**E**ff**ects of Double Di**ff**usion Convection on Third Grade Nanofluid through a Curved Compliant Peristaltic Channel**

**Hanan Alolaiyan 1, Arshad Riaz 2,\*, Abdul Razaq 2, Neelam Saleem 3, Ahmed Zeeshan <sup>4</sup> and Muhammad Mubashir Bhatti <sup>5</sup>**


Received: 22 November 2019; Accepted: 26 January 2020; Published: 8 February 2020

**Abstract:** Nanofluids are potential heat transfer fluids with improved thermophysical properties and heat transfer performance. Double diffusion convection plays an important role in natural processes and technical applications. The effect of double convection by diffusion is not limited to oceanography, but is also evident in geology, astrophysics, and metallurgy. For such a vital role of such factors in applications, the authors have presented the analytical solutions of pumping flow of third-grade nanofluid and described the effects of double diffusion convection through a compliant curved channel. The model used for the third-grade nanofluid includes the presence of Brownian motion and thermophoresis. Additionally, thermal energy expressions suggest regular diffusion and cross-diffusion terms. The governing equations have been constructed for incompressible laminar flow of the non-Newtonian nanofluid along with the assumption of long wavelength. The obtained analytical expressions for velocity, temperature, and nanoparticle concentration have been sketched for various considerable parameters. The effects of regular buoyancy ratio, buoyancy parameter, modified Dufour parameter, and Dufour-solutal Lewis number have been analyzed along with wall properties and pumping characteristics. This study concludes that fluid becomes hotter with increase in regular buoyancy ratio and a modified Dufour parameter, but a decrease in temperature is observed for the buoyancy parameter. Moreover, the solutal concentration is behaving inversely against the Defour-Solutal Lewis number.

**Keywords:** double diffusion; nanofluid; curved channel; peristaltic pumping; compliant walls; analytical solutions; third grade fluid model
