## 1 Introduction  
Magnetohydrodynamics (MHD) focuses on electrically conducting fluids, which move under the influence of a magnetic field. The induced electrical current interacts with the magnetic field to produce a body force acting on the fluid. The interaction between the flow field (fluid velocity) and the externally applied magnetic field gives rise to a magnetic (induced) field inside the fluid. The MHD-oriented research field has become an important branch of fluid dynamics. The study of MHD flow applies to many industrial and engineering systems, such as nuclear reactors, heat exchangers [1], home ventilation systems, cooling of electronic equipment, solar energy collectors, nuclear reactors, chemical processing equipment, geothermal reservoirs, magnetic behavior of plasmas in fusion reactors, petroleum industries [2], boundary layer control in aerodynamics, crystal growth, and ship propulsion [3], to name a few [4, 5]. Furthermore, MHD has been studied by many researchers, and considerable effort has been directed toward MHD flow combined with heat transfer. In fact, many authors have studied the effects of magnetic field on mixed, natural, and forced convective heat-transfer problems. [PERSON] and [PERSON] [PERSON] and [PERSON] (2016) studied the effect of a magnetic field on an electrically conducted viscoelastic fluid, reporting on the flow decrease through the increase in the magnetic field strength. [PERSON] _et al._ (2017) studied the effects of natural convection and applied magnetic field on the Couette flow of an electrically conducting fluid between two parallel plates. [PERSON] and [PERSON] (2018) reported on the thermal radiation heat transfer effects on the MHD-Rayleigh flow. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) studied the magneto-convection in a lead-lithium mixture, showing that a magnetic field, directed perpendicular to the temperature gradient, produced a complex three-dimensional flow pattern. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) studied the Rayleigh-Benard convection, subjected to various magnetic fields, over a range of Rayleigh and Hartmann numbers, and reported on the impact of the orientation and distribution of externally applied magnetic fields on the heat transfer and the flow regime (convective structures) in thermal convection of electrically conductive fluids. They studied the flow laminarization over specific range of Hartmann numbers. Through laminarization, it is possible to control thermal convection and associated heat transfer. Over the last few decades, there has been a growing interest in the heat-transfer properties of nanofluids. Nanofluids are engineered colloids, i.e., a mixture of a base fluid (usually water, oil, or glycerin) and nanosized solid particles ([PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018). Nanofluids exhibit novel properties that make them potentially useful in many applications in heat transfer, including fuel cells, pharmaceutical processes, engine cooling/vehicle heating, and heat exchangers. They possess increased thermal conductivity and heat-transfer coefficients, compared to the base fluid. However, a critical parameter for their suitability in many applications is their rheological behavior. In numerous computational studies, nanofluids are modeled as single-phase fluids, having altered physical properties compared to the ones of the base fluid ([PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018). [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) studied the combined effect of the magnetic field and the nanofluids' behavior on natural convection within a square cavity. They reported that the presence of the nanoparticles has an adverse effect on the heat transfer at a high-volume fraction of the nanoparticles. [PERSON] (2018) studied the effects of viscous dissipation. Their results show that the increase of the volume fraction of nanoparticles enhances the heat-transfer rate.