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Question:

Two materials having coefficients of thermal conductivity 3K and K and thickness 'd' and '3d', respectively, are joined to form a slab. The temperature of the outer surfaces are θ₂ and θ₁ respectively, (θ₂>θ₁). The temperature at the interface is?

θ₁3+2θ₂3

θ₁10+9θ₂10

θ₂+θ₁2

θ₁6+5θ₂6

Solution:

Correct option is B. θ₁10+9θ₂10
Let the temperature of interface be θ
i₁=i₂
Steady state conduction
3KA(θ₂-θ)d=KA(θ-θ₁)3d
9θ₂-9θ=θ-θ₁
9θ₂+θ₁=10θ
θ=9θ₂10+θ₁10.