Three-dimensional flow of nanofluid through a vertical channel considering KKL model: Hydrothermal analysis via response surface methodology

Background: The analysis of heat transfer portrays play important role in various industries for production processes particularly acting as a coolant in electronic devices. Based upon the above-mentioned fact, an electrically conducting free convection of three-dimensional nanofluid flow through a vertical parallel stretching sheet embedding within a permeable medium is analyzed. In a novel approach, the effective viscosity, as well as conductivity, is incorporated combined with Brownian diffusivity and conductivity based upon the KooKlenstreuer (KKL) model. To enrich the flow phenomena dissipative heat and thermal radiation may be comprised in the energy transfer equation. Methods: The parametric analysis of each constraint is briefly presented using the numerical treatment of the "Runge-Kutta fourth-order" technique following the similarity rules that help in transforming the governing equations in the dimensionless form. Further, a robust statistical technique likely RSM is utilized to optimize the response of heat transportation rate for a few of the characterizing factors and to validate a hypothetical test obtained by means of analysis of variance. Significant findings: The results show that increasing coupling constant for the involvement of dissipative heat and thermal radiation portrays a substantial enhancement in the thermal bounding surface thickness of the nanofluid moreover, inclusion of KKL model conductivity enhances the thermal conductivity of nanoliquid that favors in augmenting the fluid temperature. However, the axial velocity attenuates for the less pronounced inertia force in comparison to the viscous force but reverse impact is rendered for the transverse velocity. In addition, statistical approach such as RSM and the validation used by ANOVA test presents an optimized heat transportation rate for the validation of the several factors.