TEMPORAL DIFFERENTIAL TRANSFORM AND SPATIAL FINITE DIFFERENCE METHODS FOR UNSTEADY HEAT CONDUCTION EQUATIONS WITH ANISOTROPIC DIFFUSIVITY
Öz
Three unsteady heat conduction problems with anisotropic diffusivity and time-dependent heating or heat flux and/or heat source are considered in showing the utility of a hybrid method involving a combination of temporal differential transform and spatial finite difference methods. The segregation of time from the spatial component is the greatest advantage of the hybrid method that exhibits no instability of finite difference methods generally seen with parabolic equations. The easy-to-implement algorithm that is essentially a Poisson solver works with both linear and non-linear heat transport problems without any difficulty of sorts. To gain confidence in the results some simulation results are also presented of problems that have an Adomian solution. The method can be used in practical heat transfer problems concerning non-uniform materials like composites, alloys, heterogeneous porous media with thermal equilibrium or non-equilibrium, multi-layered media and such other problems.
Anahtar Kelimeler
Kaynakça
- Zhou, J.K., “Differential Transformation and its Applications for Electrical Circuits”, Huazhong University Press, Wuhan, P. R. China (1986), In Chinese.
- Bert, C.W., Zeng, H., “Analysis of axial vibration of compound bars by differential transform method”, Journal of Sound and Vibration, 275, 641- 647(2004). http://dx.doi.org/10.1016/j.jsv.2003.06.019
- Chen, C.K., Lai, H.Y., Liu, C.C., “Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam”, Microsyst. Technol., 15, 813–820 (2009). http://link.springer.com/article/10.1007/s00542-009- 0834-1
- Chen, C.L., Liu, Y.C., “Solutions of two-boundary- value problems using the differential transform method”, Journal of Optimization Theory and Application, 99, 23-35(1998).
- Jang, M.J., Chen, C.L., Liy, Y.C., “On Solving the Initial-Value Problems Using the Differential Transformation Method”, Appl. Math. Comput., 115, 145–160(2000). http://dx.doi.org/10.1016/S0096-3003(99)00137-X
- Kuo, B.L., “Applications of the differential transform method to the solutions of the free convection problem”, Appl. Math. Comput., 165, 63-79(2005). http://dx.doi.org/10.1016/j.amc.2004.04.090
- Yeh, Y.L., Wang, C.C., Jang, M.J., “Using Finite Difference and Differential Transformation Method to Analyze of Large Deflections of Orthotropic Rectangular Plate Problem”, Appl. Math Comput., 190, http://dx.doi.org/10.1016/j.amc.2007.01.099 1146-1156(2007).
- Yu, L.T., Chen, C.K., “Application of the Hybrid Method to the Transient Thermal Stresses Response in Isotropic Annular Fins”, J. Appl. Mech., 66, 340- 347(1999).
- Yu, L.T., Chen, C.K., “The solution of the Blasius Equation by the Differential Transformation Method”, Math. Comput. Modeling, 28, 101- 111(1998). http://dx.doi.org/10.1016/S0895-7177(98)00085-5
- Odibat, Z., Bertelle, C., Aziz-Alaoui, M.A., Duchamp, G.H.E., “A multi-step differential transform method and application to non-chaotic and chaotic systems”, Computers and Mathematics with Applications, 59, 1462-1472(2010). http://dx.doi.org/10.1016/j.camwa.2009.11.005
- Wazwaz, A.M., Gorguis, A., “Exact Solutions for Heat-Like and Wave-Like Equations with Variable Coefficients”, Appl. Math Comput., 149, 15- 29(2004). http://dx.doi.org/10.1016/S0096-3003(02)00946-3
Yıl 2014,
Cilt: 27 Sayı: 4, 1063 - 1076, 28.05.2014
Öz
Kaynakça
- Zhou, J.K., “Differential Transformation and its Applications for Electrical Circuits”, Huazhong University Press, Wuhan, P. R. China (1986), In Chinese.
- Bert, C.W., Zeng, H., “Analysis of axial vibration of compound bars by differential transform method”, Journal of Sound and Vibration, 275, 641- 647(2004). http://dx.doi.org/10.1016/j.jsv.2003.06.019
- Chen, C.K., Lai, H.Y., Liu, C.C., “Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam”, Microsyst. Technol., 15, 813–820 (2009). http://link.springer.com/article/10.1007/s00542-009- 0834-1
- Chen, C.L., Liu, Y.C., “Solutions of two-boundary- value problems using the differential transform method”, Journal of Optimization Theory and Application, 99, 23-35(1998).
- Jang, M.J., Chen, C.L., Liy, Y.C., “On Solving the Initial-Value Problems Using the Differential Transformation Method”, Appl. Math. Comput., 115, 145–160(2000). http://dx.doi.org/10.1016/S0096-3003(99)00137-X
- Kuo, B.L., “Applications of the differential transform method to the solutions of the free convection problem”, Appl. Math. Comput., 165, 63-79(2005). http://dx.doi.org/10.1016/j.amc.2004.04.090
- Yeh, Y.L., Wang, C.C., Jang, M.J., “Using Finite Difference and Differential Transformation Method to Analyze of Large Deflections of Orthotropic Rectangular Plate Problem”, Appl. Math Comput., 190, http://dx.doi.org/10.1016/j.amc.2007.01.099 1146-1156(2007).
- Yu, L.T., Chen, C.K., “Application of the Hybrid Method to the Transient Thermal Stresses Response in Isotropic Annular Fins”, J. Appl. Mech., 66, 340- 347(1999).
- Yu, L.T., Chen, C.K., “The solution of the Blasius Equation by the Differential Transformation Method”, Math. Comput. Modeling, 28, 101- 111(1998). http://dx.doi.org/10.1016/S0895-7177(98)00085-5
- Odibat, Z., Bertelle, C., Aziz-Alaoui, M.A., Duchamp, G.H.E., “A multi-step differential transform method and application to non-chaotic and chaotic systems”, Computers and Mathematics with Applications, 59, 1462-1472(2010). http://dx.doi.org/10.1016/j.camwa.2009.11.005
- Wazwaz, A.M., Gorguis, A., “Exact Solutions for Heat-Like and Wave-Like Equations with Variable Coefficients”, Appl. Math Comput., 149, 15- 29(2004). http://dx.doi.org/10.1016/S0096-3003(02)00946-3
Toplam 11 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Mathematics |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Mayıs 2014 |
| Yayımlandığı Sayı | Yıl 2014 Cilt: 27 Sayı: 4 |