Motivation
Analytical model of temperature step-response in a Homogenous Stationary Pipe Flow with account for the heat exchange with surroundings.
Model equally works for wellbore flow, ground, on-ground and bottom-water pipelines.
Outputs
T(t, l) | Along-hole Temperature Profile |
where
t | Flowing duration |
l | Length along pipe |
Inputs
T_s | Intake temperature | T_e(l) | Background temperature of the surroundings |
\dot m | Mass flowrate | U | Heat Transfer Coefficient (HTC) between pipe fluid and surroundings |
a_e | Thermal Diffusivity of the surroundings | r_f | Flowing pipe radius |
\lambda_e | Thermal Conductivity of the surroundings | r_w | Wellbore radius |
Equations
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Assumptions
Intake Flowrate is constant in time | Intake Temperature is constant in time |
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q_s(t) = q_s = {\rm const} | T_s(t) = T_s = \rm const |
Thermal diffusivity of the surroundings is constant along-hole | Thermal Conductivity of the surroundings is constant along-hole |
a_e(l) = a_e = \rm const | \lambda_e(l) = \lambda_e = \rm const |
Flowing pipe radius is constant along-hole | Wellbore radius is constant along-hole |
r_f(l) = r_f = \rm const | r_w(l) = r_w = \rm const |
Heat Transfer Coefficient (HTC) between pipe fluid and surroundings is constant along-hole | |
U(l) = U = \rm const |
See Also
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation / Temperature Profile in Pipe Flow @model / Temperature Profile in Homogenous Pipe Flow @model