A novel design of stochastic approximation treatment of longitudinal rectangular fin dynamical model

Abstract

The current research work focuses on the thermal effectiveness and distribution of an internal heat-generating longitudinal rectangular fin that is dependent on temperature thermal conductivity that varies exponentially. Additionally, the thermal dispersion of a longitudinal fin is studied for thermal conductivities that vary exponentially with temperature and linearly with temperature. With the use of dimensionless terms, the considered problem's governing equation is transformed into a non-linear ordinary differential equation. Using the shooting method in Mathematica software, the dataset for the Levenberg Marquardt Backpropagation based on artificial neural network is created by varying different parameters, including the thermogeometric parameter, the parameter of internal heat generation, the parameter of heat transfer, and the parameter of thermal conductivity parameter. For network modeling using the Levenberg Marquardt Backpropagation approach for various longitudinal fin model scenarios, the testing, training, and validation process is used. Error histogram, regression, training state and fitness, and mean square error are used to analyze the accuracy of the outcome. This study shows that the temperature gradient increases for larger values of the parameter of thermal conductivity but decreases for different thermogeometric parametric values. Additionally, the temperature distribution is improved by higher numbers of heat transfer and heat generation parameters.

Keywords

• Neural networks
• Levenberg-marquardt back-propagation (LMB)
• Thermogeometric
• Fin
• Best validation performance (BVP)