Transient heat-conduction time function is a crucial function for wellbore heat transfer in the process of steam injection for heavy oil production.All of the common transient heat-conduction time functions and related approximate solutions ignore wellbore heat capacity and other properties

but the heat capacity has obvious effect on the heat transfer in wellbore

especially in short time

so the error is large in the early days of steam injection.Based on a novel transient heat-conduction time function considering the effect of heat capacity of wellbore

a new approximate solution is obtained by the numerical fitting method and compared with those traditional approximate solutions

which only give good results in long time.The new approximate solution presents higher precision all the time

especially in the early period of steam injection.It is shown that the new approximate solution of transient heat-conduction time function is simple in form and easy to use

so it has good practicability in engineering with wider applicability.