This research investigates the unsteady flow of rotating Casson tetra hybrid nanofluid with dual stratification, examining the impact of variable thermal conductivity and thermal stratification on heat transfer. This study shows the unsteady behavior of tetra and ternary hybrid nanofluid flow over two different surfaces, i.e., linear and exponential surfaces. The thermophysical properties of the tetra nanoparticles, i.e., \({\text{Ag}},\;{\text{Cu}},\;{\text{SWCNTs}},\,\,{\text{and}}\,\,{\text{MWCNTs}}\) , comprise in C2H6O2–H2O (50–50%) base fluid. Similarity constraints are applied to convert the flow model equations into a system of coupled ordinary differential equations, which are then solved using MATLAB’s iteration-based bvp4c code. Results show that rotation and stretching significantly affect the velocity and temperature profiles. A comparison with existing literature indicates strong agreement, validating the current findings. Additionally, response surface methodology (RSM) for multiple linear regression is used to statistically analyze the impact of relevant parameters on the drag coefficient and rate of energy transfer of fluid over the linear elongated surface, including 3D plots illustrating these effects. Thermal stratification is utilized in energy-efficient buildings to maintain comfortable temperatures by keeping warmer air near the ceiling and cooler air near the floor. It is also employed in water reservoirs to optimize energy storage and distribution.
