A liquid food product is processed in a continuous flow sterilizer. The liquid enters the sterilizer at a temperature and flow rate of Tm,i,h=20C, mdot = 1kg/s, respectively. A time-at-temperature constraint requires that the product be held at a mean temperature of Tm=90C for 10s to kill bacteria, while a second constraint is that the local product temperature cannot exceed Tmax = 230C in order to preserve a pleasing taste. The sterilizer consists of an upstream, Lh=5m heating section characterized by uniform heat flux, an intermediate insulated sterilizing section, and a downstream cooling setion of length Lc=10m. The cooling section is composed of uninsulated tube exposed to a quiescent environment at Tinfinity=20C. The thin-walled tubing is of diameter D = 40mm. Food properites are similar to those of liquid water at T=330K.

Find: (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.