Modeling and optimization of heat transfer in non-Darcy porous media with non-Newtonian Ellis fluid using response surface methodology

A study is conducted to analyze the sequel of non-Darcy porous media and non-Newtonian Ellis fluid over a moving wedge-shaped surface. The Ellis model is a sophisticated generalization of both the Power-law and Bingham models, encapsulating a broader spectrum of the rheological behavior of complex bio-fluids and responsible for the apparent viscosity. The motion of mainstream and wedge is expressed as the power of distance from the leading boundary layer edge. Subsequently, the governing partial differential equations are reduced to a system of non-dimensional ordinary differential equations. The obtained system is then solved by employing numerical simulations that utilize the shooting technique to accomplish accurate solutions. This approach is particularly advantageous for nonlinear problems, where boundary conditions are strenuous to meet by conventional methods. The response surface methodology based on central composite design is used to study the effect of multiple non-dimensional parameters such as Ellis material parameter, Darcy drag, and Forchheimer drag on skin friction coefficient and Nusselt number. The R2 values for skin friction coefficient and Nusselt number are obtained as 99.98% and 96%, and the corresponding adjusted R2 values are 99.97% and 94.58%, respectively. The sensitivity of several parameters is also observed by performing the sensitivity analysis. Furthermore, it is observed that the surface drag and heat transfer are highly sensitive to the Ellis material parameter.