An Efficient Algorithm for Finite-Difference Analyses of Heat Transfer With Melting and Solidification

Hsiao, J. S.

doi:10.1080/01495728508961877

Cited by 61 publications

(11 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The governing equations are discretized using a finite volume formulation and solved using the SIMPLE algorithm. To incorporate the equivalent heat capacity model in the finite volume formulation for phase change problem, the idea of averaged heat capacity used by Hsiao [17] is employed. The equivalent heat capacity defined in cannot be used directly to yield the heat capacity of system.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…The heat capacity method introduces the latent heat effect onto the heat capacity of the material over the phase‐transition temperature interval [15, 16]. Of the procedures presented, the technique of Hsiao [17] is attractive because both zero and large temperature intervals in the mushy zone can be simulated. Generally, these methods are the easiest but the least accurate in the single‐domain methods.…”

mentioning

confidence: 99%

“…The finite volume formulation was used for the current research. The average heat capacity model developed by Hsiao [17] was implemented for the analysis of conjugate heat transfer during phase change. This algorithm determines the physical status, namely liquid, mushy and solid phases, associated with each node.…”

mentioning

confidence: 99%

See 2 more Smart Citations

A numerical simulation of the DC continuous casting using average heat capacity

Korti

Khadraoui

2004

Scand Jof Metallurgy

View full text Add to dashboard Cite

Continuous casting is one of the prominent methods of production of metals. The effective design and operation of continuous casting machines needs complete analysis of the continuous casting process. In this paper, a finite volume model has been developed and applied to compute the fluid flow, temperature and flux distributions within the liquid, mushy and solid zones in the mold and cooling regions of an aluminum alloy direct‐chill continuous casting machine. The average heat capacity method was successfully implemented for the analysis of conjugate heat transfer during the phase change phenomenon. The effect of phase change on convection is accounted for using a new modification in the velocity vector. The effect of casting speed on fluid flow, temperature and surface heat flux evolution was investigated. The predicted temperature distribution and surface heat flux were compared with experimental measurements and numerical solutions given in the literature. A reasonable agreement was obtained.

show abstract

Section: Numerical Proceduresmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

A numerical simulation of the DC continuous casting using average heat capacity

Korti

Khadraoui

2004

Scand Jof Metallurgy

View full text Add to dashboard Cite

show abstract

“…The single domain methods most extensively used in casting modeling are (a) Enthalpy methods, which rewrites the heat equation in terms of the enthalpy [Voller and Prakash (1987); Swaminathan and Voller (1997)]. (b) Effective specific heat methods, which replaces the specific heat by a fictitious coefficient called effective specific heat that accounts for the latent heat released in the interphase [Bonacina et al(1973); Hsiao (1985); Khadraoui et al(2000)]. [Nigro et al (2000)] present a phasewise discontinuous numerical integration method to solve thermal phase change problems in a fast and accurate way.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Fluid Flow and Heat Transfer During the Initial Phase Leading to Steady State Solidification in D. C. Cast Aluminum Alloys

Korti

2010

Int. J. Comput. Methods

View full text Add to dashboard Cite

In this paper, two dimensional unsteady flow and energy equations are employed for simulating the fluid flow, heat transfer and solidification during direct chill continuous casting of Al-Mg alloy billet. In these processes, the formation of some macro defects such as thermal cracking, hot tearing, surface cracking, etc, has been found to initiate during the starting phase of the operation. In this paper, a numerical study of these developing fluid flow and thermal phenomena from the beginning of casting operation to a steady-state is presented. The computations are based on an iterative deforming finite volume method and a single-domain enthalpy formulation to solve the growth of metal being solidified and the accompanying dynamic fluid flow and thermal behavior. The effect of phase change on convection is accounted for using a Darcy's law-type porous media treatment. The results indicate that the fluid flow and temperature fields change drastically at the initial stage but evolve slowly afterwards.

show abstract

“…Both groups could provide reasonably accurate results [24]. Two major methods in the fixed-grid schemes are used to solve the phase-change problems: the enthalpy method [25] and the equivalent heat capacity method [26,27]. Cao and Faghri combined the advantages of enthalpy and equivalent heat capacity methods and proposed a temperature transforming model (TTM) [28].…”

mentioning

confidence: 99%

Numerical Simulation of Melting in Porous Media via an Interfacial Tracking Model

Chen¹,

Yang²,

Zhang³

et al. 2011

Journal of Thermophysics and Heat Transfer

View full text Add to dashboard Cite

Melting in porous media within a rectangular enclosure with the presence of natural convection is simulated using an interfacial tracking method. This method combines the advantages of both the deforming and fixed-grid methods. Convection in the liquid region is modeled using the Navier-Stokes equation with Darcy's term and Forchheimer's extension. The results are obtained by using the interfacial tracking method, which is validated by comparing with the existing experimental and numerical results. The results show that the interfacial tracing method is capable of solving natural convection-controlled melting problems in porous media at both high and low Prandtl numbers.thermal conductivities, k=k ' K = modified dimensionless thermal conductivity K s' = ratio of thermal conductivities, k s =k ' k ' = thermal conductivity in liquid, W=m K Nu = Nusselt number at heated wall, hH=k ' P = dimensionless pressure, pH 2 = 2 l Pr = Prandtl number of liquid phase-change materials, ' = ' p = pressure, Pa Ra = Rayleigh number, Gr Pr S = dimensionless location of solid-liquid interface, s=H Ste = Stefan number, c ' T h T m =h s' s = location of solid-liquid interface, m S 0 = dimensionless location of solid-liquid interface at last time step T = temperature, K t = time, s U = dimensionless velocity in x direction, uH= ' u = velocity component in x direction, m=s U I = dimensionless solid-liquid interfacial velocity, u I H= ' u I = solid-liquid interfacial velocity, m=s, @s=@t V = dimensionless velocity in y direction, vH= ' , or volume, m 3 v = velocity component in y direction, m=s W = width of enclosure, m X = dimensionless coordinate, x=H x = dimensional coordinate, m Y = dimensionless coordinate, y=H y = dimensional coordinate, m = thermal diffusivity, m 2 =s = liquid fraction in Eq. (2) = liquid fraction in Eq. (3) " = porosity = dimensionless temperature, T T m =T h T m = permeability, m 2 = viscosity of the liquid phase-change materials, kg=ms = kinematic viscosity, m 2 =s = density, kg=m 3 = dimensionless time, ' t=H 2 = heat capacity ratio, c=c ' Subscripts c = cold E = east e = east face of control volume eff = effective f = fluid h = heated I = interface i = initial ' = liquid m = melting point N = north n = north face of control volume p = porous matrix ref = reference S = south s = solid W = west w = west face of control volume

show abstract

An Efficient Algorithm for Finite-Difference Analyses of Heat Transfer With Melting and Solidification

Cited by 61 publications

References 14 publications

A numerical simulation of the DC continuous casting using average heat capacity

A numerical simulation of the DC continuous casting using average heat capacity

Numerical Simulation of Fluid Flow and Heat Transfer During the Initial Phase Leading to Steady State Solidification in D. C. Cast Aluminum Alloys

Numerical Simulation of Melting in Porous Media via an Interfacial Tracking Model

Contact Info

Product

Resources

About