MANFIS approach for predicting heat and mass transport of bio-magnetic ternary hybrid nanofluid using Cu/Al₂O₃/MWCNT nanoadditives

Abstract

A mathematical flow model is envisioned to predict heat and mass transport of bio-magnetic ternary hybrid nanofluid (THNF) flow of different shapes over a moving wedge with radiation effect. The nonsimilar variables led the envisaged mathematical flow model to the physical flow problem. The shooting technique together with Runge-Kutta-Fehlberg’s fourth fifth-order (RKF-45) integration scheme is involved in computing the non-linear system of ordinary differential equations (ODEs). Influence of various physical parameters on friction factor $\left({\check{C}}_{fx}\right)$, rate of heat transport $\left({\check{H}}_{tx}\right)$, Sherwood number$\left({\check{S}}_{hx}\right)$, and motile microorganisms’ flux $\left({\check{N}}_{hx}\right)$ have been examined and visualized through graphs. Furthermore, the multi-output adaptive neuro-fuzzy inference system (MANFIS) simulation was developed and tested to predict the thermal and energy transport of bio ternary hybrid nanofluid flow. The physical parameters and the physical quantities such as the friction factor $\left({\check{C}}_{fx}\right)$, rate of heat transport $\left({\check{H}}_{tx}\right)$Sherwood number$\left({\check{S}}_{fx}\right)$, and motile microorganisms’ flux $\left({\check{N}}_{hx}\right)$ are the input and output of the established MANFIS simulation. The RMSE, MAE, MSE, sum of squared error, and R² of statistical indicators values for $\left({\check{C}}_{fx}\right)$, ${\check{H}}_{tx}$  ${\check{S}}_{hx}$, and ${\check{N}}_{hx}$were calculated using MANFIS. The predicted values are very close to the numerical results, and the coefficient of determination R² of ${\check{C}}_{fx}$, ${\check{H}}_{tx}$,  ${\check{S}}_{hx}$, and ${\check{N}}_{hx}$ are 0.9602, 0.9928, 0.9847, and 0.9859, respectively, indicating the best settlement. However, the results show that ternary hybrid nanofluid with blade-shaped nanoparticle intensifies rate of heat transport as compared to other shapes of hybrid nanofluid.