Performance of Heat Transfer in Micropolar Fluid with Isothermal and Isoflux Boundary Conditions Using Supervised Neural Networks

• Published in: Mathematics (Basel) Vol. 11; no. 5; p. 1173
• Main Authors: Sulaiman, Muhammad, Khan, Naveed Ahmad, Alshammari, Fahad Sameer, Laouini, Ghaylen
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2023
• Subjects: Artificial intelligence; Boundary conditions; Boundary value problems; Continuity (mathematics); Darcian porous channel; Exact solutions; Finite difference method; Finite element method; Fluid dynamics; Fluid flow; Heat transfer; Investigations; Local optimization; Machine learning; Magnetic fields; Mathematical models; Mathematical research; micropolar fluid; Micropolar fluids; Network reliability; Neural networks; Non-Newtonian fluids; nonlinear differential equation; Nonlinear differential equations; numerical computation; Optimization algorithms; Ordinary differential equations; Parameters; Partial differential equations; Prandtl number; Reynolds number; Runge-Kutta method; Suction; supervised neural networks; Temperature profiles; Tests, problems and exercises; Viscosity; Pakistan
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11051173

The current study delivers a numerical investigation on the performance of heat transfer and flow of micropolar fluid in porous Darcy structures with isothermal and isoflux walls (boundary conditions) of a stretching sheet. The dynamics and mechanism of such fluid flows are modelled by nonlinear partial differential equations that are reduced to a system of nonlinear ordinary differential equations by utilizing the porosity of medium and similarity functions. Generally, the explicit or analytical solutions for such nonlinear problems are hard to calculate. Therefore, we have designed a computer or artificial intelligence-based numerical technique. The reliability of neural networks using the machine learning (ML) approach is used with a local optimization technique to investigate the behaviours of different material parameters such as the Prandtl number, micropolar parameters, Reynolds number, heat index parameter, injection/suction parameter on the temperature profile, fluid speed, and spin/rotational behaviour of the microstructures. The approximate solutions determined by the efficient machine learning approach are compared with the classical Runge–Kutta fourth-order method and generalized finite difference approximation on a quasi-uniform mesh. The accuracy of the errors lies around 10−8 to 10−10 between the traditional analytical solutions and machine learning strategy. ML-based techniques solve different problems without discretization or computational work, and are not subject to the continuity or differentiability of the governing model. Moreover, the results are illustrated briefly to help implement microfluids in drug administering, elegans immobilization, and pH controlling processes.