There is a method using semilogarithmic graph paper known as the graphical analysis method to analyze heat conduction in a cylinder. This method is sometimes troublesome because the logarithmic scale has to be transformed into a normal scale after semilogarithmic plotting. In the new method of graphical analysis shown in this work, nornal scale section paper can be used by adding supplementary lines before plotting. The principle of this method is based on the one dimentional difference equation of the polar coordinates, in which difference of the time
Δt is defined as follows :
Δt=
Δr
2c
γ/4
λ, where
Δr is the difference of the radial distance, c is the specific heat,
γ is the specific weight and
λ is the heat conductivity of the cylinder. Therefore, this new method can be easily converted to simple numerical calculation.
When the front of the molten metal passes through the mold cavity, a thin solid metal layer covers the surface of the cavity everywhere. The average temperature
θm at the cross section of the molten metal flowing inside the metal layer is expressed by the equations approximately :
Θm=1 −2√
τ⋅⋅⋅⋅⋅⋅
τ<0.063
Θm=0.72 exp (−5.82
τ)⋅⋅⋅⋅⋅⋅
τ>0.063
where
Θm=(
θm−
θf)/(
θp−
θf),
θf is the melting point,
θp is the initial temperature of the molten metal with an uniform temperature distribution and
τ is the dimentionless time defined by the expression (
λ/c
γ)t/r?? in which t is the time.
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