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measured by an IRT camera which will indicate the Again,
temperature of the outer surface of the pipe. Sherikar
[1] proposed a technique that uses IRT to quantify Δh = Cp * ΔT (2)
internal leakages from steam valves by measuring
surface temperatures from a length of un-insulated Where:
pipe downstream of the relevant internally leaking
valve. The theory upon which the leakage flow may be Cp is an average specific heat of a steam at constant
determined is that the heat loss across a length of bare pressure
pipe causes a drop in temperature of the leakage flow,
which corresponds to a loss of enthalpy of the steam ΔT is the change in temperature of the fluid measured at
flow across the length of pipe. By measuring the surface two locations in the system.
temperatures at two points separated by 1.5 to 2 meters,
the heat loss from the length of un-insulated pipe can and Qflow is the combination of radiation (Qr) and
be calculated. Since energy is conserved the heat loss conductive () heat transfer through the bare pipe surface.
from the fluid flow through the length of un-insulated
pipe is equal to the heat loss from the pipe surface for Qflow = Qr + Qc (3)
the same length of pipe. By assuming the expansion of
steam through the valve an isenthalpic process, Sherikar By substituting equation (2) and equation (3) into
[1] concludes that the loss of enthalpy of the fluid equation (1) we get:
downstream of the valve is equivalent to the heat loss
of the downstream un-insulated length of pipe. Sulaiman Qr + Qc = m * Cp * (T1 – T2 ) (4)
[2] has validated this technique with less than 20% error
in estimation. Now:
Qr = ∈ * σ * A * F * ( T4av sur – T4 ) (5)
amb (6)
Qc = hc * A * ( T4av sur – T4 )
amb
Figure 2: Where:
∈ is the thermal emissivity of the pipe surface.
σ is the Stefan-Boltzmann constant.
F is the shape factor.
hc is the convection coefficient.
A is the surface area of the outer surface along the
un-insulated length of the pipe.
Tav sur is an average temperature of T1, T2.
Tamb is the ambient temperature.
To calculate the convection coefficient the following
equations are used:
Quantum of Steam Loss Nud (hc * Dout ) (7)
The relationship is expressed as: k
Qflow = m*(h1 – h2) (1) Where:
Where: Nud is the Nusselt number.
k is the thermal conductivity of air
Qflow is the heat loss from the fluid.
Dout is the outer diameter of the un-insulated pipe length.
h1 – h2 is the loss of enthalpy of the fluid across the The Nusselt number is obtained from an empirical
un-insulated pipe. relation developed by Churchill and Chu [3] which is a
M is the mass flow rate of the steam.
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temperature of the outer surface of the pipe. Sherikar
[1] proposed a technique that uses IRT to quantify Δh = Cp * ΔT (2)
internal leakages from steam valves by measuring
surface temperatures from a length of un-insulated Where:
pipe downstream of the relevant internally leaking
valve. The theory upon which the leakage flow may be Cp is an average specific heat of a steam at constant
determined is that the heat loss across a length of bare pressure
pipe causes a drop in temperature of the leakage flow,
which corresponds to a loss of enthalpy of the steam ΔT is the change in temperature of the fluid measured at
flow across the length of pipe. By measuring the surface two locations in the system.
temperatures at two points separated by 1.5 to 2 meters,
the heat loss from the length of un-insulated pipe can and Qflow is the combination of radiation (Qr) and
be calculated. Since energy is conserved the heat loss conductive () heat transfer through the bare pipe surface.
from the fluid flow through the length of un-insulated
pipe is equal to the heat loss from the pipe surface for Qflow = Qr + Qc (3)
the same length of pipe. By assuming the expansion of
steam through the valve an isenthalpic process, Sherikar By substituting equation (2) and equation (3) into
[1] concludes that the loss of enthalpy of the fluid equation (1) we get:
downstream of the valve is equivalent to the heat loss
of the downstream un-insulated length of pipe. Sulaiman Qr + Qc = m * Cp * (T1 – T2 ) (4)
[2] has validated this technique with less than 20% error
in estimation. Now:
Qr = ∈ * σ * A * F * ( T4av sur – T4 ) (5)
amb (6)
Qc = hc * A * ( T4av sur – T4 )
amb
Figure 2: Where:
∈ is the thermal emissivity of the pipe surface.
σ is the Stefan-Boltzmann constant.
F is the shape factor.
hc is the convection coefficient.
A is the surface area of the outer surface along the
un-insulated length of the pipe.
Tav sur is an average temperature of T1, T2.
Tamb is the ambient temperature.
To calculate the convection coefficient the following
equations are used:
Quantum of Steam Loss Nud (hc * Dout ) (7)
The relationship is expressed as: k
Qflow = m*(h1 – h2) (1) Where:
Where: Nud is the Nusselt number.
k is the thermal conductivity of air
Qflow is the heat loss from the fluid.
Dout is the outer diameter of the un-insulated pipe length.
h1 – h2 is the loss of enthalpy of the fluid across the The Nusselt number is obtained from an empirical
un-insulated pipe. relation developed by Churchill and Chu [3] which is a
M is the mass flow rate of the steam.
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