Natural Heat Transfer Phenomenon in MHD Fractional Second Grade Fluid

Salah Uddin,Rozaini Roslan,Obaid Ullah Mehmood,Mghazali Kamardan,Mahmod Abd Hakim Mohmad,Mahathir Mohamad

doi:10.13189/ujme.2019.071605

Abstract

This paper aims at the heat transfer phenomenon and the effect of magnetic field on the second-grade fluid in a vertical oscillating cylinder. By applying a perpendicular magnetic field, the fluid gets magnetized. Fractional MHD flow was modeled with Caputo-Fabrizio non-integer derivative approach. Exact solution of the governing equations was obtained by Laplace and finite Hankel transforms. Mathematical computations and graphical plots were used to investigate the quantitative effects of emerging dimensionless physical parameters on the second-grade fluid flow, such as magnetic field and Prandtl number.

Highlights

Nowadays BFD and MHD are gaining significant attention in fractional-order electromagnetism, bio-engineering and neurons modeling in biology
Heat transfer has a major impact on the non-Newtonian flow problems in industry and engineering
Visco-elastic fluid flow inside the circular cylinder was investigated by Choudhury and Deka [7]

Summary

Introduction

Nowadays BFD (biomagnetic fluid dynamics) and MHD (magneto hydrodynamics) are gaining significant attention in fractional-order electromagnetism, bio-engineering and neurons modeling in biology. In the analytical study of Nehad and Ilyas [1], fractional parameter enhances the fluid velocity in the vertical oscillating plate. Visco-elastic fluid flow inside the circular cylinder was investigated by Choudhury and Deka [7]. Non-Fourier heat flux and thermal conductivity for temperature-dependent fluid were numerically investigated by Hayat et al [10]. Blood and fluid flow problems without singularity in the fractional domain were analytically studied by Uddin et al [11], [12], [13]& [14]. Shojaei et al [18] analytically examined the Soret and Dufour effects along stretching cylinder Both were in negative correlation with heat and mass transfer rate. Thermoelectric characteristics were reflected by the simulated results and especially the temperature distribution across the device. Density, βT is the fluid volumetric coefficient of thermal expansion, g is the gravitational acceleration, Cp is the fluid heat capacity at constant pressure and k is the fluid thermal conductivity

Dimensionless Time Fractional Model

Mathematical Model

Temperature Field

Velocity Field

Numerical Results and Discussion

Conclusions