A solid metal rod of length \(L\) has a uniform cross-sectional area and perfectly insulated sides. The rod is initially at a uniform temperature \(T_C\). At time \(t = 0\), the left end at \(x = 0\) is placed in thermal contact with a heat reservoir at constant temperature \(T_H\) (where \(T_H > T_C\)), while the right end at \(x = L\) is maintained at \(T_C\).

Which of the following graphs best represents the rate of heat transfer through the rod, \(H\), as a function of position \(x\) along the rod at an early time \(t_1\) before steady state is reached and at a later time \(t_2\) after steady state has been established?