Investigation of Magnetized Casson Nanofluid Flow along Wedge: Gaussian Process Regression

Abstract

An unsteady two-dimensional magnetized Casson nanofluid flow model is constructed over a wedge under the effect of thermal radiation and chemical reaction. The multiple slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. This study investigates the application of soft computing techniques to address the challenges posed by the complexity of problem modeling and numerical methods. Traditional approaches incorporating various model factors may struggle to provide accurate solutions. To resolve this issue, Gaussian process regression (GPR) is employed to predict the solution of the proposed flow model. With the help of the numerical shooting method together with Runge–Kutta–Fehlberg fourth-fifth-order (RKF-45) reference data, the GPR model is trained. The numerical simulation illustrated that the Casson fluid parameter $\left(\beta \right)$ and the unsteadiness parameter $\left(S\right)$ strengthen the friction factor, and the heat transfer rate is enhanced as the radiation parameter $\left(R_d\right)$ becomes larger. In addition, the Biot numbers $\left(B{i}_1\&B{i}_2\right)$ lead to strengthen nanoparticle temperature; an opposite behavior is noticed with the skin friction coefficient $\left({\tilde{S}}_{fx}R{e}_x^{0.5}\right)$, heat transfer rate $\left({\tilde{H}}_{tx}R{e}_x^{0.5}\right)$, and nanoparticle transfer rate $\left({\tilde{C}}_{tx}R{e}_x^{0.5}\right)$. The GPR model with the exponential Kernel function provided better performance than other functions on both training and checking datasets to predict ${\tilde{S}}_{fx}R{e}_x^{0.5},{\tilde{H}}_{tx}R{e}_x^{0.5}$, and ${\tilde{C}}_{tx}R{e}_x^{0.5}$. Statistical metrics including RMSE, MAE, MAPE, MSE, $R^2,$ and R are employed to check the accuracy and convergences of the predicted and numerical solutions obtained through GPR and RKF-45. It is observed that all three GPR models had an $R^2$ value of higher than 0.9. The proposed study demonstrates the advantages of employing soft computing methods (GPR) to effectively analyse the behavior of complex flow models.