Abstract This work examines the Casson nanofluid flow on a varying porous bi-directional stretchable sheet that has not yet conducted with effects of inclined magnetic field by incorporating Levenberg-Marquardt back propagation (LMBP) through ANN approach. The effect of temperature and space dependent heat sources have incorporated in energy equations along with thermal radiations effects. The flow system is affected by magnetic field in inclined direction. The diffusions of mass and heat has controlled through the use of thermophoresis and Brownian motion effects. In this examination the boundary value solver (bvp4c) serves as the data source for artificial neural networks (ANNs) known as Levenberg-Marquardt back-propagation (LMBP). As outcomes of this study, it has established that both primary and secondary velocities are retarded with growth in magnetic factor, variable porous factor and concentration of nanoparticles. Thermal profiles have amplified with escalation in radiation factor, thermal dependent heat source factor, nanoparticles concentration, thermal Biot number and thermal relaxation time factor. Concentration distribution amplified with progression in thermophoresis factor and concentration Biot number while deteriorated with surge in Schmidt number and mass relaxation time factor. For all the eight cases the gradient values are associated at 3.6671 × 10 −6 , 8.88 × 10 −6 , 8.32 × 10 −6 , 7.5442 × 10 −7 , 2.38 × 10 −8 , 8.34 × 10 −7 , 8.70 × 10 −7 and 8.35 × 10 −7 with corresponding epochs 790, 712, 692, 864, 1,000, 1,000, 864 and 712. The outcomes of this study can be applied in various engineering and industrial processes where heat and mass transfer play a critical role, such as cooling of electronic devices, polymer processing, thermal management in energy systems, and biomedical engineering involving nanofluids.
Algehyne et al. (2026) studied this question.