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The important feature of the current work is to consider the pressure variation, heat transport, and friction drag in the hydromagnetic radiative two-dimensional flow of a hybrid nanofluid depending on the viscous dissipation and Joule heating across a curved surface. The curved surface has been considered with the binary heating process called as prescribed heat flux and surface temperature. The basic partial differential equation (PDEs) has been converted into the non-dimensional ordinary differential equations (ODEs) by applying some specified dimensionless transformations. The bvp4c built-in package in MATLAB has been considered to find the numerical solution of the consequential equations. The graphical results have been plotted in terms of pressure, friction drag, velocity, temperature, and heat transport. Several important results have also been plotted for the plan level surface $$($$ ( The condition of $$K\to \infty )$$ K → ∞ ) . It is found that the heat transport rate respectively reduces and enhances with the enhancement of radiation parameter and Hartmann number as well as the friction drag is enhancing with the high-volume fraction of nanoparticles and Hartmann number. Moreover, enhancing curvature parameter, enhances the friction drag and declines the heat transport rate. The current work renders uncountable applications in several engineering and industrial systems like electronic bulbs, electric ovens, geysers, soil pollution, electric kettle, fibrous insulation, etc. Moreover, the heating as well as the cooling systems of electrical, digital, and industrial instruments, are controlled by the heat transport in fluids. Thus, it is important to use such flows in these types of instruments.