Exact solution for a Stefan problem with convective boundary condition and density jump

Tarzia, Domingo A.

doi:10.1002/pamm.200700815

Cited by 12 publications

(12 citation statements)

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“…Taking into account the results proved in Tarzia and Tarzia, if the heat transfer coefficient

h

satisfies

h > h_{0} = \frac{k_{2} θ_{0}}{a_{2} \sqrt{π} false(- θ^{*} false)},

then Problem

P_{1}

has a unique similarity type solution given by

θ_{1} false(x, t false) = \frac{- h \sqrt{π} a_{1} θ^{*} ([], erf ((), \frac{x}{2 a_{1} \sqrt{t}}) - erf ((), \frac{γ}{a_{1}}))}{k_{1} + h \sqrt{π} a_{1} erf ((), \frac{γ}{a_{1}})}, 0 < x < s false(t false), t > 0,

θ_{2} false(x, t false) = \frac{θ_{0} ([], erf ((), \frac{γ}{a_{2}} ϵ + \frac{x}{2 a_{2} \sqrt{t}}) - erf ((), \frac{γ}{a_{2}} ((), ϵ + 1)))}{erfc ((), \frac{γ}{a_{2}} ((), ϵ + 1))}, x > s false(t false), t > 0,

where …”

Section: Asymptotic Behavior Of the Solution To P1 When H→+∞mentioning

confidence: 99%

“…We consider the two‐phase Stefan problem for a semi‐infinite material

x > 0,

taking into account a density jump under the change of phase studied in previous studies . The free boundary

s = s false(t false) > 0

, defined for

t > 0

, and the temperatures

θ_{i} false(x, t false), i = 1, 2

satisfying the following conditions (problem

P_{1}

α_{1} θ_{1 x x} = θ_{1 t}, 0 < x < s false(t false), t > 0,

α_{2} θ_{2 x x} + \frac{ρ_{1} - ρ_{2}}{ρ_{2}} \overset{s}{true} false(t false) θ_{2 x} = θ_{2 t}, x > s false(t false), t > 0,

θ_{1} ((), s false(t false), t) = θ_{2} ((), s false(t false), t) = 0, t > 0,

k_{1} θ_{1...}

…”

Section: Introductionmentioning

confidence: 99%

“…We consider the two-phase Stefan problem for a semi-infinite material x > 0, taking into account a density jump under the change of phase studied in previous studies. 15,16 The free boundary s = s(t) > 0, defined for t > 0, and the temperatures i (x, t), i = 1, 2 satisfying the following conditions (problem P 1 ):…”

Section: Introductionmentioning

confidence: 99%

“…From now on, we assume that 1 ≠ 2 ; for most materials, they differ by up to 10% and in extreme cases by up to 30%. 1 In previous studies, 15,16 an explicit solution of similarity type for the temperature of both phases and the solid-liquid interface was obtained. The explicit solution to the particular case 1 = 2 was given in Zubair and Chaudhry.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary

Briozzo

Natale

2020

Math Methods in App Sciences

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We consider a two‐phase Stefan problem for a semi‐infinite body x>0, with a convective boundary condition including a density jump at the free boundary with a time‐dependent heat transfer coefficient of the type hfalse/t, h>0 whose solution was given in D. A. Tarzia, PAMM. Proc. Appl. Math. Mech. 7, 1040307–1040308 (2007). We demonstrate that the solution to this problem converges to the solution to the analogous one with a temperature boundary condition when the heat transfer coefficient h→+∞. Moreover, we analyze the dependence of the free boundary respecting to the jump density.

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“…Taking into account the results proved in Tarzia and Tarzia, if the heat transfer coefficient