## 1 Introduction  
The inherently moderate thermal conductivity of regular fluids, such as water, oil, etc., causes a deterioration in the performance of engineering systems. To overcome this barrier, researchers add metallic nanoscale particles--owing to the fact that they have a higher thermal conductivity than regular fluids--to these fluids. This combination is called a nanofluid. Nanofluids have higher thermal conductivity in comparison with regular fluids. Most recently, a vast number of studies have been carried out concerning heat transfer and the flow of nanofluids [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. Entropy generation on a magnetohydrodynamic nanofluid toward a stagnation-point flow over a penetrable expanding wall was investigated by [PERSON] and [PERSON] [1]. They observed the increasing velocity of the fluid due to the pronounced effects of the magnetic field and the porosity parameter. Moreover, they noted that the entropy generation number increased with increasing Brinkman number and Reynolds number. Entropy generation for a non-Newtonian Eyring-Powell nanofluid through a penetrable expanding wall was analyzed by [PERSON] et al. [2]. They deduced that the velocity profile rises owing to the high impact of the suction parameter. Moreover, they concluded that Brownian motion and thermophoresisraised the temperature profile remarkably. The impacts of the flow of an electromagnetohydrodynamic nanofluid over a Riga sheet were analyzed by [PERSON] et al. [3]. The convective Poiseuille boundary-layer flow of an ethylene glycol (C\({}_{2}\)H\({}_{6}\)O\({}_{2}\))-based nanofluid with suspended aluminum oxide (Al\({}_{2}\)O\({}_{3}\)) nanoparticles through a porous wavy channel was investigated by [PERSON] et al. [4]. In the presence of thermal radiation, the heat transfer and flow of a magnetohydrodynamic Go-water nanofluid between parallel surfaces were examined by [PERSON] et al. [5]. They determined that the Nusselt number and temperature profile both increased as the radiation parameter decreased and the solid volume fraction increased. [PERSON] and [PERSON] [6] examined nanofluid flow, mass, and heat transfer between non-parallel surfaces subject to a magnetic field. They concluded that concentration and temperature profiles along with the Nusselt number go up as the Schmidt number rises.  
Recently, several researchers have considered the natural convection flow of a pure fluid and nanofluid in enclosures [25; 26; 27; 28; 29; 30; 31] due to the extensive scientific and engineering applications. Heat transfer and fluid flow in a wavy enclosure subject to a porous medium and nanoparticles were explored by [PERSON] et al. [25]. They illustrated that an increasing Rayleigh number causes a secondary vortex and temperature stratification core in the left bottom corner and center of the cavity, respectively. In a wavy enclosure containing nanoparticles and a porous medium, natural convection and the influence of thermal dispersion was studied by [PERSON] et al. [26]. They determined that the heat transfer was enhanced with the Rayleigh number, undulation number, and dispersion parameter. [PERSON] et al. [27] analyzed entropy generation and nanofluid flow in an enclosure. The outcomes indicate that a higher wavenumber leads to greater mean entropy generation. Numerical and experimental investigations on natural convection in a cavity were conducted by [PERSON] et al. [28].  
This concise review illustrates that it is still worthwhile to allocate more effort to the study of natural convection in enclosures using a combination of metallic nanoscale particles and normal fluids. Therefore, this work analyzed magnetohydrodynamic nanofluid natural convection in an enclosure and the impact of the shape factor of the nanoparticles and thermal radiation using control-volume finite element method (CVFEM) and also obtained a correlation with the average Nusselt number. The flow and heat transfer effects of diverse control parameters were explored.