Thin Film Flow of Couple Stress Magneto-Hydrodynamics Nanofluid with Convective Heat over an Inclined Exponentially Rotating Stretched Surface

Asifa Tassaddiq,Meshal Shutaywi,Saeed Islam,Farhad Ali,Asad Ullah,Ibni Amin,Zahir Shah

doi:10.3390/coatings10040338

Abstract

In this article a couple stress magneto-hydrodynamic (MHD) nanofluid thin film flow over an exponential stretching sheet with joule heating and viscous dissipation is considered. Similarity transformations were used to obtain a non-linear coupled system of ordinary differential equations (ODEs) from a system of constitutive partial differential equations (PDEs). The system of ordinary differential equations of couple stress magneto-hydrodynamic (MHD) nanofluid flow was solved using the well-known Homotopy Analysis Method (HAM). Nusselt and Sherwood numbers were demonstrated in dimensionless forms. At zero Prandtl number the velocity profile was analytically described. Furthermore, the impact of different parameters over different state variables are presented with the help of graphs. Dimensionless numbers like magnetic parameter M, Brownian motion parameter Nb, Prandtl number Pr, thermophoretic parameter Nt, Schmidt number Sc, and rotation parameter S were analyzed over the velocity, temperature, and concentration profiles. It was observed that the magnetic parameter M increases the axial, radial, drainage, and induced profiles. It was also apparent that Nu reduces with greater values of Pr. On increasing values of the Brownian motion parameter the concentration profile declines, while the thermophoresis parameter increases.

Highlights

The word nanofluid denotes a mixture of nanoparticles and base fluids
Pr and Kthrough were explored for radial film flow with and transfer a steady rotating inclined surface was analyzed
The flow past an exponential stretching sheet of couple stress nanofluid with the impacts of MHD, viscous dissipation, and Joule heating was investigated analytically

Summary

Introduction

The word nanofluid denotes a mixture of nanoparticles and base fluids. Usually nanoparticles contain metals such as silver, copper, aluminum, nitrides like silicon nitride, carbides such as silicon carbides, oxides e.g., aluminum oxide and nonmetals such as graphite. Choi et al [1] introduced the term nanofluid and heat transfer features of vile fluids and studied the thermal conductivity enhancement. Heat transfer enhancement and thermal conductivity variation of fluids by the addition of copper nanoparticles were studied by Eastman et al [3,4]. Bianco et al [7] studied the implication between nanoparticles and liquid matrix in two-phase flow; further, nanofluids involuntary convection in circular tubes was deliberated. Ullah et al [23] analyzed the Reiner–Philippoff fluid model analytically over a stretching surface They studied the thermophoresis and Brownian motion impacts over the thin film. The heat transfer enhancement depends on the nanoparticles added, and depends on the nature of the fluid. The couple stress impacts with joule heating and viscous dissipation have been studied and analyzed by different researchers over different surfaces [24,25,26]

Results

Discussion

Conclusion