A liquid food product is processed in a continuous-flow

QUESTION:

A liquid food product is processed in a continuous-flow sterilizer. The liquid enters the sterilizer at a tem-perature and flow rate of Tm,i,h?20C, m.?1 kg/s,respectively. A time-at-temperature constraint requiresthat the product be held at a mean temperature ofTm?90C for 10 s to kill bacteria, while a second con-straint is that the local product temperature cannotexceed Tmax?230C in order to preserve a pleasingtaste. The sterilizer consists of an upstream, Lh?5mheating section characterized by a uniform heat flux, an intermediate insulated sterilizing section, and adownstream cooling section of length Lc?10 m. Thecooling section is composed of an uninsulated tubeexposed to a quiescent environment at T??20C. The thin-walled tubing is of diameter D?40 mm.Food properties are similar to those of liquid water atT?330 K. (a) What heat flux is required in the heating section toensure a maximum mean product temperature ofTm?90C? (b) Determine the location and value of the maximumlocal product temperature. Is the second constraintsatisfied?(c) Determine the minimum length of the sterilizingsection needed to satisfy the time-at-temperatureconstraint.(d) Sketch the axial distribution of the mean, surface,and centerline temperatures from the inlet of theheating section to the outlet of the cooling section