Impacts of magnetic field and non-homogeneous nanofluid model on convective heat transfer and entropy generation in a cavity with heated trapezoidal body A. I. Alsabery 1,2 • R. Mohebbi 3 • A. J. Chamkha 4,5 • I. Hashim 2 Received: 5 January 2019 / Accepted: 8 April 2019 Ó Akade ´miai Kiado ´, Budapest, Hungary 2019 Abstract A numerical study is made on the entropy generation and magnetohydrodynamics natural convection of Al 2 O 3 -water non- homogeneous nanofluid inside a square enclosure equipped with a heated trapezoidal body. The Galerkin weighted residual finite element method is applied to solve the dimensionless governing equations within the utilized computational domain along with the algorithm of Newton–Raphson iteration that is used for simplifying the nonlinear terms in the equations. The characteristics of fluid flow fields, temperature distributions and entropy generation are studied for an enormous range of the Rayleigh number ð10 3  Ra  10 6 Þ, volume fraction of nanoparticles (0  /  0:04), Hartmann number ð0  Ha  50Þ, thermal conductivity of the trapezoidal solid body (k w ¼ 0:5, 0.76, 1.95, 7 and 16) and the height of the trapezoidal solid body (0:15  D  0:45). It is shown that the streamlines pattern is more sensitive to the increase in the Hartmann number in comparison with the augmentation of the volume fraction of nanoparticles. Also, for a more thermodynamically optimized system, the higher Hartmann number at a higher solid volume fraction of nanofluid is recommended as they show less entropy generation. Keywords Non-homogeneous nanofluid model  Magnetic field  Entropy generation  Solid trapezoidal body  Thermophoresis effects  Brownian motion List of symbols B Applied magnetic field B Magnitude of magnetic field Be Bejan number C p Specific heat capacity d f Diameter of the base fluid molecule d p Diameter of the nanoparticle D Dimensionless length of the trapezoidal solid body, D ¼ d=L D B Brownian diffusion coefficient D B0 Reference Brownian diffusion coefficient D T Thermophoretic diffusivity coefficient D T0 Reference thermophoretic diffusion coefficient g Acceleration of the gravity GEG Dimensionless global entropy generation H Dimensionless width of the trapezoidal solid body, H ¼ h=L Ha Hartmann number k Thermal conductivity K r Square wall to nanofluid thermal conductivity ratio, K r ¼ k w =k nf L Width and height of enclosure Le Lewis number & A. I. Alsabery ammar_e_2011@yahoo.com 1 Refrigeration and Air-conditioning Technical Engineering Department, College of Technical Engineering, The Islamic University, Najaf, Iraq 2 School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia 3 School of Engineering, Damghan University, P.O. Box: 3671641167, Damghan, Iran 4 Department of Mechanical Engineering, Prince Sultan Endowment for Energy and the Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia 5 RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box 10021, Ras Al Khaimah, United Arab Emirates 123 Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-019-08249-x