Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are '$\theta $2' and '$\theta $1' respectively, ($\theta $2 > $\theta $1). The temperature at the interface is :-

Question

Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are '$\theta $₂' and '$\theta $₁' respectively, ($\theta $₂ > $\theta $₁). The temperature at the interface is :-

${{{\theta _1}} \over {10}} + {{9{\theta _2}} \over {10}}$

${{{\theta _2} + {\theta _1}} \over 2}$

${{{\theta _1}} \over {6}} + {{5{\theta _2}} \over {6}}$

${{{\theta _1}} \over {3}} + {{2{\theta _2}} \over {3}}$

Solution

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