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This paper explores the potentiality of the evolutionary algorithms such as Genetic Algorithm (GA) and Particle Swam Optimization (PSO) applied in the field of inverse heat transfer to estimate the unknown parameter. The unknown heat flux, applied to the base of the mild steel fin, is estimated using evolutionary algorithms for the known temperature distribution. The direct/forward solution is developed as a conjugate heat transfer model which forges the estimation of the unknown parameters still more promising. To shelter conjugate heat transfer phenomenon, a domain is created around the fin setup and air is considered as the fluid medium. Heat transfer from the fin to the ambient is through natural convection and hence Boussinesq approximation is incorporated to treat density as a function of temperature. Use of Neural Network as a replacement for the numerical forward model reduces the computational time to arrive at new forward solution. Experiments are conducted for different power input and the temperature is recorded for the corresponding heat flux. The objective of the inverse method is to estimate the unknown parameter with the information of the temperature. GA and PSO combined with Levenberg Marquardt method (LM) are used as the inverse method distinguishingly for the estimation of the unknown heat flux. Initially surrogate data is used to validate the estimation process and later the estimation is carried out for the experimental data. Finally, a comparison of both the methods is dealt in detail based on the results.