To study the frequency response of the embedded thermocouple we consider the surface temperature to fluctuate as with unit amplitude. The amplitude of temperature along the axis as a function of will determine the extent of attenuation of the surface signal before it reaches the thermocouple. At any location in the shield the diffusion equation is valid and expressed as
where is thermal diffusivity of the metallic shield. Let . Hence satisfies
with unit amplitude. The amplitude of temperature along the axis as a function of 
will determine the extent of attenuation of the surface signal before it reaches the thermocouple. At any location in the shield the diffusion equation is valid and expressed as 
is thermal diffusivity of the metallic shield. Let 
. Hence 
satisfies 
and the second boundary condition is 
