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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: 1

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

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.

Heat Conduction Analysis of Two-Dimensional Anisotropic Plate

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: 1

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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Durmuş Yarımpabuç Bu kişi benim

Ertuğrul Cihan Bu kişi benim

Kerimcan Çelebi Bu kişi benim

Mehmet Eker

Yayımlanma Tarihi 31 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 35 Sayı: 1

Kaynak Göster

APA Yarımpabuç, D., Cihan, E., Çelebi, K., Eker, M. (2020). Heat Conduction Analysis of Two-Dimensional Anisotropic Plate. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 35(1), 139-148. https://doi.org/10.21605/cukurovaummfd.764670
AMA Yarımpabuç D, Cihan E, Çelebi K, Eker M. Heat Conduction Analysis of Two-Dimensional Anisotropic Plate. cukurovaummfd. Mart 2020;35(1):139-148. doi:10.21605/cukurovaummfd.764670
Chicago Yarımpabuç, Durmuş, Ertuğrul Cihan, Kerimcan Çelebi, ve Mehmet Eker. “Heat Conduction Analysis of Two-Dimensional Anisotropic Plate”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35, sy. 1 (Mart 2020): 139-48. https://doi.org/10.21605/cukurovaummfd.764670.
EndNote Yarımpabuç D, Cihan E, Çelebi K, Eker M (01 Mart 2020) Heat Conduction Analysis of Two-Dimensional Anisotropic Plate. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35 1 139–148.
IEEE D. Yarımpabuç, E. Cihan, K. Çelebi, ve M. Eker, “Heat Conduction Analysis of Two-Dimensional Anisotropic Plate”, cukurovaummfd, c. 35, sy. 1, ss. 139–148, 2020, doi: 10.21605/cukurovaummfd.764670.
ISNAD Yarımpabuç, Durmuş vd. “Heat Conduction Analysis of Two-Dimensional Anisotropic Plate”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35/1 (Mart 2020), 139-148. https://doi.org/10.21605/cukurovaummfd.764670.
JAMA Yarımpabuç D, Cihan E, Çelebi K, Eker M. Heat Conduction Analysis of Two-Dimensional Anisotropic Plate. cukurovaummfd. 2020;35:139–148.
MLA Yarımpabuç, Durmuş vd. “Heat Conduction Analysis of Two-Dimensional Anisotropic Plate”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, c. 35, sy. 1, 2020, ss. 139-48, doi:10.21605/cukurovaummfd.764670.
Vancouver Yarımpabuç D, Cihan E, Çelebi K, Eker M. Heat Conduction Analysis of Two-Dimensional Anisotropic Plate. cukurovaummfd. 2020;35(1):139-48.

Cited By

THERMAL ANALYSIS OF BI-DIRECTIONAL FUNCTIONALLY GRADED PLATES SUBJECTED TO HEAT GENERATION
Heat Transfer Research
https://doi.org/10.1615/HeatTransRes.2023049340