chemical physics of discharges - Argonne National Laboratory

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and -k (%)= h (t-ts) AT f =R
Solving Equations (11) through (15) gives:
and Pn ar,e the first, second, third, etc., roots of the equation:
and . .
PnJI(fin) - I/mr Jo(Pn) =.O
The surface to solid thermal resistance ratio, mr is
I x, = a8/R2
~ and
is :
(18)
frIr = k/hR (19 1
The complete differential equation for the case shown in Fig. 1
the solution to Equation (21) is:
, eqn. 22 becomes: . .
I
If the center temperature defined at r = 0, x = 0 is tc, then
tC’+S
Yc= - = Yr
to ’tS
Y,
where y,
1
and YX are evaluated at r = 0 and x = 0.
i The preceding mathematical analysis shows that the rate of cooling,
lor change in center temperature for a cyclindrical briquette is a function
I of, time (8 ) , density ( e) , thermal conductivity (k) , the surface heat
) transfer coefficient (h) , specific heat (C,) and the briquette dimensions
I as expressed by Equation (23).
The experimental technique can now be described in terms of th;
~p~vious discussion. If the change in center temperature with time is Rsa-
,sued experimentally for a material of known thermal and physical prop-
‘erties (standard briquette) , the surface heat transfer coefficient can be
calculated from Equation (23), since it is the only unknown.
(20)