Investigation of Temperature-Dependent Parameters Effect on Thermal Fin Performance Using the Response Surface Methodology

Document Type : Research Paper

Authors

Department of Chemical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

Thermal fins, as one of the key components in enhancing the performance of heat transfer systems, play a vital role in various industries. This study investigates the effects of key dimensionless, temperature-dependent parameters, including the thermo-geometric parameter 𝑀, which represents the ratio of convective to conductive heat transfer, as well as the heat transfer coefficient exponent 𝑛, and the thermal conductivity exponent 𝛽 on the thermal efficiency of fins. These parameters were defined to nondimensionalize the available analytical solutions in the literature. To achieve this, Response Surface Methodology (RSM) was employed as an advanced statistical and modeling tool. A full factorial design with six levels for each parameter was used. The proposed model demonstrated excellent predictive accuracy, with an R² value of 0.990 and a p-value < 0.0001. Results revealed that increasing the parameter 𝑀 decreases thermal efficiency due to enhanced convective losses and localized temperature gradients. Similarly, higher values of 𝑛 lead to efficiency reduction by concentrating heat transfer in hotter regions of the fin. Conversely, variations in 𝛽 showed a smaller effect on overall performance but contributed to a more uniform temperature distribution. The use of the response surface method not only reduces the computational cost, but also allows for rapid and accurate analysis of complex conditions. The results of this research can be used as an effective guide for the optimal design of fins in the heat transfer industries.

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References

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Journal of Modeling in Engineering
Volume 24, Issue 84
March 2026
Pages 253-264

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History

  • Receive Date: 27 January 2025
  • Revise Date: 02 June 2025
  • Accept Date: 23 June 2025

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