An Efficient Algorithm for Finite Element Solution to Two-Dimensional Heat Transfer With Melting and Freezing

Hsiao, J. S.; Chung, Benjamin T.F.

doi:10.1115/1.3246948

Cited by 32 publications

(17 citation statements)

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“…It is worth mentioning here that C (in the governing equation of the liquid-solid interface) is the averaged specific heat for the solid and liquid in the temperature range T ph -DT and T ph + DT, and bL accounts for the latent heat effect where b = 1/(2 DT) and (2 DT) is a small but finite temperature interval assumed for phase change to take place, as given in Hsiao and Chung (1986). The heat transfer coefficient in the governing equations, summarized in Table I, is assumed constant for specific freezing product shape and dimension.…”

Section: Mathematical Modelmentioning

confidence: 99%

Freezing time calculations for various products

Mokheimer

El-Aziz

Amin³

et al. 2003

Int. J. Energy Res.

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SUMMARYThis article presents a numerical simulation that estimates the freezing time for different products. In this regard, the freezing process is mathematically modelled by transient heat conduction equations that incorporate the physical properties of the three distinct regions that exist during a freezing process. These regions are namely, the solid phase region, the liquid phase region and the interface region. This model is experimentally validated and used to estimate the freezing time for three different food products, which are namely, fish balls, cherry juice and peas balls. The freezing times estimated numerically through the present model agree well with those reported in the literature and are in excellent agreement with the experimental data.

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Section: Mathematical Modelmentioning

confidence: 99%

Freezing time calculations for various products

Mokheimer

El-Aziz

Amin³

et al. 2003

Int. J. Energy Res.

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show abstract

“…The specific heat capacity in the solidification area is calculated by an algorithm which estimates the mass fractions of the different phases inside the freezing element. [51] This method is used in the stationary period of the casting process, when the accuracy of the time-derivative term in the energy Eq. [14] is of less importance, since this term approaches zero at stationary conditions (the convective terms are evaluated explicitly from the enthalpy field).…”

Section: B Energy Equationmentioning

confidence: 99%

A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

Mortensen

1999

Metall Mater Trans B

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A finite-element method model for the time-dependent heat and fluid flows that develop during directchill (DC) semicontinuous casting of aluminium ingots is presented. Thermal convection and turbulence are included in the model formulation and, in the mushy zone, the momentum equations are modified with a Darcy-type source term dependent on the liquid fraction. The boundary conditions involve calculations of the air gap along the mold wall as well as the heat transfer to the falling water film with forced convection, nucleate boiling, and film boiling. The mold wall and the starting block are included in the computational domain. In the start-up period of the casting, the ingot domain expands over the starting-block level. The numerical method applies a fractional-step method for the dynamic Navier-Stokes equations and the ''streamline upwind Petrov-Galerkin'' (SUPG) method for mixed diffusion and convection in the momentum and energy equations. The modeling of the start-up period of the casting is demonstrated and compared to temperature measurements in an AA1050 200 ϫ 600 mm sheet ingot.

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“…Pour des applications pratiques, on a généralement recours à des méthodes numériques. Les méthodes des différences finies (Lazaride, 1970;Bonacina et Comini et Fasans et Primiceris, 1973) et des éléments finis (Comini et al 1974;Rolph III et Bathe, 1982;Hsiao et Chung, 1984) sont parmi les plus utilisées (Furzeland,1980;Crank, 1981;Crank, 1984).…”

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Simulation du transfert de chaleur lors du changement de phase solide-liquide d'une substance pure /

Li¹

1990

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An Efficient Algorithm for Finite Element Solution to Two-Dimensional Heat Transfer With Melting and Freezing

Cited by 32 publications

References 0 publications

Freezing time calculations for various products

Freezing time calculations for various products

A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

Simulation du transfert de chaleur lors du changement de phase solide-liquide d'une substance pure /

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