Aliquid food product is processed in a continuous-flow sterilizer. the liquid enters the sterilizer at a temperatureand flow rate of tm, i,h = 20°c, , respectively. a time-at-temperature constraint requires that the productbe held at a mean temperature of tm = 90°c for 10 s to kill bacteria, while a second constraint is that the localproduct temperature cannot exceed tmax = 230°c in order to preserve a pleasing taste. the sterilizer consists of anupstream, lh = 5 m heating section characterized by a uniform heat flux, an intermediate insulated sterilizingsection, and a downstream cooling section of length lc = 10 m. the cooling section is composed of an uninsulatedtube exposed to a quiescent environment at t[infinity] = 20°c. the thin-walled tubing is of diameter d = 40 mm. foodproperties are similar to those of liquid water at t = 330 k.(a) healt flux required in heating section to ensure a maximum mean product temperature of tm=90c (b) location and value of the maximum local product temperature (c) minimum length of the sterilizing section needed to satisfy the time-at-temperature constraint.