## 1 Introduction
However, intensification of viscous dissipation has a negative effect in the heat-transfer rate. [PERSON] (2018) studied the free convection heat transfer in rectangular enclosure. The obtained results showed that the rate of heat transfer increased only at low Rayleigh numbers. This contradicting behavior has not been studied with adequate consideration and is one of the objectives of the present work. Additionally, intensive research is conducted in order to comprehend the underlying physics of nanofluids, particularly the phenomena related to their increased thermal conductivity, compared to the thermal conductivity of the base fluid. Seven main mechanisms have been proposed toward a more comprehensive understanding of their physical properties, and, among them, nanoparticle microrotation seems to play a crucial role ([PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018). A mathematical model that takes into consideration the microrotation has been used in the study of [PERSON] and [PERSON] [PERSON] and [PERSON] (2018). Therein, authors applied the micropolar flow theory to model the nanofluid. They used an experimentally obtained formula for the thermal conductivity and the dynamic viscosity of the nanofluids, and compared the numerical results with experimental data, with the accuracy being excellent. Considerable effort has been directed toward heat-transfer studies for natural convection in porous media ([PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018). [PERSON] (2018) studied the heat transfer with natural convection of an inclined partially cooled rectangular enclosure filled with a porous medium. Natural convection heat transfer in a cavity saturated with porous media in the presence of magnetic fields is a new branch of thermo-fluid mechanics. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) studied MHD natural convective heat transfer in a rectangular enclosure filled with a porous medium, considering Joule and viscous heating effects. In the present study, the micropolar flow theory is utilized to study the natural convection of a micropolar nanofluid in a square cavity filled with a porous medium and subjected to a magnetic field. Given its practical interest in the engineering and medical fields, including blood flow and purification [24], exportation of geothermal energy, purifications of metals, and solar heating systems [33], the topic needs to be further explored. The work on natural convection in a square cavity filled by a micropolar nanofluid [25] is extended here to account for the applied magnetic field in the presence of a porous medium. We developed a robust, efficient, and accurate meshless strong form collocation solver to numerically solve the governing flow equations. The latter are a set of nonlinear, fully coupled partial differential equations (PDEs), which express the conservation of mass, energy, linear momentum, and angular momentum, in addition to the magnetic induction. In the present study, the velocity-vorticity formulation is used, in order to avoid the problem of determining the pressure boundary conditions explicitly. To this end, a sophisticated five-step algorithm is implemented numerically. The criterion for terminating the algorithm is the normalized root-mean-square error of all field variables becoming less that a predefined value. An advanced Discretization Corrected Particle Strength Exchange (DC PSE) interpolation method is reformulated to calculate the spatial derivatives up to the second order in an Eulerian framework. The physical aim of this study is to investigate the effect of the magnetic field magnitude and the intensity of the flow field, as well as the volume fraction of the nanoparticles and the permeability of the medium, on the convective heat transfer of an Al\({}_{2}\)O\({}_{3}\)/water nanofluid.