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Numerical investigation of nonlinear power-law fin type problem using hybrid heuristic computation

In this paper, the temperature distribution of a straight fin is investigated using an elegant scheme combining Genetic algorithm (GA) and Bernstein polynomials. The solution of the fin problem which is described by the nonlinear ordinary differential equation (NODE) is approximated by Bernstein polynomials with unknown constants. The unknown constants are obtained by transforming the NODE into an equivalent optimization problem. The optimization problem is solved by employing the Genetic algorithm (GA) and hybrid approach combining GA with interior point algorithm (IPA). The efficacy of the proposed scheme is illustrated by numerically solving the power-law fin type problem. Moreover, the variation in convective-conductive parameter and different modes of heat transfer are also investigated. The results confirm that the proposed technique is quite effective in the analysis of strongly nonlinear fin type problems.