The molten metal in the mold flows in different two ways. The molten metal flows inside the metal layers particularly at the tip and flows in contact with the bare surface of the mold remelting solid layers once formed. This report deals with the latter case. If the molten metal flows with a constant velocity in the mold cavity with equal thickness T, the average temperature
θm of the molten metal that flows flows t
1 seconds behind the tip of molten metal is expressed approximately as follows ;
θm=
θp−Mt
2/c
γT√t
1where
θp is the initial molten metal temperature, M is a mold constant, t
2 is the running time from the entrance, c is the specific heat and
γ is the specific weight of the molten metal. The temperature distribution of the molten metal in the normal direction of metal flow is given by a similar expression. The temperature
θ at a distance x from the center is expressed as follows ;
θ=
θm+(MT/8
λ√t
1)(1/3−
ξ2)
where
λ is the thermal conductivity of the molten metal and
ξ is the relative length denoted by
ξ=x/(T/2).
Solutions obtained from those approximate expressions were compared with strict Fourier solution under the condition of the constant heat flux. The approximation results and the strict solutions of
θm agree precisely, and those of
θ agree closely within the range that the dimensionless time (
λ/c
γ)t
2/(T/2)
2 is greater than 0.3.
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