A cylindrical rod of length \(L\), cross-sectional area \(A\), and thermal conductivity \(k\) connects a heat reservoir at constant temperature \(T_H\) to a large block of ice at \(0\text{ }^\circ\text{C}\). The latent heat of fusion of ice is \(L_f\). Assuming no heat is lost through the sides of the rod, which of the following gives the correct expression for the rate \(\dfrac{\Delta m}{\Delta t}\) at which the ice melts, and provides the correct physical justification for why the temperature of the ice remains at \(0\text{ }^\circ\text{C}\) during the melting process?