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

Question

Two materials having coefficients of thermal conductivity

3 K

and

K

and thickness

d

and

3 d

respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are

θ_{2}

and

θ_{1}

respectively,

(θ_{2} > θ_{1}) .

The temperature at the interface is

Aicharya · Accepted Answer

Let the temperature of the junction T ° C . Rate of heat flow in Rod 1 = rate of heat flow in Rod 2 3 kA d θ 2 - T = kA 3 d T - θ 1 ⇒ 9 θ 2 - T = T - θ 1 ⇒ 10 T = 9 θ 2 + θ 1 ⇒ T = 9 θ 2 + θ 1 10 = θ 1 10 + 9 θ 2 10

Two materials having coefficients of thermal conductivity 3 K and K and thickness d and 3 d respectively,…

Solution