Two slabs of different materials are connected in parallel between two temperature reservoirs. Both slabs have the same uniform thickness. The first slab has a cross-sectional area A and thermal conductivity K . The second slab has a cross-sectional area 2A and thermal conductivity 3K . What is the equivalent thermal conductivity of the composite parallel combination?

Step-by-step solution

For a parallel combination of thermal conductors, the total rate of heat flow is the sum of the individual rates of heat flow: H_ eq = H₁ + H₂ Let T be the temperature difference and L be the thickness of the slabs. The equivalent thermal conductivity K_ eq is defined for the total area A_ eq = A₁ + A₂ = A + 2A = 3A . K_ eq (3A) T L = K₁ A₁ T L + K₂ A₂ T L Substituting the given values: K_ eq (3A) = K(A) + (3K)(2A) 3 K_ eq A = KA + 6KA 3 K_ eq A = 7KA K_ eq = 7K 3 Answer: 7K 3