The interaction between magnetic fields and nanofluids represents a fascinating frontier in thermal engineering research. When nanofluids—special fluids containing suspended nanoparticles—are placed within a porous cavity and subjected to an external magnetic field, they exhibit unique heat transfer behaviors that can be precisely controlled. This magnetohydrodynamic (MHD) phenomenon occurs because the electrically conductive particles in the nanofluid respond to magnetic forces, creating the Lorentz effect that significantly alters flow patterns and heat distribution. Understanding these magnetic field effects is critically important for developing advanced cooling systems, microfluidic devices, and renewable energy applications. In our study, we investigate how varying magnetic field strengths affect natural convection within a square porous cavity filled with nanofluids, examining how factors like Rayleigh number, field orientation, and nanoparticle concentration influence overall thermal performance. Based on the reference paper entitled “ MHD Natural Convection Heat Transfer in a Porous Square Cavity Filled by Nanofluids with Viscous Dissipation “, the present CFD simulation is performed.

• Reference [1]: Haritha, C., Balla Chandra Shekar, and Naikoti Kishan. “MHD natural convection heat transfer in a porous square cavity filled by nanofluids with viscous dissipation.”  Nanofluids7.5 (2018): 928-938.
• Reference [2]: Khanafer, Khalil, Kambiz Vafai, and Marilyn Lightstone. “Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids.” International journal of heat and mass transfer19 (2003): 3639-3653.

Reference [3]: Hussain, Sajid, et al. “Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface.” Open Physics 15.1 (2017): 867-876

Figure 1: Physical model and coordinate system [1]

Simulation Process

The primary model and structured mesh production are carried out in the initial step without difficulties. The flow characteristics are calculated by non-dimensional parameters such as Rayleigh number (Ra), magnetic field parameter (M), and Eckert number (Ec).

The MHD module must be activated via the console part in ANSYS Fluent to apply a magnetic field to the cavity. The Porous zone is also considered, addressing the cavity’s porosity specifications. Further, the mixture of nanofluid and base fluid is simulated by considering a single-phase approach.

Post-processing

The velocity streamline visualization reveals a distinct primary vortex formation within the square porous cavity, demonstrating how the magnetic field influences the nanofluid flow pattern. The streamlines show a clockwise circulation with intensified flow along the vertical walls, particularly the right boundary where higher velocity gradients (yellow-green regions) are observed. This asymmetric flow distribution results from the combined effects of buoyancy forces and magnetic damping, with the streamlines becoming more tightly packed in regions where the Lorentz force interacts with the thermal buoyancy. The temperature contour plot displays a diagonal stratification pattern from the heated left wall (292.9K, red) to the cooled right wall (283.2K, blue), with isotherms bending toward the flow direction. This characteristic distortion of the temperature field directly correlates with the strength of the magnetic field and the resulting suppression of convective currents.

Figure 2: Temperature patter under the influence of magnetic field

The relationship between Rayleigh number and heat transfer performance is quantified in the table below, showing a clear trend of increasing Nusselt number with higher Rayleigh values:

This data confirms that heat transfer enhancement becomes more pronounced at higher Ra values, with the Nu value increasing approximately 724% from Ra=10 to Ra=10000, despite the consistent thermal conductivity ratio (k_nf/k_f=1.33). This demonstrates how the magnetic field produces increasingly significant flow modifications as thermal buoyancy strengthens, creating complex interactions between the magnetohydrodynamic forces and natural convection within the porous medium.

Figure 3: Magnetic field effect in the cavity