Thermal dynamics in electrically conducting tangent hyperbolic nanofluid flow: Hybrid-empirical modelling approach using RSM

The dynamics of nanofluids with electrical conductivity are the focus of the advanced field of electrically conducting nanofluid flow, which lies at the intersection of fluid mechanics and heat transfer. When exposed to electric fields, these nanofluids, which are composed of nanoparticles suspended in base fluids, display distinctive behaviors. Their flow is influenced by variables such as the applied electric field, size, shape, concentration of nanoparticles, and properties of the base fluid. Joule heating, electrokinetic effects, and electrophoresis are important processes in these flows. There is great promise for improved heat transfer systems, microfluidics, energy conversion devices, and biomedical technologies in the field of electrically conducting nanofluid flow research. Nonetheless, there are still issues to be resolved, like preserving the stability of nanoparticle suspension and comprehending the intricate relationships between fluid, particles, and fields. Sensitivity analysis of different input parameters plays a very important role in fluid mechanics problems. In this work, the authors aim to do a sensitivity analysis of different input parameters for magnetohydrodynamics Tangent hyperbolic nano fluid. To complete this task, we have adopted the non-linear partial differential equations, and then numerical values of transformed ordinary differential equations are calculated by using MATALB built-in software bvp4c. Performance evaluation is conducted by employing sensitivity analysis. Firstly, an empirical relation for output responses, that is, skin friction, Nusselt number $$( {N{u}_x} )$$, and Sherwood number $$(S{h}_x$$) using response surface methodology. The best fitted model is determined with the help of Analysis of Variance table. The results show that coefficient of determination for skinfriction coefficient $$(C{f}_x)$$, $$N{u}_x$$, and $$S{h}_x$$ are 100%, 99.99%, and 97.73% respectively. This means that we have obtained best fitted empirical relations. The results of sensitivity analysis disclosed that $$C{f}_x$$ is most sensitive to Weissenberg number (We). Both the $$N{u}_x$$ and $$S{h}_x$$ are most sensitive to thermophoresis parameter (Nt).