Question

Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities $K$ and $2\, K,$ respectively. The equivalent thermal conductivity of the slab is

• A. $\frac{2}{3} K$
• B. $\sqrt 2 K$
• C. 3K
• D. $\frac{ 4}{3} K$

Answer 1

Answer: (D)

$\frac{ 4}{3} K$

Answer 2

$\frac{2 \ell}{ K _{ eq }( A )}=\frac{\ell}{2 KA }+\frac{\ell}{ KA }$
$\left(\right.$ series connection $\left.R = R _{1}+ R _{2}\right)$
$\Rightarrow K _{ eq }= \frac{4}{3}\, K$