A solid cylinder of radius 
, made of a material of thermal conductivity 
is surrounded by a hollow cylinder of inner radius 
and outer radius 
made of material of thermal conductivity 
. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
Text Solution
Verified by ExpertsB
It is given that solid cylinder of radius 
(made of a material of thermal conductivity 
is surrounded by a hollow cylinder of inner radius 
and other radius 
(made of material of thermal conductivity 
).
Rate of flow of heat in the combined system = Rate of flow of heat through cross-section of inner cylinder + Rate of flow of heat through cross-section of outer cylinder
= 
KA 
K 
So, the effective thermal conductivity of the system is 
.
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