Não Ferrosos

Determination of unidirectional heat transfer coefficient during

unsteady-state solidification at metal casting–chill interface

Hacı Mehmet S
ahin a,*, Kadir Kocatepe a, Ramazan Kayıkcı b, Nes
et Akar a

a Gazi U¨ niversitesi, Teknik Eg˘ itim Faku¨ ltesi, Teknikokullar, Ankara 06503, Turkey

b Sakarya U¨ niversitesi, Teknik Eg˘ itim Faku¨ ltesi, Sakarya, Turkey

Received 9 October 2004; accepted 30 March 2005

Available online 11 May 2005

Abstract

In this study, the interfacial heat transfer coefficient (IHTC) for vertically upward unidirectional solidification

of a eutectic Al–Si casting on water cooled copper and steel chills was measured during solidification.

A finite difference method (FDM) was used for solution of the inverse heat conduction problem

(IHCP). Six computer guided thermocouples were connected with the chill and casting, and the time–

temperature data were recorded automatically. The thermocouples were placed, located symmetrically,

at 5 mm, 37.5 mm and 75 mm from the interface. As the lateral surfaces are very well heat isolated, the

unidirectional solidification process starts vertically upward at the interface surface. The measured time–

temperature data files were used by a FDM using an explicit technique. A heat flow computer program

has been written to estimate the transient metal–chill IHTC in the IHCP. The experimental and calculated

temperatures have shown excellent agreement. The IHTC during vertically upward unidirectional solidification

of an Al–Si casting on copper and steel chills have varied between about 19–9.5 kW/m2 K and 6.5–

5 kW/m2 K, respectively.

2005 Elsevier Ltd. All rights reserved.

Keywords: Casting–mold interface; Heat transfer coefficient; Al–Si eutectic

0196-8904/$ - see front matter
2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2005.03.021

* Corresponding author. Tel.: [phone]; fax: [phone].

E-mail address: [e-mail] (H.M. S
ahin).

www.elsevier.com/locate/enconman

Energy Conversion and Management 47 (2006) 19–34

1. Introduction

The subject of metal–chill interfacial heat transfer, because of its important influence on the

solidification rate of metal castings, has been investigated by several previous studies. Some

researchers have studied the heat transfer mechanism of castings to find the influencing factors

on the IHTC as well as the macroheat transfer values. In these previous works, the IHTC has been

dependent on many factors including the presence and thickness of surface coatings, casting surface

orientation and casting size, chill or mold material, applied pressure, alloy type and composition,

liquid alloy surface tension, mold and chill preheat, alloy superheat and chill surface

roughness [1–11]. The effects of the direction of gravity in relation to the interface have been

examined by investigation with the chill placed on the bottom, top or side of the mold [1].

An exact estimation of the heat transfer during the liquid alloy solidification in a casting mold

depends on determination of the boundary conditions during the solidification, properties of the

mold, properties of the casting alloy temperature distribution in the casting. During the solidification,

these parameters are changing as a function of temperature and time. For the purpose of

Nomenclature

_q

heat flux, W/m2

q000 heat generation rate per unit volume, W/m3

h interfacial heat transfer coefficient, W/m2 K

TC temperature of casting surface, K

TM temperature of mold (chill) surface, K

T temperature, K

t time, s

x distance, m

k thermal conductivity, W/m K

C specific heat capacity, J/kg K

M sub-region number

l latent heat, J/kg

L length, m

Greek symbols

q density of material, kg/m3

Dt time interval

Dx distance interval

Subscript

m node point

Superscript

p time denoted

20 H.M. S
ahin et al. / Energy Conversion and Management 47 (2006) 19–34

accurate modeling of solidification processes, it is required that correct boundary conditions

should be set up [12–14].

Estimation of the heat transfer coefficient in a metal casting–chill interface is usually calculated

from time–temperature data measured during the solidification of a unidirectional chilled experimental

casting. The casting alloy and chill material used for experimental casting are, generally,

made of