Determination of unknown thermal coefficients for Storm’s-type materials through a phase-change process

Briozzo, Adriana C.; Natale, María Fernanda; Tarzia, Domingo A.

doi:10.1016/s0020-7462(98)00036-5

Cited by 28 publications

(12 citation statements)

References 8 publications

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“…Proof a)See Briozzo et al b)Taking into account the definitions given by , we have

\lim_{x \to 0^{+}} H (x) = \lim_{x \to 0^{+}} \frac{x}{Q (x)} = \lim_{x \to 0^{+}} \frac{1}{\sqrt{π} \exp (x^{2}) erfc (x)} = \frac{1}{\sqrt{π}} .

From properties of

Q

immediately follow that

H false(+ \infty false) = + \infty

and

H^{'} (x) = \frac{Q (x) - x Q^{'} (x)}{Q^{2} (x)} = \frac{2 x^{2} (1 - Q (x))}{Q^{2} (x)} > 0 .

c)By using , it is easy to see that

M_{1} false(0 false) = - θ^{*} a_{1} a_{2} h \sqrt{π}

and

M_{1}^{'} false(x false) < 0

for

x > 0

. Taking into account that

γ_{0}

is the solution to and from definition of

H

, we have …”

Section: Monotone Dependence Of the Free Boundary With Respect To Thementioning

confidence: 96%

See 1 more Smart Citation

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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“…Proof a)See Briozzo et al b)Taking into account the definitions given by , we have

\lim_{x \to 0^{+}} H (x) = \lim_{x \to 0^{+}} \frac{x}{Q (x)} = \lim_{x \to 0^{+}} \frac{1}{\sqrt{π} \exp (x^{2}) erfc (x)} = \frac{1}{\sqrt{π}} .

From properties of

Q

immediately follow that

H false(+ \infty false) = + \infty

and

H^{'} (x) = \frac{Q (x) - x Q^{'} (x)}{Q^{2} (x)} = \frac{2 x^{2} (1 - Q (x))}{Q^{2} (x)} > 0 .

c)By using , it is easy to see that

M_{1} false(0 false) = - θ^{*} a_{1} a_{2} h \sqrt{π}

and

M_{1}^{'} false(x false) < 0

for

x > 0

. Taking into account that

γ_{0}

is the solution to and from definition of

H

, we have …”

Section: Monotone Dependence Of the Free Boundary With Respect To Thementioning

confidence: 96%

“…where P −1 is the inverse function of P, which is given by (34). For h > h 0 , J is a positive and continuous function, it satisfies…”

Section: Asymptotic Behavior Of the Solution To P 1 When H → +∞mentioning

confidence: 99%

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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“…Remark 15. Explicit solutions for the determination of unknown coefficients are given in (Briozzo et al, 1999) for Storm's type materials.…”

Section: Determination Of One or Two Unknown Thermal Coefficients Thrmentioning

confidence: 99%

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Tarzia¹

2011

Advanced Topics in Mass Transfer

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“…A majority of available studies refer to the onedimensional inverse Stefan problem (see [1][2][3][4][5][6], and references therein), whereas studies regarding the twodimensional inverse Stefan problem are scarce. The first study concerning the 2-D inverse design Stefan problem is Colton's work [7].…”

Section: Numerical Computation Of the Heat Transfer Coefficient In Thmentioning

confidence: 99%

Numerical Computation of the Heat Transfer Coefficient in the 2-D Inverse Design Stefan Problem

Słota¹

2007

AIP Conference Proceedings

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This paper presents an example of the application of a genetic algorithm to a 2-D design problem, which consists in the reconstruction of the function that describes the convective heat transfer coefficient, when the position of the moving interface of the phase change is well-known. In numerical calculations the Tikhonov regularization, the genetic algorithm and the alternating phase truncation method were used. The featured examples of calculations show a very good approximation of the exact solution and the stability of the procedure.

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Determination of unknown thermal coefficients for Storm’s-type materials through a phase-change process

Cited by 28 publications

References 8 publications

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

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

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Numerical Computation of the Heat Transfer Coefficient in the 2-D Inverse Design Stefan Problem

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