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

Step-by-step solution

Let q 1 and q 2 be the rate of flow of heat through inner part from outer part respecting net flow of heat q = q 1 + q 2 = K 1 π R 2 l . Δ T + K 2 . π 2 R 2 - R 2 l . Δ T = π R 2 l Δ T K 1 + 3 K 2 If the cylinder is replaced by a single material of thermal conductivity K then q = K . 2 R 2 l . Δ T On comparison, K = K 1 + 3 K 2 4 .