Unsupervised neural networks for Maxwell fluid flow and heat transfer over a curved surface with nonlinear convection and temperature‐dependent properties

• Published in: International journal for numerical methods in fluids Vol. 96; no. 9; pp. 1576 - 1591
• Main Authors: Ganga, Sai, Uddin, Ziya, Asthana, Rishi
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.09.2024
• Subjects: Contact lenses; Convection; curved surface; Deborah number; Flow velocity; Fluid flow; Heat transfer; Machine learning; Magnetic field; Magnetic fields; Magnetic lenses; Magnetic properties; Maxwell fluid; Maxwell fluids; Neural networks; nonlinear convection; nonlinear radiation; Nonlinear systems; Nonlinearity; Parameters; Physics; PINN; Polymers; Suction; Temperature; Temperature dependence; Temperature ratio; temperature‐dependent properties; Thermal conductivity; Unsupervised learning; Velocity; Viscosity
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.5298

Maxwell fluid flow over a curved surface with the impacts of nonlinear convection and radiation, temperature‐dependent properties, and magnetic field are investigated. The governing equations of the physical system are solved using wavelet based physics informed neural network, a machine learning technique. This is an unsupervised method, and the solutions have been obtained without knowing the numerical solution to the problem. Given the nonlinearity of the coupled equations, the methodology used is flexible to implement, and the activation function used improves the accuracy of the solution. We approximate the unknown functions using different neural network models and determine the solution by training the network. The special case of the obtained results is examined with the available results in the literature for validation of the proposed methodology. It is observed that the proposed approach gives reliable results for the analyzed problem of study. Further, an analysis of the influence of flow parameters (deborah number, variable thermal conductivity and viscosity parameter, velocity slip parameter, temperature ratio parameter, suction parameter, and convection parameters) on temperature and fluid flow velocity is carried out. It is observed that as the flow parameter Deborah number, velocity slip parameter, and viscosity parameter increase, there is a decline in velocity and an enhancement in temperature. This study of fluid flow over a curved surface has applications in the polymer industry, which plays an important role in the manufacturing of contact lenses. Wavelet‐based physics‐informed neural networks without utilizing any labeled data sets are employed to examine the study of non‐Newtonian Maxwell fluid flow over a curved surface. We have used three different models to approximate different solutions to non‐linear coupled equations that were trained parallely. We have also employed a wavelet activation function for improved accuracy. The proposed method is very flexible to implement in comparison to the existing numerical schemes and gives accurate results for all the flow parameters.