Radiation–Conduction Heat-Transfer Study for Mold Flux by Thermoviewer-Enhanced Infrared Emitter Technique

  • Wanlin Wang
  • Kaixuan Zhang
  • Haihui ZhangEmail author


A thermoviewer-enhanced infrared emitter technique was developed in this article to study the heat-transfer behavior of mold flux in the continuous casting mold. Then, a radiation–conduction heat-transfer model was built to determine the radiative/conductive heat flux, thermal conductivity, and optical properties of slag. The results showed that the mold/slag interfacial thermal resistance decreases with the increasing temperature of slag surface at the mold side, and then reaches the minimum when the slag surface is the hottest, and finally increases slightly with further increase in slag crystallization. In addition, the radiative heat flux decreases with the increasing depth of radiation propagating into the slag. While the amount of heat of radiation lost is being converted to produce an additional radiative heat source to heat the slag, the increase in the conductive heat flux in the slag is realized. Furthermore, the apparent transmittivity is obtained as 0.63 for the glassy slag disk and as 0.41 for the partially crystallized slag disk. Besides, when mold heat flux decreases from the maximum to a saturation value due to the further slag crystallization, the corresponding apparent transmittivity of slag disk decreases from 0.58 to 0.41, and the ratio of the heat across the slag disk by radiation decreases from 67.3 to 50.0 pct.



Specific heat (J/kg·K)


Stefan–Boltzmann constant, 5.670 × 10−8 W/m2 K4


Thickness of slag disk (m)


Exponential integral function


Incident radiation (W·m−2)


Convective heat-transfer coefficient (W/m2 K)


Intensity of radiation (W/m2sr)


Blackbody intensity (Planck function) (W/m2sr)


Free path of phonons (m)


Total number of measurement (–)


Point of maximum temperature in the slag (mm)


Refractive index of slag bottom surface (–)


Refractive index of slag top surface (–)


Heat flux (W m−2)


Bare copper heat flux (W m−2)


Conductive flux in the slag (W m−2)


Radiative flux of infrared lamp (W m−2)


Mold heat flux (W m−2)


Radiative flux in the slag (W m−2)


Thermal resistance between mold and slag (m2 K W−1)


Geometric path length (m)

\( \hat{s} \)

Unit vector into a given direction (–)


Temperature (K))


Temperature of slag bottom surface (K)


Slag top surface temperature (K)


Temperature of ambient air (K)


Temperature of mold surface (K)


Sonic velocity (m/s)

x, y, z

Cartesian coordinates (m)

Greek Symbols


Extinction coefficient (m−1)


Extinction coefficient of j-th medium (m−1)


Emissivity of mold–slag interface (–)


Emissivity of air–crystal interface (–)


Emissivity of mold surface (–)


Angle between the direction of the radiation intensity and the positive vertical direction (rad)


Thermal conductivity (W/m K)


Radiation conductivity (W/m K)


Absorption coefficient (m−1)


Absorption coefficient of j-th medium (m−1)


Direction cosine (of polar angle), cosθ (–)


Density (kg/m3)


Reflectivity of mold–slag interface (–)


Reflectivity of air–crystal interface (–)


Reflectivity of mold surface (–)


Scattering coefficient (m−1)

σs ,j

Scattering coefficient of j-th medium (m−1)


Optical depth τ(z) =  \(\int\nolimits_{0}^{z} \beta dz\)(–)


Slag optical thickness (–)


Single scattering albedo (–)


Single scattering albedo of j-th medium (–)


Azimuthal angle (rad)


Solid angle (sr)





Glass (g), crystal (c)


Copper mold







The financial supports from the National Natural Science Foundation of China (51661130154, 51704333, and U1760202), Newton Advanced Fellowship (NA150320), and the Fundamental Research Funds for the Central Universities of Central South University (2018zzts437) are gratefully acknowledged.


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  1. 1.School of Metallurgy and EnvironmentCentral South UniversityChangshaChina

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