Journal Article10.1007/S00231-015-1579-2
Integral solutions to transient nonlinear heat (mass) diffusion with a power-law diffusivity: a semi-infinite medium with fixed boundary conditions
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TL;DR: In this article, a closed form approximate solution to nonlinear heat (mass) diffusion equation with power-law nonlinearity of the thermal diffusivity has been developed by the integral-balance method avoiding the commonly used linearization by the Kirchhoff transformation.
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Abstract: Closed form approximate solutions to nonlinear heat (mass) diffusion equation with power-law nonlinearity of the thermal (mass) diffusivity have been developed by the integral-balance method avoiding the commonly used linearization by the Kirchhoff transformation. The main improvement of the solution is based on the double-integra- tion technique and a new approach to the space derivative. Solutions to Dirichlet and Neumann boundary condition problems have been developed and benchmarked against exact numerical and approximate analytical solutions avail- able in the literature. List of symbols a Thermal diffusivity (m 2 /s) a0 Thermal diffusivity of the linear problem (m = 0) (m 2 /s) b Coefficient in Eq. (24b) which should be defined trough the ini - tial condition �(t = 0) = 0 C p Specific heat capacity (J/kg)
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References
•Book
Advances in Heat Transfer
J. P. Hartnett,Thomas F. Irvine,Young I. Cho,George Alanson Greene +3 more
- 15 Aug 2003
TL;DR: Advances in Heat Transfer as mentioned in this paper provides in-depth review articles over a broader scope than in traditional journals or texts, which serve as a broad review for experts in the field and are also of great interest to non-specialists who need to keep up to date with the results of the latest research.
1.6K
Theory of Growth of Spherical Precipitates from Solid Solution
TL;DR: In this paper, the radius of a spherical precipitate particle growing in a solid solution of initially uniform composition was shown to be equal to α(Dt)½, where D is the atomic diffusion coefficient, t the time of growth, and α, the growth coefficient, is a dimensionless function of the pertinent compositions.
1K