Optimization of straight fins with a step change in thickness and variable thermal conductivity by homotopy perturbation method

Kanat malzemesinin verimli kullanılabilmesi için kademeli kanat olarak isimlendirilen yeni bir kanat geometrisi önerilmiştir. Bu çalışmada, ısıl iletkenliği sıcaklıkla değişen dikdörtgen kesitli kademeli kanatların ısıl analizi ve optimizasyonu yapılmıştır. Kanat içindeki sıcaklık dağılımı, sonsuz kuvvet serisi şeklinde analitik bir çözüm sağlayan Homotopi Pertürbasyon Metodu (HPM) ile elde edilmiştir. Bu çözüm, verilen sabit bir kanat hacmi için ısı geçişini maksimum yapan kanat geometrisinin bulunması için kullanılmıştır. Elde edilen sonuçlar, aynı ısıl koşullar ve aynı kanat hacmi için kademeli kanadın düz kanada göre daha fazla ısı geçişi sağladığını göstermiştir. Optimizasyondan elde edilen sonuçlar, bu tip kanatların tasarımı için kullanılabilir.

Isıl iletkenliği sıcaklıkla değişen kademeli kanatların homotopi pertürbasyon yöntemi ile optimizasyonu

For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the thermal analysis and optimization of convective straight fins with a step change in thickness and temperature-dependent thermal conductivity have been addressed. Temperature distribution within the fin has been evaluated using homotopy perturbation method (HPM) which provides an analytical solution in the form of an infinite power series. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found by using the data from the solution. It has been observed that a SF is the better choice for transferring rate of heat in comparison with the flat fins for the same fin volume and identical thermal conditions. The derived condition of optimality gives an open choice to the designer.

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Ascher, U., and Petzold, L., Computer methods for ordinary differential equations and differentialalgebraic equations, SIAM, Philadelphia, 1998.
Aziz, A., Optimum design of a rectangular fin with a step change in cross-sectional area, International Communications in Heat and Mass Transfer, 21, 389- 401, 1994.
Cowdhury, M. S. H., and Hashim, I., Analytical solutions to heat transfer equations by homotopyperturbation method revisited, Physics Letters A, 372, 1240-1243, 2008.
Cowdhury, M. S. H., Hashim, I., and Abdulaziz, O., Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fintype problems, Communications in Nonlinear Science and Numerical Simulation, 14, 371-378, 2009.
He, J. H., Homotopy perturbation technique, Computational Methods in Applied Mechanics and Engineering, 178, 257-262, 1999.
He, J. H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics, 35, 37- 43, 2000.
He, J. H., Homotopy perturbation method: A new nonlinear analytical technique, Applied Mathematics and Computation 135, 73–79, 2003.
Hollands, K. G. T., and Stedman, B. A., Optimization of an absorber plate fin having a step change in local thickness, Solar Energy 49, 493-495, 1992.
Kern, Q. D., and Kraus, D. A., Extended Surface Heat Transfer, McGraw-Hill, New York, 1972.
Kundu, B., and Das, P. K., Performance analysis and optimization of annular fin with a step change in thickness, Journal of Heat Transfer, 123 601-604, 2001.
Kundu, B., and Das, P. K., Performance analysis and optimization of straight taper fins with variable heat transfer coefficient, International Journal of Heat and Mass Transfer, 45, 4739-4751, 2002.
Kundu, B., and Das, P. K., Performance analysis and optimization of elliptic fins circumscribing a circular tube, International Journal of Heat and Mass Transfer, 50, 173-180, 2007.
Kundu, B., Analysis of thermal performance and optimization of concentric circular fins under dehumidifying conditions, International Journal of Heat and Mass Transfer, 2646-2659, 2009.
Malekzadeh P., Rahideh, H., and Karami, G., Optimization of convective-radiative fins by using differential quadrature method, Energy Conversion and Management, 47, 1505-1514, 2006.
Öziş, T., and Ağırseven, D., He’s homotopy perturbation method for solving heat-like and wave-like equations with variable coefficients, Physics Letters A, 372, 5944-5950, 2008.
Saadatmandi, A., Dehghan, M., and Eftekhari, A., Application of He’s homotopy perturbation method for nonlinear system of second-order boundary value problems, Nonlinear Analysis: Real World Applications, 10, 1912-1922, 2009.