A cylindrical metal rod of length \(L\), cross-sectional area \(A\), and thermal conductivity \(k\) is thermally insulated along its outer cylindrical surface. The left end of the rod is maintained at temperature \(T_L\) and the right end is maintained at temperature \(T_R\), where \(T_L > T_R\). An internal electrical element located at the midpoint \(x = \dfrac{L}{2}\) generates heat at a constant rate \(P\). Assuming the system has reached a steady state, which of the following expressions represents the rate of heat flow, \(H_R\), out of the right end of the rod and into the cold reservoir?