Abstract This research focuses on the stochastic analysis of the nonlinear radiative transfer of heat energy in a steady, incompressible Casson fluid flow over a vertically permeable stretchable surface within a non-Darcy porous medium, considering magnetic field effects. Using similarity transformations, the governing PDEs are transformed into nonlinear ODEs. A dataset is produced for Levenberg-Marquardt-algorithm (LBMA) with respect to influential parameters in Mathematica using the Adams method. To evaluate the outcome against the benchmark solution, the dataset is split into three segments wherein 70% is assigned for training, 30% for validation and testing each to improve the model accuracy. The proposed scheme demonstrated optimal performance across all scenarios, with mean squared error (MSE) values of 1.131E-07, 1.1087E-07, 1.2489E-07, 6.4137E-08, 2.3414E-10,2.3414E-10, 4.6675E-10 and 1.2455E-09 for each corresponding scenario, respectively. Velocity of the fluid increases with increase of magnetic field, whereas temperature profile increases with increase in Eckert parameter, Magnetic number and Prandtl number but, decreases with increase of Thermal radiation number. Concentration profile have inverse relation for chemical reaction number, Soret and Schmidt numbers. The analysis of the reference and proposed datasets confirms the reliability and accuracy of LBMA through error assessment. These estimates are about E-04 to E-06 for the velocity profile, E-03 to E-07 for the temperature profile and E-03 to E-08 for the concentration profile.
Zhang et al. (Thu,) studied this question.