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Exact Solution of Heat Transfer in a Slab with Time-Dependent Boundary Conditions of First Kind
並列摘要
The shifting function method is utilized to find the exact solution for the one dimensional heat conduction of a slab at two surfaces with time-dependent boundary conditions of the first kind. The proposed method is shown to be simple and accurate. Two examples chosen from the literature are given to reveal the methodology. The convergence rate of the present analysis is very fast and we find that when the dimensionless Fourier number is greater than 1.0, the error for the three-term approximation solution of the infinite series solution can be less than 2%. Moreover, we use alternative shifting functions to solve the problem, but we find that more terms of the infinite series solution are required for numerical calculation.
延伸閱讀
- Wu, K. S. Y. (1968). Analytic Solution of Heat Conduction Problem Involving Moving Interface with Spherical Boundaries. Chinese Journal of Physics, 6(2), 80-87. https://www.airitilibrary.com/Article/Detail?DocID=05779073-196810-201310040009-201310040009-80-87
- Wu, K. S. Y. (1968). An Analytic Solution of Heat Conduction Problem with Phase Change. Chinese Journal of Physics, 6(1), 29-38. https://www.airitilibrary.com/Article/Detail?DocID=05779073-196804-201305200001-201305200001-29-38
- Miguel, A. F. (2014). Diffusive Mass Transport in Periodic Boundary Conditions. International Journal of Engineering Practical Research, 3(3), 47-51. https://doi.org/10.14355/ijepr.2014.0303.01
- Chiba, R. (2014). A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab. Abstract and Applied Analysis, 2014(), 326-334-1135. https://doi.org/10.1155/2014/684293