Abstract This research paper aims to investigate the peristaltic transport of a nanofluid (NF) in a tapered asymmetric channel. Initially, the governing equations for the balance of mass, momentum, temperature, and volume fraction for the NF using Reiner–Philippoff (RP) based NF are formulated. Subsequently, these equations are employed to analyze long wavelength and small Reynolds number scenarios. The numerical results for various flow features are thoroughly examined and discussed. Dual solutions have been examined for some factors. So, stability assessment is implemented to find stable solution. Novelty of the existing is to investigate the peristaltic motion of Buongiorno's NF model and its stability which has not investigated in the previous literatures. It has been demonstrated that modifying the RPF parameter leads to a transition in the fluid's velocity, changing it from a dilatant liquid to a Newtonian fluid and from Newtonian to pseudoplastic. The findings indicate that the temperature curves rise as Brownian motion and thermophoretic factors increase, while they decrease as the Prandtl number increases. Furthermore, a concise mathematical and graphical analysis is carried out to examine the impact of each key parameter on the flow characteristics.

Peristaltic transport with multiple solutions of heat and mass transfer using modified Buongiorno nanofluid model over tapered channel with long wave‐length at small Reynolds number