Abstract
To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ (τ is nondimensional time) equals 0.1 near the boundaries of ξ =1 (ξ is nondimensional space coordinate) and ξ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate ξ.
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WANG H J, DAI W Z, LIONEL G H. A finite difference method for studying thermal deformation in a double-layered thin film with imperfect interfacial contact exposed to ultrashort pulsed lasers [J]. International Journal of Thermal Science, 2008, 47: 7–24.
YIN H, WANG L, FELICELLI S D. Comparison of two-dimensional and three-dimensional thermal models of the LENS process [J]. Journal of Heat Transfer, 2008, 130: 1–7.
GE X Y, MIKI W, YAN G G. Analytical solutions for time-dependent heat conduction equation of soil moisture [J]. Nonlinear Analysis: Real World Applications, 2009, 10: 1923–1931.
GANDJALIKHAN S A, MARAMISARAN M. Transient numerical analysis of a multi-layered porous heat exchanger including gas radiation effects [J]. International Journal of Thermal Sciences, 2009, 48: 1586–1595.
LÜ X, LU T, VILJANEN M. A new analytical method to simulate heat transfer process in buildings [J]. Applied Thermal Engineering, 2006, 26: 1901–1909.
VODICKA V. Wärmeleitung in geschichteten kugelundzylinderkörpen[M]. Schweiz: Arch Press, 1950: 297–304.
MIKHAILOV M D, ÖZISIK M N, VULCHANOV N L. Diffusion in composite layers with automatic solution of the eigenvalue problem [J]. International Journal of Heat and Mass Transfer, 1983, 26: 1131–1141.
CARSLAW H S, JAEGER J C. Conduction of heat in solids [M]. London: Oxford University Press, 1959: 218–235.
HUANG S C, CHANG Y P. Heat transfer in unsteady periodic and steady states in laminated composites [J]. Journal of Heat Transfer, 1980, 102: 742–748.
FENG Z G., MICHAELIDES E E. The use of modified Green’s functions in unsteady heat transfer [J]. International Journal of Heat and Mass Transfer, 1997, 40: 2997–3002.
SIEGEL R. Transient thermal analysis of parallel translucent layers by using Green’s functions [J]. Journal of Thermophysics and Heat Transfer, 1999, 13(1): 10–17.
HAJISHEIKH A, BECK J V. Green’s functions partitioning in Galerkin-based integral solution of the diffusion equation [J]. Journal of Heat Transfer, 1990, 112: 28–34.
HEIDEMANN W, MANDEL H, HAHNE E. Computer aided determination of closed form solutions for linear transient heat conduction problems in inhomogeneous bodies [J]. Transactions on Engineering Sciences, 1994, 5: 19–26.
YENER Y, ÖZISIK M N. On the solution of unsteady heat conduction in multi-region finite media with time-dependent heat transfer coefficient [C]//Proceedings of the Fifth International Heat Transfer Conference. Tokyo: JSME, 1974: 188–192.
MONTE F D. Transient heat conduction in one-dimensional composite slab: A ‘natural’ analytic approach [J]. International Journal of Heat and Mass Transfer, 2000, 43: 3607–3619.
MONTE F D. An analytic approach to the unsteady heat conduction processes in one-dimensional composite media [J]. International Journal of Heat and Mass Transfer, 2002, 45: 1333–1343.
SUN Y Z, WICHMAN I S. On transient heat conduction in a one-dimensional composite slab [J]. International Journal of Heat and Mass Transfer, 2004, 47: 1555–1559.
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Foundation item: Projects(50576007, 50876016) supported by the National Natural Science Foundation of China; Projects(20062180) supported by the National Natural Science Foundation of Liaoning Province, China
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Zhou, L., Bai, Ml., Lü, Jz. et al. Theoretical solution of transient heat conduction problem in one-dimensional double-layer composite medium. J. Cent. South Univ. Technol. 17, 1403–1408 (2010). https://doi.org/10.1007/s11771-010-0649-3
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DOI: https://doi.org/10.1007/s11771-010-0649-3