In the present problem, two-phase mixed convection of a non-Newtonian nanofluid in a porous H-shaped cavity is studied. Inside the enclosure there are four rotating cylinders, using the Boussinesq approximation, mixed convection is created. Nanofluid includes H2O + 0.5% CMC and copper oxide nanoparticles. The mixture model was used to model physical phenomena. Different aspect ratios were used in order to achieve the best heat transfer rate. The Darcy and Richardson numbers ranges are 10(-4) <= Da <= 10(-2) and 1 <= Ri <= 100 respectively. Also, the aspect ratio and dimensionless angular velocities of cylinders ranges are 1.4 <= AR <= 1.6 and -10 <= Omega <= 10 respectively. Streamlines and isotherm-lines contours have been obtained for the variation of Darcy and Richardson numbers, aspect ratio and angular velocity. The heat transfer rates have been obtained for various aspect ratios, Darcy and Richardson numbers, and the direction of the cylinder's rotation, and are compared with each other. The results show that the direction of cylinders rotation influences the strength and extent of the generation vortices. Also, the use of porous material in high permeability can be a good alternative to lowering the angular velocity of the cylinders and ultimately reducing the need for less energy. (C) 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.