Cool Down Considerations
As
per IEEE 515
In no flow conditions,
with no additional heat from a heating device, the length of time to cool down
can be calculated from this Equation:-
t = H X Ln {(U X (Tf – Ta)) / (U X (Ti– Ta))} +
{(P1 X Vc1 X hf) / (U X (Tsc– Ta))}
Where: -
t = Desired Cool Down Time (s)
H = Thermal Time Constant (s)
U = Heat Loss per Unit Length of
Pipe per Degree of Temperature (W/M·°C)
Ti = initial temperature of the pipe (°C)
Tf = final temperature of the fluid and the pipe (°C)
Ta = ambient temperature (°C)
P1 = density of product in the pipe (kg/m3)
Vc1 = internal volume of the pipe (m3/m)
hf = Latent Heat Of
Fusion For The Product (J/Kg)
Tsc = Temperature at Which Phase
Change Occurs (°C)
We calculate heat loss: -
U = 1 / ((1 / (Pie X D1 X hi)) + (Ln (D2 / D1) / (2 X Pie X k1)) + (Ln
(D3 / D2) / (2 X Pie X k2)) + (1 / (Pie X D3 X hco)) + (1 / (Pie X D3 X ho)))
Where: -
U = Heat Loss per Unit Length of
Pipe per Degree of Temperature (W/M·°C)
D1= Inside Diameter of the Insulation
Layer (M)
D2 = Outside Diameter of the Inner
Insulation Layer (M)
D3 = Outside Diameter of the Outer
Insulation Layer (M)
k1 = Thermal Conductivity of
the Inner Insulation Evaluated At Its Mean Temperature (W/M·°C)
k2 = Thermal Conductivity of the
Outer Insulation Evaluated At Its Mean Temperature (W/M·°C)
hco = Inside Air Contact
Coefficient of the Weather Barrier (W/M·°C)
hi = Inside Air Contact
Coefficient From The Pipe To The Inside Insulation Surface (W/M·°C)
ho = Outside Air Contact
Coefficient of the Weather Barrier To The Ambient Temperature (W/M2·°C)
We calculate Thermal Time
Constant: -
H = ((P1
X Vc1 X Cp1) + (P2 X Vc2 X Cp2) + (0.5 x P3 X Vc3 X Cp3)) / U
Where:-
H = Thermal Time Constant (s)
P1 = density of product in the pipe (kg/m3)
Cp1 = specific heat of the product (J/kg·°C)
Vc1 = internal volume of the pipe (m3/m)
P2 = density of the pipe (kg/m3)
Cp2 = specific heat of the pipe (J/kg·°C)
Vc2 = pipe wall volume (m3//m)
P3 = density of the insulation (kg/m3)
Cp3 = specific heat of the insulation (J/kg·°C)
Vc3 = insulation wall volume (m3/m)
U = Heat Loss per Unit Length of
Pipe per Degree of Temperature (W/M·°C)
