Response surface methodology and sensitive analysis for optimizing heat transfer rate on the 3D hybrid nanofluid flow through permeable stretching surface

Abstract

The current problem analyses the three-dimensional flow of a water-based hybrid nanofluid through an expanding/contracting surface embedded within a porous medium. The significant contribution of electrically conducting fluid is due to the interaction of an applied magnetic field in association with velocity slip and convective heat transfer condition enriches the study. The proposed dimensional form of the governing equations gets converted into its corresponding non-dimensional form in association with the various parameters obtained by employing the suitable similarity rules. Further, traditional numerical method such as traditional Runge–Kutta–Fehlberg with shooting technique is adopted to solve these transformed equations. The parametric behaviour, most importantly the particle concentrations of the nanoparticles formulating the thermophysical properties such as fluid viscosity and thermal conductivity, is displayed using graphs, and further, the simulated rate coefficients are also presented through tables. The novelty of the current research is reflected by the use of optimized technique, i.e. response surface methodology, for the response of heat transfer rate. Various factors, i.e. particle concentration, magnetic parameter, and the heat source parameter, are utilized for the regression model. Further, a statistical approach of F-value and p-value is obtained to predict the model's validity and a good fit. For the performance of sensitivity analysis, one of the important statistical approaches, i.e. analysis of variance, is utilized with the help of the Taguchi method.

Appendix

$u,v,z$	Velocity components along $x, \, y, \, z$ -axes
$M$	Magnetic parameter
Da	Darcy number
Pr	Prandtl number
$Q$	Heat source parameter
Bi	Biot number
$k$	Thermal conductivity
${\rm Cf}_{\rm x}$	Skin friction (along $x$ axis)
${\rm Cf}_{\rm y}$	Skin friction (along $y$ axis)
${\rm Nu}_{\rm x}$	Nusselt number
$q_{\rm w}$	Heat flux
$T$	Temperature
Greek symbols
$\tau_{\rm wx}$	Shear stress along $x$ direction
$\tau_{\rm wy}$	Shear stress along $y$ direction
$\beta$	Velocity slip parameter
$\mu$	Dynamic viscosity
$\rho$	Density
$\rho c_{\rm p}$	Heat capacity
$\phi$	Total volume concentration of Cu and Al2O3
Subscripts
f	Base fluid
nf	Nanofluid
hnf	Hybrid nanofluid
s	Solid particle