A fermenter containing 40 m' of medium (25°C) is going to be sterilized by the direct injection of saturated steam. The typical bacterial count of the medium is about 5 X 102 m, which needs to be reduced to such an extent that the chance for a contaminant surviving the sterilization is 1 in 1,000. The stream (345 kPa, absolute pressure) will be injected with a flow rate of 5,000 kg/hr, which will be stopped when the medium temperature reaches 122 °C. During the holding time, the heat loss through the vessel is assumed to be negligible. After a proper holding time, the fermenter will be cooled by passing 100 m/ hr of 20°C water through the cooling coil in the fermenter until the medium reaches 30 °C. The coil has a heat - transfer area of 40 m and for this operation the average overall heat – transfer coefficient (U) for cooling is 2,500 kJ/hr m K. The heat resistant bacterial spores in the medium can be characterized by an Arrhenius coefficient (K) of 5.7 X 109 hr' and activation energy (E) of 2.834 X 10 kJ / kmol (Deindoerfer and Humphrey, 1959). The heat capacity and density of the medium are 4.187 kJ/kg K and 1,000 kg/m', respectively. Estimate the required holding time. The enthalpy of the saturated steam at 345 kPa is 2636 kJ/kg. The time temperature profile during heating and cooling are Where H = Enthalpy of steam. J/Kg M = Initial mass of the medium C= Sp heat of the medium, J/Kg K U= Overall heat transfer coefficient A = Surface area , m? Tco = Absolute temperature of the heat sink To = Initial absolute temperature m, = Steam mass flow rate m, = Coolant mass flow rate

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Transcribed Image Text:Problem A fermenter containing 40 m' of medium (25°C) is going to be sterilized by the direct injection of saturated steam. The typical bacterial count of the medium is about 5 X 10" m', which needs to be reduced to such an extent that the chance for a contaminant surviving the sterilization is 1 in 1,000. The stream (345 kPa, absolute pressure) will be injected with a flow rate of 5,000 kg/hr, which will be stopped when the medium temperature reaches 122 °C. During the holding time, the heat loss through the vessel is assumed to be negligible. After a proper holding time, the fermenter will be cooled by passing 100 m/ hr of 20°C water through the cooling coil in the fermenter until the medium reaches 30 °C. The coil has a heat – transfer area of 40 m' and for this operation the average overall heat – transfer coefficient (U) for cooling is 2,500 kJ/hr m² K. The heat resistant bacterial spores in the medium can be characterized by an Arrhenius coefficient (K) of 5.7 X 109 hr' and activation energy (E) of 2.834 X 10 kJ / kmol (Deindoerfer and Humphrey, 1959). The heat capacity and density of the medium are 4.187 kJ/kg K and 1,000 kg/m', respectively. Estimate the required holding time. The enthalpy of the saturated steam at 345 kPa is 2636 kJ/kg. The time temperature profile during heating and cooling are Where H = Enthalpy of steam. J/Kg M = Initial mass of the medium C = Sp heat of the medium, J/Kg K U = Overall heat transfer coefficient A = Surface area , m? Tco = Absolute temperature of the heat sink To = Initial absolute temperature m, = Steam mass flow rate m. = Coolant mass flow rate

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