On the Stefan Problem With Nonlinear Thermal Conductivity
Keyword(s):
The solution is obtained and validated by an existence and uniqueness theorem for the following nonlinear boundary value problem \[ \frac{d}{dx}(1+\delta y+\gamma y^{2})^{n}\frac{dy}{dx}]+2x\frac{dy}{dx}=0,\,\,\,x>0,\,\,y(0)=0,\,\,\,y(\infty)=1, \] which was proposed in 1974 by [1] to represent a Stefan problem with a nonlinear temperature-dependent thermal conductivity on the semi-infinite line (0;1). The modified error function of two parameters $\varphi_{\delta,\gamma}$ is introduced to represent the solution of the problem above, and some properties of the function are established. This generalizes the results obtained in [3, 4].
2003 ◽
Vol 41
(15)
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pp. 1685-1698
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1997 ◽
Vol 20
(4)
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pp. 537-540
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2010 ◽
Vol 9
(5)
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pp. 1209-1220
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1994 ◽
Vol 17
(2)
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pp. 130-134
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1991 ◽
Vol 18
(4)
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pp. 503-516
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2017 ◽