In this paper, the exact implicit solution of the second order nonlinear ordinary differential equation which governing heat transfer in rectangular fin is obtained using symmetry reduction methods. General relationship among the temperature at the fin tip, the temperature gradient at the fin base, the mode of heat transfer, 𝑛 and the fin parameters 𝑁 and ℰ is obtained. Some numerical examples are discussed and it is shown that the temperature of fin increases when approaching from the heat source. The relationship between the fin efficiency and the temperature of fin tip is obtained for any value of the mode of heat transfer 𝑛. The relationship between the fin efficiency and both the parameter 𝑁 and ε the temperature gradient at the fin base is obtained. To our best knowledge, solutions obtained in this paper are new.
Abdel Latif, M. S.; Abdel Kader, A. H.; and Nour, H. M.
Exact implicit Solution of Nonlinear Heat Transfer in Rectangular Straight Fin Using Symmetry Reduction Methods,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 10,
2, Article 15.
Available at: https://digitalcommons.pvamu.edu/aam/vol10/iss2/15