Abstract
A numerical analysis of transient heat transfer during the flow of a melt in a cylindrical mould is presented. The analysis includes thermal resistance at the melt-mould interface, and axial conduction inside both melt and mould. Energy equations are formulated in a domain that expands continuously due to the advance of the melt inside the empty mould, and solved by the finite difference method using a time-stepping procedure. Calculations are compared to existing analytic results. It is found that axial conduction in the melt can significantly influence the rate of heat loss from the flowing melt, and that analytic approximations, which neglect axial conduction, may give erroneous predictions for the rate of heat loss.
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Abbreviations
- c :
-
specific heat
- h :
-
heat transfer coefficient
- k :
-
thermal conductivity
- l :
-
liquid
- L :
-
length
- m :
-
mould
- Q :
-
heat content
- r :
-
radius from axis of channel
- R c :
-
cooling rate
- t :
-
time
- t c :
-
cooling time
- T :
-
temperature
- T f :
-
fusion temperature
- T i :
-
interface temperature
- T 0 :
-
room temperature
- T p :
-
pouring temperature
- u :
-
liquid velocity
- x :
-
distance along channel
- ϱ :
-
density
- α :
-
thermal diffusivity
- δ :
-
spatial grid spacing
- Δt :
-
time-step
- Δx :
-
distance travelled in Δt
- Δθ :
-
non-dimensional superheat
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Hanumanth, G.S., Scott, D.M. & Smith, T.J. A numerical study of heat transfer during flow of melt in a cylindrical mould. Appl. Sci. Res. 46, 323–333 (1989). https://doi.org/10.1007/BF01998549
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DOI: https://doi.org/10.1007/BF01998549