International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:20 No:01 98 I J E N S IJENS © February 2020 IJENS - IJMME - 4 3 34 - 201601 MHD Mixed Convection in Square Enclosure Filled with non-Newtonian Nanofluid with Semicircular- Corrugated Bottom Wall 1* Farooq H. Ali , 1 Hameed K. Hamzah , 1 Ahmed , Saba Y. 3 , Emad D. Aboud 2 , Hayder K. Rashid 1 Hussein M. Jassim Iraq. – Hilla – Babylon City - University of Babylon - Mechanical Engineering Department - College of Engineering 1 Iraq. – lla Hi – Babylon City - University of Babylon - Ceramic Engineering Department - College of Material Engineering 2 Iraq. – Hilla – Babylon City - University of Babylon - Automobile Engineering Department - Musayab - College of Engineering/ Al 3 * Corresponding author: Farooq Hassan Ali [E-mail addresses:farooq_hassan77@yahoo.com] Abstract-- Many researchers have been tried to discuss the parameters that used to enhance the heat transfer rate within different shapes of enclosure that exerted by an external magnetic field with a lid driven. So, in this research, combined effect of non-Newtonian fluid that contains Nano- particles Al2O3 within new square enclosure heat geometry shapes (four cases that will be elaborated in this research: case I :small wavy notched shape, case II: small semicircle notched, case III: bigger semicircle notched and the last one case IV has a large wavy notched) have been solved numerically by finite element method that base on the Galerkin weighted residual formulation where used in COMSOL Multiphasic under a relevant dimensionless parameters: 0.001  Ri  1, 0  Ha  60, solid volume fraction 0    0.1, power law index 0.2  n  1.4, Grashof number Gr=100. However, the innovation of the boundary conditions are a new heating geometry shape wall has an alternating effect with the variation of the power index parameters and Richardson number. It can be shown that case II of small circular notched is the best cases that justified of improving forced and mixed convection heat transfer. The magnetic field strength interplay negative effect on improving the forced convection flow within the enclosure. The average Nusselt number increases by evolution of the power law index value while independent on the shape geometry of the heating cavity wall. Index Term-- MHD, Square enclosure, Non-Newtonian, nano-fluid, semicircular corrugated hot wal 1. INTRODUCTION There are many engineering applications of enclosure with lid driven at different wall heating geometrical shapes with presence of external magnetic field. The effect of magnetic field is to produce a force that will counteract the fluid flow direction which induced by buoyancy force. The mechanistic of this type of forces due to the applied magnetic field reported in details by many previous researchers. However, the magnetic field strength plays an important role in many engineering requests. The mechanism of external magnetic field applied on electrically conducting fluid called Magneto- hydrodynamics (MHD). Besides, the working fluid and nanofluid particle properties are very important to restrict the convection flow. The mutually effect between the power index for dilatant fluid and volume fraction of nanoparticles on convective heat transport with presence magnetic field can be detected in many applications. These applications associated with the alternating effect of different cavity conditions, have typical in many thermal systems, electronic devices, MHD flow meter, plasma physics and geophysics. On the other hand, fluid type and geometry shape have a relevant interplay effect on flow pattern. These modes of flow exerted on the effect of heat transfer rate that occur in many actual applications like chemical processing. However, all applications need effective cooling and heat dissipation systems for all its work on time. Moreover, the turbulent flow modes will meliorates heat transfer rate. For this reason, one or more wall will move at suitable velocity to rising turbulent mode influence on the effectiveness of heat transfer rate. Hence, enormous papers illustrated and propose new enclosure conditions with lid driven dominant flush situation to get more superiority of convection. Marchi et al., 2009 [1] used the finite volume method to solve flow problems in square enclosure. Where, all parameters changed by keeping the lid velocity constant. Which presented second-order accuracy in the approximation solution to solve the governing equations with 42 variables numerically. However, the numerical solution was used multiple Richardson extrapolations to degrading the discretization error until the achieved machine round- off error. On the other hand, Al-Salem et. al , 2011 [2] investigated a numerical technique depends on the finite volume method to study the MHD mixed convection cavity. The model was adiabatic in vertical walls as well as fixed temperature at the sliding top. Moreover, the heat source of bottom wall modeled as linearly source. This study used to reveals the effect of different lid movement directions on the heat transfer enhancement. However, many parameters were merged together to get new evolve in mixed convection behavior such as: Reynolds number and Grashof number that illustrated by stream function and isotherm contour. In addition, Billah et. Al, 2011 [3] solved the lid driven square cavity problem numerically