This research examines the radiative flow and thermal characteristics of \(H_{2} O - GO - Fe_{2} O_{3}\) and \(H_{2} O - GO\) on an inclined spinning disk with a non-uniform heat source, tackling the essential issue of enhancing heat transfer efficiency in thermal systems. The emphasis lies in comprehending the influence of critical parameters, including normalized thickness, magnetic field, thermal radiation, temperature-dependent heat source, and exponential space-dependent heat source on the velocity and temperature profiles. Utilizing similarity transformations, the flow described by partial differential equations is simplified into ordinary differential equations, from which numerical solutions are derived through the Runge–Kutta method in conjunction with the shooting technique. Advanced optimization techniques, specifically Response Surface Methodology (RSM) with a face-centred approach and sensitivity analysis are utilized to assess the response function and factors significance on the rate of change in the response function. The results reveal that both axial and tangential velocities intensify as the normalized thickness parameter increases. The thermal boundary layer thickness exhibits growth under the influence of temperature-dependent and spatially varying heat source parameters. Heat transfer near the disk surface is modulated by the normalized thickness parameter. Sensitivity analysis demonstrates that at lower levels of the internal heat source, the heat transfer rate is a maximum of 5.355663 towards volume fraction and notably minimum of − 0.846828 towards heat source alongside an increased concentration of nanoparticles. This study advances prior research through a comparative analysis of RSM and sensitivity analysis, yielding quantitative results that enhance the optimization of heat transfer in practical applications.
