On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning

Abstract

It is well consensus among researchers that the constructing mathematical model for heat transfer problems results set of coupled nonlinear partial differential equations (PDEs) and the solution in this regard gets a challenging task. The present article contains an artificial neural network remedy to tackle nonlinear differential equations for heat transfer in an enclosure. In detail, we considered Casson fluid equipped in a semi-heated square cavity in the presence of both magnetic field and natural convection. The upper wall of the cavity is taken adiabatic and the lower wall is heated uniformly. The both right and left walls are considered cold. The flow is formulated in terms of coupled non-linear differential equations and solved for two different thermal flow fields namely baffle with heated tip and baffle with cold tip. An artificial intelligence-based neural model is developed to approximate the Nusselt number along the fin for both heated and cold tips of the T-shaped baffle. The low mean square error (MSE) values and perfect Regression values demonstrate the exceptional performance of the neural model being trained using the Levenberg-Marquardt algorithm. We found that the Nusselt number rises significantly with increasing Rayleigh numbers, especially in the vicinity of the heated baffle. This suggests increased buoyancy effects leading to improved convective heat transfer.