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).

In order to model the blood flow through an artery in presence of catheter, we considered a steady, laminar, incompressible, Poiseuille flow of a Herschel-Bulkley fluid between two horizontal parallel elastic walls. The power law index ( ) and yield stress ( ) are the two parameters of the Herschel - Bulkley fluid. By giving different values for the above mentioned parameters, we get the Newtonian, Bingham and Power-law fluids as special cases. The exact solutions for the flow quantities such as velocity, plug flow velocity and flux are derived. The flux is determined as a function of inlet, outlet, external pressures and the elastic property of the channel. The effect of elastic parameters on flux variation is analyzed. Further when and our results qualitatively agree with those of Rubinow and Keller [2]. In addition, velocity of the Herschel- Bulkley fluid flow is expressed in terms of elastic parameters.

This paper deals with peristaltic motion of electrically conducting nanofluid in a tapered asymmetric channel through a porous medium in presence of heat and mass transfer under the effect of slip conditions. The problem is reduced mathematically by a set of nonlinear partial differential equations which describe the conservation of mass, momentum, energy and concentration of nanoparticles. The non-dimensional form of these equations is simplified under the assumption of long wavelength and low Reynolds number. The coupled governing equations are solved analytically. The expressions for velocity, stream function, temperature and concentration are derived. The results have been presented graphically for the various interested emerging parameters and the obtained results are discussed in detail. It is observed that the magnitude of the velocity decreases in the middle of the channel while it increases near the channel walls with an increase in the non-uniform parameter  It is also noticed that the nanoparticle temperature increases with increasing thermal slip parameter . The present result coincides with the findings of Kothandapani and Prakash [19].