Insight into the thermal transport by considering the modified Buongiorno model during the silicon oil-based hybrid nanofluid flow: probed by artificial intelligence

Abstract

This work aims to analyze the impacts of the magnetic field, activation of energy, thermal radiation, thermophoresis, and Brownian effects on the hybrid nanofluid (HNF) (Ag++silicon oil) flow past a porous spinning disk. The pressure loss due to porosity is constituted by the Darcy–Forchheimer relation. The modified Buongiorno model is considered for simulating the flow field into a mathematical form. The modeled problem is further simplified with the new group of dimensionless variables and further transformed into a first-order system of equations. The reduced system is further analyzed with the Levenberg–Marquardt algorithm using a trained artificial neural network (ANN) with a tolerance, step size of 0.001, and 1,000 epochs. The state variables under the impacts of the pertinent parameters are assessed with graphs and tables. It has been observed that when the magnetic parameter increases, the velocity gradient of mono and hybrid nanofluids (NFs) decreases. As the input of the Darcy–Forchheimer parameter increases, the velocity profiles decrease. The result shows that as the thermophoresis parameter increases, temperature and concentration increase as well. When the activation energy parameter increases, the concentration profile becomes higher. For a deep insight into the analysis of the problem, a statistical approach for data fitting in the form of regression lines and error histograms for NF and HNF is presented. The regression lines show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mn>100</mml:mn><mml:mi>%</mml:mi></mml:math> of the data is used in curve fitting, while the error histograms depict the minimal zero error <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mo>−</mml:mo><mml:mn>7.1</mml:mn><mml:mi>e</mml:mi><mml:mn>6</mml:mn></mml:math> for the increasing values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:math> . Furthermore, the mean square error and performance validation for each varying parameter are presented. For validation, the present results are compared with the available literature in the form of a table, where the current results show great agreement with the existing one.