Basically, it's a cylindrical tube of steel with inlet temperature of milk at 4 degrees Celsius and the outlet temperature would be 72 degrees Celsius. The mass flow rate is 1 Kg/s while the length and diameter of the tube are to be chosen, and the heat energy requirement to fulfill the above conditions is to be found.
Can someone guide me how to proceed. What is the relationship to be used, which would include these parameters, length and diameter of the Tube and the uniform heat energy supplied to the tube to make the temperature reach 72 degrees at the outlet, from the 4 degrees inlet temperature?
Q = mdot * Cp * (Tout - Tin)
Cp for milk is about 3.93 kJ/kg.K
so, your Q:
Q = 1 * 3930 *(72 - 5) (Watt)
To design the length and diameter of the tube:
Q = h * A (Ts - Tfluid)
Ts is the surface temperature of the tube,
Tfluid is the film temperature of the milk
h is the convective heat transfer coefficient (depends on Re and Pr)
A is the surface area of the tube = pi * D * L
For milk: cp = 3.894 kJ/kgºC, calculated from composition; after: Kenneth J. Valentas, Enrique Rotstein, R. Paul Singh (Eds.), "Handbook of Food Engineering Practice", CRC Press, 1997; cf. §7.3.3, with case study.
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