Hybrid nanofluids, which are used in nanotechnology, are advanced fluid classes with enriched thermal properties that produce superior outcomes than nanofluids. There are too many applications of hybrid nanofluids in engineering cosmetics, the automotive industry, the home industry, cancer treatment, textiles, paper plastics, paints, and soaps. The purpose of this study is to investigate the heat transfer rate of magnetohydrodynamic flow of Casson hybrid non‐Newtonian nanofluid across an enlarging surface. The current work focuses on magnetohydrodynamic hybrid nanoliquid flow across an extending 3‐D sheet. Additionally, zero mass flux and an adequate convective heating procedure are used as boundary conditions in this investigation. Blood serves as the base fluid, into which copper and alumina nanoparticles are dissolved to form a hybrid nanofluid. Adjusting the applicable similarity transformation, the present modeled equations are converted into dimensionless form. The Homotopy analysis approach (HAM) computes the resulting systems and illustrates them graphically to explain the flow behavior at the extending electrically conducting surface. Additionally, for changes in the non‐dimensional physical constraint values, the variations in physical quantities such as the skin friction, temperature, Nusselt number and velocity profiles are explained. The results of the current investigation demonstrated that a magnetic field and a non‐Newtonian parameter reduce the hybrid nanoliquid's velocity. The temperature profile goes up with thermophoresis and Brownian motion. The x−$x - $ component of velocity is found to fall as the stretching ratio parameter rises, while the component of velocity in the y−$y - $ direction experiences the opposite impact. When the parameters of a chemical reaction are adjusted upwards, the concentration profile deteriorates. It is originated that the rate at which heat is transferred by hybrid nanofluids is significantly more progressive than that of nanofluids. [ABSTRACT FROM AUTHOR]