Analysis of Stokes' Second Problem for Nanofluids Using Modern Approach of Atangana-Baleanu Fractional Derivative

• Published in: Journal of nanofluids 2018-08, Vol.7 (4), p.738-747
• Main Authors: Abro, Kashif Ali, Rashidi, Mohammad Mehdi, Khan, Ilyas, Abro, Irfan Ali, Tassaddiq, Asifa
• Format: Article
• Language: English
• Subjects: Atangana-Baleanu (ab) Fractional Operator Ab(dχt); Generalized M Function Mpq(f); Nanofluids; Stokes Second Problem
• ISSN: 2169-432X
• DOI: 10.1166/jon.2018.1486

This article is proposed to investigate the analytical solutions of Stokes second problem with nanofluids in presence of magnetic field embedded in porous medium. A model of homogeneous type is taken with nanosized copper (Cu) particles suspended in ethylene glycol (EG). The modeled governing partial differential equations have been transformed in dimensionless form using modern method of Atangana-Baleanu (AB) fractional derivatives AB(Dχt). The general solutions are obtained for temperature distribution and velocity field by employing Laplace transform with inversion. These solutions are presented for two different oscillations; case-(i) sine oscillation and case-(ii) cosine oscillations. The obtained solutions have been expressed in terms of special function namely generalized M-function Mpq(F) satisfying initial and boundary conditions. Graphical illustration is based on sine and cosine oscillations separately in presence of fractional approach. Finally, in order to check the differences and similarities, several rheological parameters have been analyzed graphically.