Applications of fractional derivatives to nanofluids: exact and numerical solutions

¹ Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Kuantan, Pahang, Malaysia
² Basic Engineering Sciences Department, College of Engineering Majmaah University, Majmaah 11952, Saudi Arabia

^* Corresponding author: ilyaskhanqau@yahoo.com; i.said@mu.edu.sa

Received: 10 August 2017
Accepted: 10 January 2018

Abstract

In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.