A cylinder of radius `R` made of a material of thermal conductivity `K_(1)` is surrounded by cylindrical shell of inner radius `R` and outer radius `2R` made of a material of thermal con-ductivity `K_(2)` The two ends of the combined system are maintained at two differnet tem-peratures There is no loss of heat across the cylindrical surface and system is in steady state What is the effective thermal conductivity of the system
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A cylinder of radius r made of a material of thermal conductivity K_1 is surrounded by a cylindrical shell of inner radius r and outer radius 2r made of a material of thermal conductivity K_2 . 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. Show that the effective thermal conductivity of the system is (K_1 + 3K_2 )//4 .

A solid cylinder of radius R made of a material of thermal conductivity K_(1) is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of material of thermal conductivity K_(2) . 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

A cylinder of radius R made of a material of thermal conductivity K_1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K_2 . 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

A cylinder of radius R made of a material of thermal conductivity K_1 is surrounded by a cylinderical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K_2 . 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 effictive thermal conductivity of the system is

A cylinder of radius R made of a material of thermal conductivity K_1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K_2 . 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 (a) K_1 + K_2 (b) K_1K_2//(K_1+K_2) (c ) (K_1 + 3K_2)//4 (d) (3K_1 + K_2)//4 .

A cylinder of radius R made of a material of thermal conductivity K_1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K_2 . 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 (a) K_1 + K_2 (b) K_1K_2//(K_1+K_2) (c ) (K_1 + 3K_2)//4 (d) (3K_1 + K_2)//4 .