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The time to heat or cool a fixed mass of liquid inside a batch reactor is calculated.
The primary simplification here is that both the utility and process heat capacity as well as the overall heat transfer coefficient
are assumed constant throughout.

Liquid Jacket Utility: The jacket is a 'one pass' with a fixed flowrate of liquid at inlet temperature T1.
A closed form solution has been developed and is shown at the bottom of the page.

Steam Jacket Utility: With steam at specified inlet pressure (assumed to be saturated) the time to heat is based
on isothermal condensation in the jacket with as much steam passing through the trap as heat transfer will allow.
Simple closed form solution below.

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INPUT DATA
                                                                               
                                                                                         

Input Units (or pick and choose) Metric British		Recalculate if change individual unit selections
Reactor Contents Process Data
Liquid or Steam as jacket utility	Liquid Steam
Initial temperature, T0		C F K R
Final temperature, Tf		C F K R
Heat capacity, Cp		kJ/kg-K Btu/lb-F J/kg-K cal/g-K
Mass of liquid, m		kg lb
Jacket and Utility Liquid Data
Overall HX coefficient, U		W/m2-K Btu/hr-ft2-F
Heat transfer area, A		m2 ft2
Jacket liquid inlet temperature, T1		C F K R	Liquid Utility
Jacket liquid flowrate, W		kg/min lb/min kg/hr lb/hr kg/s lb/s	Liquid Utility
Jacket liquid heat capacity, C		kJ/kg-K Btu/lb-F J/kg-K cal/g-K	Liquid Utility
Inlet steam pressure, P0		bar psia MPa psig bar-g	Steam Utility

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RESULTS
                                    
                                                               

Heating / Cooling Time

minutes

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EQUATIONS (Liquid in Jacket)

Heat input to reactor at T = Heat loss by utility liquid with inlet temperature T1 (specified) and outlet temperature T2 (unknown)


Solving for the unknown jacket outlet temperature T2


The rate of temperature change of the liquid inside the vessel is given by


Solving the above two equations to get process temperature as a function of time:


Finally, solving for time t where T = Tf (with T = T0 at t = 0)



EQUATIONS (Steam in Jacket)