A cylinder of radius r and of thermal conductivity K₁ is surrounded by a cylindrical shell of inner radius r and outer radius 2 r made of a material of thermal conductivity K₂ . The effective thermal conductivity of the system is

Step-by-step solution

Consider a length L of the composite cylinder. The system consists of two cylindrical layers in parallel for radial heat flow. The thermal resistance R of a cylindrical shell of inner radius r₁ , outer radius r₂ , length L , and thermal conductivity K is given by R = (r₂/r₁) 2 K L . For the inner cylinder of radius r , we consider it as a solid cylinder. However, in the context of effective thermal conductivity for radial heat flow, we treat the cross-sectional area. The total cross-sectional area A of the composit