TEMPORAL DIFFERENTIAL TRANSFORM AND SPATIAL FINITE DIFFERENCE METHODS FOR UNSTEADY HEAT CONDUCTION EQUATIONS WITH ANISOTROPIC DIFFUSIVITY

Objective & Hypothesis: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.

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Key Findings & Data: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.

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Conclusion & Impact:Normal 0 21 false false false TR X-NONE X-NONE

🔬Design:Article

📍Scope:Comprehensive Sample

⚙️Variables:Differential Transform Method · Finite-difference approximation · Heat conduction

Abstract

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. Normal 0 21 false false false TR X-NONE X-NONE

Keywords

Differential Transform Method Finite-difference approximation Heat conduction anisotropic diffusivity time-dependent heating

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Cite This Article

Süngü, İ. Ç., Sungu, İ. C., Demir, H., Demır, H. (2014). TEMPORAL DIFFERENTIAL TRANSFORM AND SPATIAL FINITE DIFFERENCE METHODS FOR UNSTEADY HEAT CONDUCTION EQUATIONS WITH ANISOTROPIC DIFFUSIVITY. Gazi University Journal of Science, Volume: 27 Issue: 4. https://ajindex.com/articles/1269648

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References (11)

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