SavedAdd your journal

Journals / Çukurova Üniversitesi Mühendislik Fakültesi dergisi / 2020 / Cilt: 35 Sayı: 1

Heat Conduction Analysis of Two-Dimensional Anisotropic Plate

İki Boyutlu Anizotropik Plakanın Isı İletim Analizi

Durmuş YARIMPABUÇ
Ertuğrul CİHAN
Kerimcan ÇELEBİ
Mehmet EKER
Pages
139–148
Publication Date
2020-03-31
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The accuracy of the numerical method is demonstrated by comparing analytical and numerical solutions using simple material functions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:It is assumed that the thermal conductivity and heat generation of the material arbitrarily change in the direction of the two space variables.
💡
Conclusion & Impact:The accuracy of the numerical method is demonstrated by comparing analytical and numerical solutions using simple material functions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Anizotropik Isı iletimi · Analitik çözüm · Sonlu elemanlar yöntemi

Abstract

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.

Özet

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.

🔖

Cite This Article

YARIMPABUÇ, D., CİHAN, E., ÇELEBİ, K., EKER, M. (2020). Heat Conduction Analysis of Two-Dimensional Anisotropic Plate. Çukurova Üniversitesi Mühendislik Fakültesi dergisi, Cilt: 35 Sayı: 1, 139–148. https://ajindex.com/articles/895183

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  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