A uniform copper rod of $50\, cm$ length is insulated on the sides, and has its ends exposed to ice and steam respectively. If there is a layer of water 1 mm thick at each end, the temperature gradient (in $^{\circ}C m^{-1}$) in the bar is (Assume that the thermal conductivity of copper is $400 \, Wm^{-1} \, K^{-1}$ and water is $0.4 \, Wm^{-1} \, K^{-1}$)