Unsteady flow and entropy analysis of nanofluids inside cubic porous container holding inserted body and wavy bottom wall

•Unsteady flow and entropy analysis of nanofluids within cubic porous container with wavy bottom wall is reported.•3D finite element method with Forchheimer-Brinkman-extended Darcy model is applied to solve the governing equations.•2D and 3D comparisons with the experimental/numerical data are achieved concerning the validity of the existing code.•Impacts of permeability and porosity of porous container with the length of the inner body are established. [Display omitted] Natural convection in a cubical porous container has been controlled by allowing the bottom wall to be of wavy shape and by inserting a conductive square cylinder inside of it. This control process has been investigated transiently in this paper using an alumina-water nanofluid by implementing a numerical method based on the Galerkin weighted residual finite element method. The Darcy-Forchheimer model has been adopted. Isothermal conditions are imposed at the bottom wavy wall (cold) as well as at the vertical walls (hot). Five parameters have been altered to assess the controlling problems. These are the Darcy number, porosity, volume fraction of the nanoparticles, dimension of the central body and the number of undulations of the bottom surface. The results show that the Darcy number exhibits a larger influence on both the Nusselt number and the average temperature than the other parameters, such that when Da is raised from 10−6 to 10−2 the increase in the Nusselt number is about 30.7 at ϕ=0.04, whereas the percentages of increase due to raising ϕ from 0 to 4% is about 11.7, 3.7 and 5.9 at Da=10−6,10−3 and 10−2, respectively. It is also noticed that the entropy generation within the container is mainly due to the thermal irreversibility at lower values of the Darcy number and porosity, and at higher number of undulations and volume fraction of nanoparticles.