## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Stochastic technique for solutions of nonlinear fin equation arising in thermal equilibrium model

**ABSTRACT**

In this study, a stochastic numerical technique is used to investigate the numerical solution of the heat transfer temperature dependent system using Feed-forward artificial neural networks (ANN). The Mathematical model of Fin equation is formulated with the help of ANN. The effect of the heat on a rectangular fin with thermal conductivity and temperature dependent internal heat generation is calculated through neural networks optimization with optimizers like active set technique (AST), interior point technique (IPT), pattern search (PS), genetic algorithm (GA) and a hybrid approach of PS-IPT, GA-AST, GA-IPT and GA-SQP with different selections of weights. The governing fin equation is transformed into an equivalent nonlinear second order ordinary differential equation. For this transformed ordinary differential equation model we have performed several simulations to provide the justification of better convergence of results. Moreover, the effectiveness of the designed model is validated through a complete statistical analysis. This study reveals the importance of rectangular fins during the heat transformation through the system.

**KEYWORDS**

PAPER SUBMITTED: 2018-02-21

PAPER REVISED: 2019-01-27

PAPER ACCEPTED: 2019-02-16

PUBLISHED ONLINE: 2019-03-09

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