# Steady-state Heat Transfer through an Ice Shelf

Suppose there is an ice shelf 400 meters high, where the bottom of the ice shelf is -2ºC and the top of the ice shelf is -28ºC. The thermal conductivity of ice is $$2.1 W{m}^{-1}{K}^{-1}$$. If the conductive heat transfer through the ice shelf is in a steady state, where the conductive heat flux is approximated by $$\overrightarrow{{q}_{c}} = {q}_{0} \hat{k}$$, calculate the value of $${q}_{0}$$.

Hint: use Fourier's Law $$\overrightarrow{{q}_{c}} = -k \nabla T$$.

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