Second law analysis of MHD mixed convection heat transfer in a vented irregular cavity filled with Ag–MgO/water hybrid nanofluid Mahdi Benzema 1 • Youb Khaled Benkahla 1 • Nabila Labsi 1 • Seif-Eddine Ouyahia 1 • Mohammed El Ganaoui 2 Received: 26 September 2018 / Accepted: 8 January 2019 / Published online: 22 January 2019 Ó Akade ´miai Kiado ´, Budapest, Hungary 2019 Abstract The present paper investigates numerically the effect of an external magnetic field on heat transfer and entropy generation of Ag–MgO (50:50 vol%)/water hybrid nanofluid flow in a partially heated irregular ventilated cavity. A finite-volume FORTRAN code has been written to solve the governing partial differential equations. New empirical correlations specifically dedicated to predict the dynamic viscosity and the thermal conductivity of the considered hybrid nanofluid were employed. After validation of model, the analysis has been done for a wide range of Reynolds number (10 ^ Re ^ 600), Hartmann number (0 ^ Ha ^ 80) and total nanoparticle volume fraction (0 ^ u ^ 0.02). The results are presented in terms of streamlines, isotherms and isentropic lines as well as the average Nusselt number (Nu m ), the average entropy generation (S gen , m ) and the Bejan number (Be avg ). The criterion n = S gen , m /Nu m is adopted to discuss the thermal performances of the system. The results reveal that the intensification of the magnetic field tends to attenuate the heat transfer convection and to reduce the thickness of the thermal boundary layer, close to the active walls. Globally, adding nanoparticles to the base fluid improves the heat transfer but increases the total entropy generation. Keywords Irregular ventilated cavity  Entropy generation  Magnetic field  Mixed convection  Ag–MgO/water hybrid nanofluid List of symbols B 0 Magnetic induction (T) Be avg Average Bejan number c p Specific heat capacity (J kg -1 K -1 ) d Dimensional length of the heat source (m) D Dimensionless distance of heat source from the entrance e 1 /W e 1 Distance of heat source from the entrance (m) e 2 Distance of heat source from the right vertical wall (m) Ec Eckert number g Gravitational acceleration (m s -2 ) Gr Grashof number h Opening width (m) H Height of the cavity (m) Ha Hartmann number k Thermal conductivity (W m -1 K -1 ) Nu l Local Nusselt number Nu m Average Nusselt number Nu * Normalized Nusselt number p Pressure (Pa) P Dimensionless pressure Pr Prandtl number Re Reynolds number Ri Richardson number S gen 0 Dimensional local entropy generation (W K -1 m -3 ) S gen Dimensionless local entropy generation S avg,h Dimensionless average entropy generation due to heat transfer & Mahdi Benzema mehdi_benzema@yahoo.fr Youb Khaled Benkahla youbenkahla@yahoo.fr Nabila Labsi nabilalabsi@yahoo.fr Seif-Eddine Ouyahia seifeddine.ouyahia@yahoo.fr Mohammed El Ganaoui mohammed.el-ganaoui@univ-lorraine.fr 1 Laboratory of Transport Phenomena, Faculty of Mechanical and Process Engineering, USTHB, BP 32, El-Alia Bab- Ezzouar, 16111 Algiers, Algeria 2 LERMAB, IUT Longwy, Universite ´ de Lorraine, 54400 Cosnes et Romain, France 123 Journal of Thermal Analysis and Calorimetry (2019) 137:1113–1132 https://doi.org/10.1007/s10973-019-08017-x