where A) is the resistivity of the wire at a reference temperature 7) and a is the thermal co- 
efficient of resistance. The average wire temperature is given by 
9 (b 
T = ai T*(r) rdr [2] 
0 
In the steady state, the temperature in the wire and in the coating are solutions of the 
following differential equations. 
rsb 
Cite 
MBP LED alae |p e 
r dr dr a [3] 
OeSiee Sia 
ve (eae 
r df dr 
where starred quantities refer to steady state values and the subscripts 1 and 2 refer, respec- 
tively, to the wire and coating. The source strength uw? is 
2 
9 ye 
tae 7 b4 K 
[4] 
where x, is the thermal conductivity of the wire. 
At the outer surface of the coating, the wire is cooled by forced convection. The heat 
flux in such cases is proportional to the temperature difference between the coating surface 
and the flow medium. At the center of the wire the temperature must be finite. The two 
boundary conditions are 
dale 
kya ( 2) a {PD [T,*(a) - el =0 
: [5] 
T*() A es 
From King’s study of the heat convection from small cylinders in a moving stream, the propor- 
tionality factor P is the following function of the velocity and properties of the flow medium.? 
p= 2(Y— +1) - $3/ ODS Saale a2 ea) [6] 
27 UY 27 kK, 
where P3rCy > and kK, are, respectively, the density, specific heat, and thermal conductivity 
of the flow medium. In addition to the boundary conditions at r = a and r = O, there are two 
compatibility conditions which apply at r= 6. These conditions require that the temperature 
and heat flux be continuous across the interface. 
