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Thin-film evaporation characteristics of molten magnesium and magnesium chloride in a microchannel of titanium sponge

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Abstract

To optimize the distillation process and evaluate evaporation in the production of titanium sponge using the magnesiothermic method, it is necessary to study the microchannel evaporation process of titanium sponge. Combining the kinetic theory, heat transfer theory and augmented Young–Laplace equation, we established an analysis model for titanium sponge micropores and predicted the heat and mass transfer characteristics of the microchannel evaporation meniscus. The model considered the influence of a series of factors such as superheat, wall temperature and channel inclination on heat and mass transfer characteristics of titanium sponge pores. The results show that a high wall temperature and superheat do not necessarily enhance the heat and mass transfer performance of the matrix material and fluid, and the inclination angle of the microchannel has negligible effects on the overall evaporation. In addition, according to the calculation results, the semi-empirical relationship of Nusselt number is obtained. The well uniformity between the numerical calculation results and the fitted results is confirmed through verification.

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Data availability

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Abbreviations

A :

Hamker constant, J

C pl :

Specific heat at constant pressure, J/(kg∙K)

D :

Characteristic length, m

h fg :

Lateral heat of evaporation, J/kg

h lv :

Heat transfer coefficient, W/(m2∙K)

D :

Characteristic length, m

L :

Microchannal length, m

m " :

Evaporation mass flux, kg/(m2∙s)

N u :

Nusselt number

p :

Pressure, Pa

P r :

Prandtl number

R e :

Reynolds Number

q " :

Heat flux, W/m2

T :

Temperature, K

u :

Velocity along x-axis, m/s

x :

X-direction, m

r :

R-direction, m

δ :

Liquid layer thickness, m

δ 0 :

Non-evaporating layer thickness, m

δ ' :

The first derivative of the film thickness with respect to the x-direction

δ ” :

The second derivative of the film thickness with respect to the x-direction

δ ′” :

The third derivative of the film thickness with respect to the x-direction

v :

Kinematic viscosity, m2/s

μ :

Dynamic viscosity, Ns/m2

ρ :

Density, kg/m3

σ :

Surface tension coefficient, N/m

Γ :

Mass flow rate, kg/(m∙s)

κ :

Curvature, m−1

c :

Capillary

d :

Disjoining

l :

Liquid

lv :

Liquid-vapor interface

v :

Vapor

w :

Wall

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Funding

The author acknowledges the financial supported by GuiZhou Provincial Science and Technology Projects [grant numbers QKHJC-ZK 2021-YB 261 and QKHJC 2019-1406], the National Natural Science Foundation of China [grant number 51874108], the Talent Projects of Guizhou University [grant number GDPY 2019-20].

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Authors and Affiliations

  1. School of Materials and Metallurgy, Guizhou University, Guiyang, 550025, People’s Republic of China

    Chengqi Zhang, Wenhao Wang, Hui Yuan, Fuzhong Wu, Xiangwei Hui, Ming Qi & Sen Yang

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  1. Chengqi Zhang
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  2. Wenhao Wang
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  3. Hui Yuan
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  4. Fuzhong Wu
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Contributions

Chengqi Zhang: Investigation, Methodology, Formal analysis, Writing - Original Draft. Wenhao Wang: Supervision, Validation, Writing - Review & Editing, Funding acquisition. Hui Yuan: Writing - Original Draft. Fuzhong Wu: Conceptualization, Project administration, Funding acquisition. Xiangwei Hui: Validation. Ming Qi: Validation. Sen Yang: Validation.

Corresponding author

Correspondence to Fuzhong Wu.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Appendix

Appendix

Table 4 The relative error between the numerically calculated Nu number and the fitted Nu number is for Mg
Full size table
Table 5 The relative error between the numerically calculated Nu number and the fitted Nu number is for MgCl2
Full size table

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Zhang, C., Wang, W., Yuan, H. et al. Thin-film evaporation characteristics of molten magnesium and magnesium chloride in a microchannel of titanium sponge. Heat Mass Transfer 59, 2241–2254 (2023). https://doi.org/10.1007/s00231-023-03411-6

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  • DOI: https://doi.org/10.1007/s00231-023-03411-6

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