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WOLFRAM NOTEBOOK
Thermal Distribution in an Optical Fiber with Heat Source
Thermal Distribution in an Optical Fiber with Heat Source
The power efficiency of fiber lasers is often determined by the core temperature distribution in the fiber. The optical fiber is modeled as a doped inner core of radius and a cladding region of thickness . The length of the optical fiber is . The thermal conductivity of the inner core is taken to be and the cladding region is . The heat density within the inner core is taken to be , where is a suitable absorption coefficient. The temperature within the inner core is denoted by and the temperature in the cladding as . The thermal boundary conditions on the optical fiber are as follows. The outer surface of the cladding is subject to Newton's law of cooling with a specified heat transfer coefficient :
R
0
h=-
R
1
R
0
L
k
0
k
1
q(z)=Ω
-αz
α
T
1
T
2
h
∂
T
2
∂r
h
k
1
T
2
T
0
Newton's law of cooling is also assumed for the ends of the fiber containing cladding. Thus for the cladding region:
∂
T
2
∂r
h
k
1
T
2
T
0
z=0
z=L
At we specify a heat flux for the inner core:
z=0
∂
T
1
∂r
q
0
R
0
k
0
z=0
At we assume Newton's law of cooling for the inner core:
z=L
∂
T
1
∂r
h
k
0
T
1
T
0
z=L
This Demonstration finds the temperature distribution both in the cladding and core region for user-set values of the Biot number , thermal conductivities ratio , dimensionless heat generation , and dimensionless absorption coefficient . In order to obtain this distribution, a finite difference scheme is applied as described in depth in Details.
Bi
β
γ
Ω