chemical physics of discharges - Argonne National Laboratory

5 56
then t = to when e = 0
2) the final temperature of the briquette will be the temperature of
the surroundings : I
therefore t = t, when e = *go
3) there is no heat flow across the central plane because of symmetry: {
I
consequently -k (2;) - = 0 at x 0
The heat balance on the briquette surface is made by equating heattrans-
ferred to the surface by conduction with heat transferred from the surfac
by convect&,on.. In differential form, the heat balance is: '
-k dt = h (t - t,) at x = +a
. (a4 %
Newman') showed that the solution to Equations (1) through
in terms of a dimensionless temperature ratio Yx is:
ma
(I+$ ma2 +ma) cospn
where An= and
pn are defined as the first, second, third, etc., roots of
cendental equation:
Pn TAN pn - I /ma = 0
The surface to solid thermal resistahce ratio, ma,
ma = k/ha
and Xa is defined as: xq = ae/a2
where the thermal diffusivity is: a = k/p Cp
(5)
(5) expressed
the trans-
Similarily , considering radial heat transfer , the .radial briquettl
heat balance is
The initial condition equation is:
toto WHEN' 8=0
The final temperature equation is:
t= 1, WHEN 8. -
The boundary condition equations are:
-k (g)=O AT r=O
(7)
(12) i