Universal Journal of Mechanical Engineering 7(6C): 32-36, 2019 http://www.hrpub.org DOI: 10.13189/ujme.2019.071605 Natural Heat Transfer Phenomenon in MHD Fractional Second Grade Fluid Salah Uddin 1,* , Mahathir Mohamad 1 , Mahmod Abd Hakim Mohmad 2 , Obaid Ullah Mehmood 3 , MGhazali Kamardan 1 , Rozaini Roslan 1 1 Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Malaysia 2 Department of Mechanical Engineering, Faculty of Diploma Study Centre, Universiti Tun Hussein Onn Malaysia, Malaysia 3 Deprartment of Mathematics, Comsats University Islamabad, Pakistan Received July 30, 2019; Revised October 1, 2019; Accepted December 27, 2019 Copyright©2019 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License 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. Keywords Magnetized Solution, Buoyancy Forces, Non-integer Derivative, Conventional Fluid, Fractional Fluid 1. 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. Heat transfer has a major impact on the non-Newtonian flow problems in industry and engineering. In the analytical study of Nehad and Ilyas [1], fractional parameter enhances the fluid velocity in the vertical oscillating plate. Das et al [2] applied Runge-Kutta sixth order method to the stretching heat model. The results conclude that thermal radiation significantly increases the boundary layer velocity and temperature. Rehman et al. [3] used a homotopy analysis method to find the Erying Powell fluid stagnation point inside the vertical cylinder. Keller box scheme was employed by Prasad et al. [4] to numerically simulate the incompressible second-grade fluid. Numerical results show that the heat transfer rate and velocity gradient decelerates with streamwise coordinate. Alao et al. [5] solved the viscous dissipation model by spectral relaxation method. It was shown that thermal radiation rise resulted in the cooling plate. Fourth-grade thin-film flow was analytically studied by using Adomian decomposition method and Homotopy asymptotic method by Gul et al. [6]. Graphical results were compared and found in good agreement with both of the methods. Visco-elastic fluid flow inside the circular cylinder was investigated by Choudhury and Deka [7]. Meksyn application model of steepest descent method was applied, where it was found that Nusselt number and visco-elastic absolute value reduced the shearing stress. Hayat et al. [8] discussed the heat absorption and heterogeneous reactions due to a rotating disk for the second-grade fluid. Appropriate initial guesses were made to assure the solution convergence. Computed results depicted that visco-elastic parameter and Schmidt number were the increasing functions of concentration profile. Shear stress and velocity profile were evaluated by using the fractional derivative approach in Raza et al. [9] model. The hybrid technique involves semi-analytical fractional-order solutions condensed to the ordinary form. Non-Fourier heat flux and thermal conductivity for temperature-dependent fluid were numerically investigated by Hayat et al. [10]. HAM solution showed that the velocity profile accelerated with visco-elastic and curvature parameter. Moreover, temperature decayed with increasing thermal stratification and Prandtl number. Blood and fluid flow problems without singularity in the fractional domain were analytically studied by Uddin et al. [11], [12], [13]& [14]. Temperature distribution for solid oxide fuel cell studied