Question

Batch heating is a typical operation encountered in food processing. Consider a liquid food material that has to be heated in a highly agitated vessel that is fully insulated as shown in the diagram below: T. Cailed tubing Liquid Food TI Containment 1, Insulation The liquid food is to be heated by passing a hot fluid through a coiled thin walled tube with a surface area A. The known parameters are as below: mass flowrate of the hot liquidem mean inlet temperature of the hot fluid = Th specific heat of the hot fluid Car initial temperature of the cold liquid food = To which is less than the hot fluid inlet temperature Tas volume of liquid food = V, density of the liquid food = p. specific heat of the liquid food Ce overall heat transfer coefficient from the hot fluid to the liquid food = U. Using the basic fundamental energy balance and heat transfer equation for convection, derive an expression that can determine the liquid food temperature Tu(t) and the exit temperature of the hot Muid, Tro(t) as a function of time (t) using the known parameters described above. i You can follow the steps below: Write an expression for heat transfer rate (Q) for an elemental volume of the cold liquid food based on energy balance. Assume lump system analysis applies to the liquid food (.e. no spatial variation exists in the temperature at any point in the volume of the food due to sufficient stirring) i Write the expression for heat flow rate (0) for the hot liquid based on the intet and outlet temperature of the horquid in the coil. NI Write an expression for heat transfer rate (Q) for the transfer of heat from the hot liquid to the cold liquid food based on the log mean temperature difference and the 11

PLEASE WRITE WITH CLEAR HANDWRITING & MENTION WHICH TABLE ARE USED. THANK YOU.

Answer 1

1 Solp : > The batch heating process used to processed the liquid food. The food processed anangmeist as shoon in figure belo bot Pluid inn. Thi Tholt) -Coiled tubing S Liquid food containment Vessel "Insulation stirret Hot flaid Liquid food mn-mass flow rate, kg/s Oph= specific heat, 3 Irgk Ve= volume, m3 Se= pensity, kolme cpe = specific heat, I liga This Inlet temperatust, oc Tho - Ouset temperatuse, oc Tc.i= Inlet temperature, ac Tc, o- Outlet temperature ac Uo- Overall heat trauster coefficient for heat transfer from hot fluid to liquid food wwwkk. 0 The heat transfer rate cas for an elemental volume of the cold cliquid food.

4T2= Tho - Tc,o Oculet temperature difference for both ATI = Thin - Tc, in 3 Inlet temperature difference from both fluids fluids. (AT LPITO AT - IT2 In (AT/AT2) [(Thin- Tc. in) - (Tho-Tc,o)] Int (Th, in- Tc. in) (Tho-Teo) Q = Vox Asx [(Thin-Tc, in ) - ( Tho Tea] Int (Thin- Te, in E Thor Te,o)