Sensitivity along with statistical response for optimizing shear and heat transfer rate on the flow over power-law deformable plate considering bi-hybrid nanofluid

The heat transfer efficiency of nanofluids is more effective than the conventional coolants and they are being evaluated for the automotive cooling systems. Improved engine performance and fuel economy may result from this. However, the use of nanofluids in hyperthermia therapy, a medical intervention in which specific tissues are heated to high temperatures, the flow of bi-hybrid nano liquid over a deformable surface plays crucial role. Based on several needs in different sectors the present study briefly describes the flow proposed liquid over a three-dimensional deformable absorbent surface. The impact of magnetization along with thermal radiation enriches the flow profiles significantly. Suitable similarity rules are adopted for the dimensional governing equation to re-formulate them into non-dimensional form. The system of designed model problem is handled numerically by means of “ Runge-Kutta fourth-order ” technique. The novelty of the study arises due to the use of robust statistical approach i.e. “ Response Surface Methodology (RSM)” to optimize both shear and heat transfer rate for several factors. For the validation of the result a hypothetical test is proposed utilizing analysis of variance (ANOVA) and then parametric optimization is proposed employing sensitivity analysis for the response of both the shear and heat transfer rate. The study reveals that magnetization and particle concentration remarkbaly influence shear rate and heat transportation, where higher nanoparticle aggregation reduces shear but augments thermal transport, while increased thermal radiation improves the Nusselt number and overall heat transfer efficiency. Statistical validation through residual plots confirms the model's accuracy, ensuring reliable predictions for shear and heat transfer behavior.