Exact solution of fin problem with linear temperature-dependent thermal conductivity

• Autorzy: Kader A. H. A. , Latif A. S. A. , Nour H. M.

Identyfikatory

DOI

10.17512/jamcm.2016.4.06

• Języki publikacji: EN

Abstrakty

EN

In this paper, we obtain the general exact solution of a nonlinear fin equation which governs heat transfer in a rectangular fin with linear temperature-dependent thermal conductivity using the partial Noether method. The relationship between the fin efficiency and the thermo-geometric fin parameter is obtained. Additionally, we obtained the relationship among the fin effectiveness, the thermo-geometric fin parameter and the Biot number.

Słowa kluczowe

EN

exact solution; fin equation; fin efficiency; thermal conductivity

PL

żebro prostokątne; sprawność żebra; wymiana ciepła; przewodność cieplna

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 4
• Strony: 51--61
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Kader A. H. A.

• Mathematics and Engineering Physics Department, Faculty of Engineering Mansoura University

autor

Latif A. S. A.

• Mathematics and Engineering Physics Department, Faculty of Engineering Mansoura University, Egypt

autor

Nour H. M.

• Mathematics and Engineering Physics Department, Faculty of Engineering Mansoura University, Egypt

Bibliografia

• [1] Seiyed Ghasemi E., Ali Zolfagharian, M. Hatam, Ganji D.D., Analytical thermal study on nonlinear fundamental heat transfer cases using a novel computational technique, Applied Thermal Engineering 2016, 98, 88-97.
• [2] Saeed Dinarvand, Reza Hosseini, Optimal homotopy asymptotic method for convectiveradiative cooling of a lumped system, and convective straight fin with temperature-dependent thermal conductivity, Afr. Mat. 2013, 24, 103-116.
• [3] Srikumar Panda, A study on nonlinear wet fin problem using homotopy analysis method, Int. J. Appl. Comput. Math, 2016, DOI: 10.1007/s40819-016-0188-1.
• [4] Mustafa Inc: Application of homotopy analysis method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Mathematics and Computers in Simulation 2008, 79, 189-200.
• [5] Kulkarni D.B., Joglekar M.M., Residue minimization technique to analyze the efficiency of convective straight fins having temperature-dependent thermal conductivity, Applied Mathematics and Computation 2009, 215, 2184-2191.
• [6] Safa Bozkurt Coskun, Mehmet Tarik Atay, Fin efficiency analysis of convective straight fins with temperature dependent thermal conductivity using variational iteration method, Applied Thermal Engineering 2008, 28, 2345-2352.
• [7] Cihat Arslanturk, A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, International Communications in Heat and Mass Transfer 2005, 32, 831-841.
• [8] Ching-Huang Chiu, Cha’o-Kuang Chen, A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, Int. J. Heat and Mass Transfer. 2002, 45, 2067-2075.
• [9] Abdel Latif M.S., Abdel Kader A.H., Nour H.M., Exact implicit solution of nonlinear heat transfer in rectangular straight fin using symmetry reduction methods, Appl. Appl. Math. 2015, 10, 2, 864-877.
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• [11] Abdel Kader A.H., Abdel Latif M.S., Nour H.M., General exact solution of the fin problem with the power law temperature - dependent thermal conductivity, Math. Meth. Appl. Sci. 2016, 39, 1513-1521.
• [12] Srikumar Panda, Arka Bhowmik, Ranjan Das, Ramjee Repaka, Subash Martha C., Application of homotopy analysis method and inverse solution of a rectangular wet fin, Energy Conversion and Management 2014, 80, 305-318.
• [13] Arka Bhowmik, Srikumar Panda, Ranjan Das, Ramjee Repaka, Subash Marthaet C., Inverse analysis of conductive-convective wet triangular fin for predicting thermal properties and fin dimensions, Inverse Problems in Science and Engineering 2014, 22(8), 1367-1393.
• [14] Srikumar Panda, Arka Bhowmik, Homotopy analysis method for thermal analysis of wet fin with all nonlinearity, International Conference on Engineering (NUiCONE), 2013, 1-6, DOI:10.1109/NUiCONE.2013. 6780197.
• [15] Kara A.H., Mahomed F.M., Naeem I., Wafo Soh C., Partial Noether operators and first integrals via partial Lagrangians, Math. Meth. Appl. Sci. 2007, 30, 2079-2089.
• [16] Naeem I., Mahomed F.M., Noether, partial Noether operators and first integrals for a linear system, J. Math. Anal. Appl. 2008, 342, 70-82.
• [17] Frank Olver W.J., Lozier D.W., Boisvert R.F., Clark C.W., Nist Handbook of Mathematical Functions 2010.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.