through graphs. The variation in flux for different nanofluids like pure water H2O, Copper-water nanofluid CuO + H2O, Silver-water Ag + H2O and Titanium oxide-water nanofluid TiO2 + H2O are illustrated through graphs. The variation in flux for various physical parameters such as amplitude ratio, heat source parameter, Grashof number, viscosity parameter and elastic parameters are discussed. The flux takes higher values for nano particles case when compared to pure water. The flux enhances with amplitude ratio, Grashof number, heat source/sink factor and viscosity factor. The flux is more for the Titanium oxide-water nanofluid TiO2 + H2O when compared to remaining cases. The important observation is that pressure rise along mean flow rate is increase due to raise in temperature of source or sink in puming region and decreases in co pumping region. In the absence of elastic parameter (α″ = 0), the results observed in the present study are similar to that of results observed by O. A. Beg et al., Results in Physics 7, 413 (2017).

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