PyTorch-based deep neural network model for the calendering process of non-Newtonian fluids with temperature-dependent viscosity

The objective of the present study is to develop a PyTorch-based deep neural network framework to predict velocity and temperature profiles in the calendering process of incompressible, non-Newtonian fluids with temperature-dependent viscosity. The governing partial differential equations are non-dimensionalized using appropriate variables and simplified using the lubrication approximation theory, which reduces them to a system of nonlinear ordinary differential equations. Analytical solutions for pressure, velocity, and temperature fields are obtained using a perturbation method. Key engineering quantities, including detachment point, sheet thickness, roll separation force, power input, Nusselt number, and streamlines, are evaluated using the Regula Falsi method and numerical integration. Symbolic solutions are visualized to analyze the influence of various physical parameters. The artificial neural network model is developed in Python using PyTorch, employing sigmoid activation functions. Model performance is assessed through loss curves, absolute error analysis, and comparative bar plots. The framework achieves remarkable precision, with mean squared error values of (Formula presented.) for velocity profiles and (Formula presented.) for temperature profiles, with coefficients of determination (Formula presented.) for both cases. Furthermore, the influence of key parameters on convective heat transfer is analyzed through the Nusselt number. Results indicate that increasing the Weissenberg number enhances heat transfer, while a higher material parameter leads to its reduction. Additionally, an increase in the Brinkman number decreases both the sheet thickness and power input. This framework enables real-time optimization of polymer sheet thickness, reduces roll separation forces in rubber processing, and facilitates energy-efficient nanomaterial coating applications.

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