A solid cylinder of radius 
made of a material of thermal conductivity 
is surrounded by a cylindrical shell of inner radius 
and outer radius 
made of a material of thermal conductivity 
. The two ends of the combined system are maintained at two different temperatures. Then 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
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Area of cross-section of inner cylinder 
Area of cross-section of outer shell
Rate of heat flow in inner cylinder
Rate of heat flow in outer shell
Rate of heat flow in the combined system
At steady state, 
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