Conjugate magnetohydrodynamic free convection of internal heat-producing nanofluid in a corrugated square chamber containing a heat-producing solid block

• Conjugate MHD free convection and entropy generation in a corrugated enclosure. • Heat is generated internally in a copper block and Cu–EG nanofluid. • Removing magnetism boosts heat transfer with lowest thermal performance cost. • Low internal heat generation in nanofluid improves convective heat performance. • High wall amplitude and low frequency maximize convective heat transfer efficiency. This study examines entropy dissipation and thermal transport in a square-shaped enclosure with wavy side walls occupied by heat-generating ethylene glycol-based copper nanofluid, subject to magnetohydrodynamic effects. A copper-based heat-producing solid block is centrally placed at the bottom wall, acting as the system’s primary heat source. The numerical model is formulated based on the governing Navier-Stokes and heat transport equations for the nanofluid domain and the heat conduction equation for the solid domain. These equations are simultaneously solved utilizing the Galerkin finite element method. A comprehensive parametric analysis is conducted to evaluate the influences of Rayleigh number (10 4 ≤ Ra ≤ 10 7 ), Hartmann number (0 ≤ Ha ≤ 20), internal heat production parameter of the nanofluid (0.10 ≤ Δ nf ≤ 0.50), dimensionless corrugation amplitude (0.01 ≤ A ≤ 0.05), corrugation frequency (2.5 ≤ f ≤ 4.5) and solid block geometries on the thermal behavior and fluid movement inside the enclosure. The simultaneous investigation of various shapes of a heat-generating solid block immersed in a heat-generating nanofluid under magnetic influence inside a corrugated square cavity represents the primary novel contribution of this study to the field of thermo-fluidic convection. The results indicate a 40% enhancement in the heat transfer rate when a square-shaped solid block is combined with increased corrugation amplitude and reduced corrugation frequency, without a magnetic field and at a minimal nanofluid internal heat generation coefficient.