İki Boyutlu Anizotropik Plakanın Isı İletim Analizi

Yıl 2020, Cilt: 35 Sayı: 1, 139 - 148, 31.03.2020

Durmuş Yarımpabuç Ertuğrul Cihan Kerimcan Çelebi Mehmet Eker

https://doi.org/10.21605/cukurovaummfd.764670

Cited By: 4

https://izlik.org/JA46HP24YY

Öz

Homojen olmayan genel sınır koşullarına sahip iki boyutlu anizotropik bir plakanın ısı iletim problemi, kartezyen koordinat sisteminde ANSYS Fluent kullanılarak çözülmüştür. Malzemenin termal iletkenliği ve ısı üretiminin keyfi olarak iki uzay değişkeni yönünde değiştiği varsayılmıştır. Bu koşullar altında sistemi modelleyen değişken katsayılı diferansiyel denklem elde edilir. Bu tür denklemlerin analitik çözümleri, bazı basit malzeme fonksiyonları dışında elde edilemez. İki uzay değişkenine bağlı olarak değişen ısı iletim katsayısı ve hacimsel ısı üretimi ile homojen olmayan sınır koşullarını içeren değişken katsayılı diferansiyel denklem ANSYS Fluent kullanıcı tanımlı fonksiyon (UDF) ile sayısal olarak ele alınmıştır. Sayısal yöntemin doğruluğu, basit malzeme fonksiyonları kullanılarak analitik ve sayısal çözümler karşılaştırılarak gösterilmiştir.

Anahtar Kelimeler

Anizotropik Isı iletimi , Analitik çözüm , Sonlu elemanlar yöntemi , UDF

Heat Conduction Analysis of Two-Dimensional Anisotropic Plate

https://izlik.org/JA46HP24YY

Öz

The heat conduction of a two dimensional anisotropic plate with non-homogeneous general boundary conditions is solved by using ANSYS Fluent in the cartesian coordinate system. It is assumed that the thermal conductivity and heat generation of the material arbitrarily change in the direction of the two space variables. Under these conditions, a variable coefficient differential equation is obtained. Analytical solutions of such equations cannot be obtained except for some simple material functions. The variable coefficient differential equation, which includes the heat conduction coefficient and volumetric heat generation depending on the two space variables and non-homogeneous boundary conditions, is handled numerically by ANSYS Fluent user-defined function (UDF). The accuracy of the numerical method is demonstrated by comparing analytical and numerical solutions using simple material functions.

Anahtar Kelimeler

Anisotropic heat conduction , Analytical solution , Finite element method , UDF

Kaynakça

• 1. Zedan, M., Schneider, G.E., 1982. A Physical Approach to the Finite-difference Solution of the Conduction Equation in Generalized Coordinates, Num.H Trans., Part A, 5(1), 1-19.
• 2. Comini, G., Guidice, S., Lewis, R.W., Zienkiewicz, O.C., 1974. Finite Element Solution on Nonlinear Heat Conduction Problems with Special Reference to Phase Change, Int. J. for Num. Methods in Eng., 8, 613-624.
• 3. Wrobel, L.C., Aliabadi, M.H., 2002. The Boundary Element Method: Applications in Solids and Structures, 2 Volume Set, John Wiley and Sons, USA, 1066.
• 4. Hsieh, M.H., Ma, C.C., 2002. Analytical Investigations for Heat Cond. Prob. in Anisotropic Thin-layer Media with Embedded Heat Sources, Int.J.H.M.Trans., 45(20), 4117-4132.
• 5. Ma, C.C., Chang, S.W., 2004. Analytical Exact Solutions of Heat Conduction Problems for Anisotropic Multi-layered Media, Int. J. Heat Mass Trans., 47(8-9), 1643–1655.
• 6. Mera, N.S., Elliot, L., Ingham, D.B., Lesnic, D., 2001. A Comparison of Boundary Element Method Formulations for Steady State Anisotropic Heat Conduction Problems, Eng. Anal. Bound. Elem., 25(2), 115–28.
• 7. Florez, W.F., Power, H., 2001. Comparison Between Continuous and Discontinuous Boundary Elements in the Multidomain Dual Reciprocity Method for the Solution of the Two-dimensional Navier-Stokes Equations, Eng. Anal. Bound. Elem., 25(1), 57–69.
• 8. Tadeu, A., Antonio, J., 2000. Use of Constant, Linear and Quadratic Boundary Elements in 3D Wave Diffraction Analysis, Eng. Anal. Bound. Elem., 24(2), 131–144.
• 9. Wang, H., Qin, Q.H., Kang, Y.L., 2005. A New Meshless Method for Steady-state Heat Conduction Problems in Anisotropic and Inhomogeneous Media, Arc. App. Mech., 74(8), 563–579.
• 10. Sladek, J., Sladek, V., Atluri, S.N., 2004. Meshless Local Petrov-Galerkin Method for Heat Conduction Problem in an Anisotropic Medium, CMES, Comput Model Eng. Sci., 6(3), 309–318.
• 11. Hsieh, M.H., Ma, C.C., 2002. Analytical Investigations for Heat Conduction Problems in Anisotropic Thin-layer Media with Embedded Heat Sources, Int.J.H.M.Trans., 45(20), 4117-4132.
• 12. Haji-Sheikh, A., Beck, J.V., Agonafer, D., 2003. Steady-state Heat Conduction in Multi- layer Bodies, Int. J. Heat Mass Transfer, 46(13), 2363–2379.
• 13. Shiah, Y.C., Tan, C.L., 1997. BEM Treatment of Two-dimensional Anisotropic Field Problems by Direct Domain Mapping, Engineer. Anly. Bound. Element, 20(4), 347-351.
• 14. Shiah, Y.C., Tan, C.L., 2004. BEM Treatment of Three-dimensional Anisotropic Field Problems by Direct Domain Mapping, Engineer. Anly. Bound. Element, 28(1), 43–52.
• 15. Shiah, Y.C., Hwanh, P.W., Yang, R.B., 2006. Heat Conduction in Multiply Adjoined Anisotropic Media with Embedded Point Heat Sources, J. Heat Transfer, 128(2), 207–214.
• 16. Shiah, Y.C., Lee, B.J., 2011. Boundary Element Modeling of 3-D Anisotropic Heat Conduction Involving Arbitrary Volume Heat Source, Math.Comp.Mod., 54(9-10), 2392-2402.
• 17. Yarımpabuç, D., Cihan, E., Eker, M., Celebi, K., 2016. Analytical and Numerical Solutions of Anisotropic Heat Conduction Problems with Location-dependent Heat Generation, 1st International Mediterranean Science and Engineering Congress (IMSEC 2016), 1673-1680, Paper ID:496.
• 18. Ferziger, J.H., Peric, M., 2002. Computational Methods for Fluid Dynamics, Third Ed. Springer, 431, USA.
• 19. ANSYS, Inc., 2009. Ansys Fluent 12.0 UDF Manual, 2070.