A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and oputer radius 2R. The thermal conductivity of the material of the inner cylinder si `k_(1)` and that of the outer cylinder is `K_(2)` ,Assumming no loss of heat , the effective thermal conductivity of the system for heat flowing along the length of the cylionder is :

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and oputer radius 2R. The thermal conductivity of the material of the inner cylinder is k_(1) and that of the outer cylinder is K_(2) ,Assumming no loss of heat , the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

A cylinder of radius R made of material of thermal conductivity K_(1) is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity K_(2) . The two ends of the combined system are maintained at two different temperatures. What is the effective thermal conductivity of the system ?

Calculated thermal conductance for radial flow of a spherical sheel of inner and outer radius r_(1) and r_(2) . Assume that thermal conductivity of the material is K

Calculated thermal conductance for radial flow of a spherical sheel of inner and outer radius r_(1) and r_(2) . Assume that thermal conductivity of the material is K

A copper cylindrical tube has inner radius a and outer radius b. The resistivity is p. The resistance of . the cylinder between the two ends is

A copper cylindrical tube has inner radius a and outer radius b. The resistivity is p. The resistance of . the cylinder between the two ends 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. 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