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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