A composite slab consists of two materials having coefficients of thermal conductivity K and 2 K , thickness x and 4 x respectively. The temperatures of two outer surfaces of a composite slab are T₂ and T₁ respectively ( T ₂> T ₁ ). The rate of heat transfer through the slab in a steady state is [ A (T₂-T₁ ) K x ] f , where f is equal to

Step-by-step solution

The thermal resistance for a material is given by R = L KA , where L is thickness, K is thermal conductivity, and A is cross-sectional area. For material 1 with thickness x and conductivity K , R₁ = x KA . For material 2 with thickness 4x and conductivity 2K , R₂ = 4x 2KA = 2x KA . The total resistance for materials in series is R_ total = R₁ + R₂ = x KA + 2x KA = 3x KA . Heat transfer rate is Q t = T R_ total = T₂ - T₁ 3x KA = A(T₂ - T₁)K 3x . Comparing with the given form [ A(T₂-T₁) K x ] f , we find f = 1 3 . Fi