Mathematical analysis of advanced thermal assessment of nanofluids using a Levenberg–Marquardt-based feed forward artificial neural network

Their expanding and contracting flow has created a lot of interest in the research of Cross nano fluids, which can be made use of for the development of more efficient, adaptive as well as responsive systems in various engineering, healthcare as well as environmental contexts. The concept of an expanding /contracting cylinder represents a novel approach in rheological studies and the flow behavior in such scenarios has not yet been explored using Artificial Neural Networks. This innovative analysis holds its significance for numerous technological and industrial applications. The system of the non-linear PDEs is a mathematical representation of the contemporary physical problem. The mathematical representation of the contemporary physical problem is given by the system of non-linear PDEs. With a well-chosen similarity transformation, a system of the nonlinear ODEs evolved from a set of nonlinear PDEs was used to solve the mathematical model that governs the system. The system is then acted on by Mathematica, running the NDSolve algorithm. Three important physical parameters of flow, temperature and concentration spreading out over large range and the effect being examined as flow progresses. These controlling parameters are analysed using parametric analysis, the effects of which are seen on the thermal boundary, momentum, and concentration boundary layers. The new predictability of the study, which resulted from the execution of an AI based framework using Levenberg-Marquardt backpropagation neural network, is implemented in MATLAB. A numerical solution from the conventional solver is used as a training set for a neural network that is then used to create an accurate predictive model. The behaviour of the function approximation and performance evaluation graphs. Results indicate that the designed neural-network can learn the nonlinear dynamics of the flow system and efficiently and approximately reproduce the response in terms of functions with high accuracy. The research also reveals that the physics parameters in control do affect considerably the flow, temperature and concentration fields giving rise to either enhanced or suppressed patterns depending on the magnitudes of each. Lastly, accuracy of the proposed computational framework is checked by comparing the results with previous publications obtained by the classical RK45-Fehlberg method. The close agreement from the two sets of results along with the reduced prediction error gotten by the neural network mode also supports the robustness, accuracy and reliability of the approach in the case of the artificial intelligence supported methodology.