Fig. (a) shows different flow rates and their effect on the analytical solution (see three green curves). For high flow rates, the temperature decreases more quickly. At late times, the temperature approaches a steady state greater than 𝑇 𝑖𝑛𝑗 because conduction brings heat into the system at the same rate the working fluid removes it. This steady state is achieved at earlier times and lower temperatures for higher flow rates. In contrast, the no-conduction analytical solutions all approach 𝑇 𝑖𝑛𝑗 at a late time because there is no heat recharge. Fig. (b) compares the base case to a thin reservoir, highlighting that reservoir size and aspect ratio affect how long before thermal depletion occurs and how important conduction is. The base-case reservoir has a large volume, and therefore holds a lot of heat initially, which takes a long time to deplete, even if no conduction occurs. It takes 20 and 44 years, respectively, for the average temperature and the production temperature to deplete by 20%. Neglecting conduction makes little difference to these results; the times for the average and production temperature to deplete by 20% are reduced by only 7% and 10%, respectively. On the other hand, the thinner reservoir holds less heat initially, and the average and production temperature deplete by 20% after only 4 and 6 years, respectively. Conduction seems to play a relatively larger role for the thin reservoir. If conduction is neglected, the time for the average and production temperature to deplete by 20% are reduced by 60% and 40%, respectively.