Fault detection for distributed parameter processes (heat processes, fluid processes, etc.) is vital for safe and efficient operation. On one hand, the existing data-driven methods neglect the evolution dynamics of the processes and cannot guarantee that they work for highly dynamic or transient processes; on the other hand, model-based methods reported so far are mostly based on the backstepping technique, which does not possess enough redundancy for fault detection since only the boundary measurement is considered. Motivated by these considerations, we intend to investigate the robust fault detection problem for distributed parameter processes in a model-based perspective covering both boundary and in-domain measurement cases. A real-time fault detection filter (FDF) is presented, which gets rid of a large amount of data collection and offline training procedures. Rigorous theoretic analysis is presented for guiding the parameters selection and threshold computation. A time-varying threshold is designed such that the false alarm in the transient stage can be avoided. Successful application results on a hot strip mill cooling system demonstrate the potential for real industrial applications.