<p>The pipes used in heat exchangers are of circular, square, etc., cross-sectional shapes. But the heat transfer depends on the surface area of the source or sink. So the regular cross-sectional shapes are most common, but the heating through a projection into the fluid certainly affects characteristics of the heat and mass transfer. This study investigates the turbulent flow heat and mass transfer characteristics of CuO–water nanofluid in a square channel with an inner triangular groove that is continuously heated. By applying a transverse magnetic field, the governing coupled and nonlinear equations are solved using the Galerkin finite element method across various flow regimes, including laminar, transitional, and turbulent flows. The analysis provides comprehensive insights into the effects of different parameters through stream plots and contour plots. The heat transfer rate, represented by the Nusselt number (Nu), is graphically presented for the heated inner triangular groove and thoroughly discussed. The novel results of the study are that the heat transfer rate increases by 5% with the inclusion of 3% metal in the base fluid. To achieve this, the Reynolds number has to be preferred around 100; also, the heat transfer rate enhances by 15–20% when Nb = Nt = 1.6.</p>