==> $1\frac{J}{{{m^2} \times sec \times {K^4}}} = \frac{{{{10}^7}erg}}{{{{10}^4}c{m^2} \times sec \times {K^4}}}$
$ = {10^3}\frac{{erg}}{{c{m^2} \times sec \times {K^4}}}$
If heat flows through them from $x = 0$ to $x = 2L$ at a steady rate and conductivities of the metals are $K_{cu}$ and $K_{steel}$ $(K_{cu} > K_{steel}),$ then the temperature varies as (convection and radiation are negligible)