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

Both the cylinders are in parallel, for the heat flow from one end as shown So, K_ eq = K₁ A₁+K₂ A₂ A₁+A₂ where, A₁= area of cross-section of inner cylinder = R^2 and A₂= area of cross-section of cylindrical shell aligned & = (2 R)^2-(R)^2 =3 R^2 K_ eq & = K₁ ( R^2 )+K₂ (3 R^2 ) R^2+3 R^2 = 1 4 (K₁+3 K₂ ) aligned