the final solutions are 
b, (r,t) = *(d) coke -F [228s anes | 
TG) PIA RED 2 Eo 
[59] 
Se) way ee crwed pads 00 
Za ie Jo (a, TG. O) 
a He log — oo M. ( 2 
[S0) —s7/3 0 
GO ac@) | i. OSE n 60 
#2 Y Law? fon E mame ee 
K b Rite 
2 
The coefficient D, is 
u? 2(G, - Q) A, 
Pao ea? G (A+ ZS) 2 ed) 2) NelPa8 ace D [61] 
Ky tanga te og 
where A, is the coefficient of the former problem, Equation [41]. The coefficients D, may be 
obtained as functions of M, (8,, 5) instead of No (6, 2) by applying Equation [57]. 
The wire response, or the average temperature increment in the wire ¢, (¢), is obtained 
by integrating ¢, (7, ¢) over the cross-sectional area of the wire 
SO aey i 
2Q(1+F) ies 
Ay) ee b*(b le peel (Ae ee 
bu = age #0) y in, = ab [62] 
n=1 
where F is written for 
1 + Eos 2) 
2 
(2 ates [63] 
Q(pu aa log +) “2 
If » 6 is small enough so that the series expansion can be used for Q/k, , F may be written as 
P=9 Late Noes oa _ 5 uf o4 
Fs G-4 tO 225) [64] 
384 
4k, Q+Z2 + — log 2) 
When the heat conductivity of the wire is large compared with that of the flow medium, F is 
very small compared with unity. 
The following identities are assumed to hold 
14 
