The goal of this study was to investigate water and solute transport, with a focus on sodium transport (T$_{\rm Na}$) and metabolism along individual nephron segments under differing physiological and pathophysiological conditions. To accomplish this goal, we developed a computational model of solute transport and oxygen consumption (Q$_{\rm O2}$) along different nephron populations of a rat kidney. The model represents detailed epithelial and paracellular transport processes along both the superficial and juxtamedullary nephrons, with the loop of Henle of each model nephron extending to differing depths of the inner medulla. We used the model to assess how changes in T$_{\rm Na}$ may alter Q$_{\rm O2}$ in different nephron segments, and how shifting the T$_{\rm Na}$ sites alters overall kidney Q$_{\rm O2}$. Under baseline conditions, the model predicted a whole-kidney T$_{\rm Na}$/Q$_{\rm O2}$, which denotes the number of moles of Na$^+$ reabsorbed per moles of O$_2$ consumed, of about 15, with T$_{\rm Na}$ efficiency predicted to be significantly greater in cortical nephron segments than medullary segments. The T$_{\rm Na}$/Q$_{\rm O2}$ ratio was generally similar among the superficial and juxtamedullary nephron segments, except for the proximal tubule, where T$_{\rm Na}$/Q$_{\rm O2}$ was $\sim$20\% higher in superficial nephrons, due to the larger luminal flow along the juxtamedullary proximal tubules and the resulting flow-induced, higher transcellular transport. Moreover, the model predicted that an increase in single-nephron glomerular filtration rate (SNGFR) \Red{does not significantly affect} T$_{\rm Na}$/Q$_{\rm O2}$ in the proximal tubules but generally increases T$_{\rm Na}$/Q$_{\rm O2}$ along downstream segments. The latter result can be attributed to the generally higher luminal [Na$^+$], which raises paracellular T$_{\rm Na}$. Consequently, vulnerable medullary segments, such as the S3 segment and medullary thick ascending limb, may be relatively protected from flow-induced increases in Q$_{\rm O2}$ under pathophysiological conditions.