In the vulcanization of a rubber article, if the article is thick, the temperature in the interior may never reach the temperature of the heating medium, and unsteady state conduction occurs during the whole cure. Therefere, it is difficult to obtain thick rubber articles cured uniformly. In order to obtain the best performance from the thick vulcanized article, the rate of cure of interior compounds must be adjusted until they show satis factory balance during the curing period. In such a case, the theoretical method for obtaining temperature-time relations at selected points within a rubber article might be very useful. Authors have solved the basic equation for heat conduction in one dimension, assuming the shape of rubber article is a uniform thick slab having constant c, ρ, k, the whole slab is initially at a temperature θ', and one side of surface is exposed to a heating medium of temp θi, the other side of surface is exposed to a heating medium of temp θe, the rate of heat transfer from the heating medium to the surface is infinitely great, the heat of chemical reaction between rubber and sulfur is negligible.
The solution for the temperature θ selected points within a slab is :
θ (p, q) = θ
if
i (p, q) +θ
ef
e (p, q) +θf
0 (p, q)
f
i (p, q) = [1- {p+φ' (p, q)+φ' (p, q)}]
f
e (p, q) = {p+φ' (p, q)}
f
0(p, q)=φ' (p, q)
φ' (p, q) =2/π∞Σ
s= (-1) /S
s2π
2qsin (2S+1) πp
φ' (p, q) =4/π∞Σ
s=01/2S+1
e- (2S+1)
2πqsin (2S+1) πp p=x/a, q=αt/a
2, α=k/cρ
a : thickness, t : time, c : specific heat,
ρ : density, k : Thermal conductivity if θ
i=θ
eθ (p, q) =θ
i {1-f
0 (p, q)} +θ'f
0 (p, q)
Then authors have explained the application of theoretical equation to vulcanization and the practical method for obtaining temperature time relations at selected points within a slab.
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