In this study, a new error estimator for coupled transport equations has been developed and successfully implemented. The error norm, based on the definition of the energy norm for the system of coupled equations, is evaluated and used in the process of error estimation and calculation of the sizes of the elements in the adapted mesh. A new adaptive strategy for transient problems was also implemented. The performance of the proposed methodology is evaluated by applying it to selected examples. The results showed that the proposed error estimator is suitable for this type of analysis. The adaptive strategy utilized has proved to be efficient, avoiding unnecessary remeshings.