<p>The on-going analysis considers the consequences of multiple slips effects on the tri-hybrid nanofluid movement by the inclusion of TiO₂, Cu and Al₂O₃ in the base liquid water across an enlarging plane. The Maxwell model velocity slip with the Smoluchowski slip temperature is examined in conjunction with thermal radiation, and a heat sink is implemented in this study. The mathematical framework is constructed according to the stated assumptions, which are nonlinear and a suitable transformation is required to transform these into dimensionless governing equations for both the velocity and temperature. Further, these systems of equations are tackled numerically; adopting a Runge-Kutta of order four assisted shooting technique. The authentication of the outcome, combined with the convergence analysis of the methodology, is showcased for certain values of the factors used to evaluate the heat efficiency rate, and the physical interpretation of the allied parameters, equipped with the flow profile, is graphically presented. The assessment of tri-hybrid nanofluid is vital for the heat transport properties assigned in various sectors such as industries, bio-medical, engineering, etc. In particular, the cooling solutions for electronics, the cancer therapy and waste heat energy recovery, etc., the contribution of tri-hybrid nanofluid is essential. A rigorous statistical approach, such as “response surface methodology (RSM)” adopting “central composite design (CCD)” is utilized for optimizing heat transfer rate for the inclusion of distinct factors, and “analysis of variance (ANOVA)” is used for the validation of the result through testing. The observation reveals that the fluid velocity is controlled by the enhanced velocity slip. Further, the radiative heat presented by the inclusion of thermal radiation encourages the heat transport properties. Again, the correlation between the factors and the response of the Nusselt number with the value of R lead to a best fit quadratic model obtained statistically.</p>