Motivation
One of the key challenges in Pipe Flow Dynamics is to predict the along-hole temperature distribution during the stationary fluid transport.
Pipeline Flow Temperature Model is addressing this problem with account of the varying pipeline trajectory, pipeline schematic and heat transfer with the matter around pipeline.
In many practical cases the along-hole temperature distribution during the stationary fluid flow can be approximated by homogenous fluid flow model.
Outputs
| along-pipe temperature distribution and evolution in time |
Inputs
Assumptions
Equations
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| \rho \, c \, \frac{\partial T}{\partial t} = \frac{d}{dl} \, \bigg( \lambda \, \frac{dT}{dl} \bigg) - \rho \, c \, v \, \frac{dT}{dl} + \frac{2 \lambda}{\lambda_e} \cdot \frac{r_f}{r_w^2} \cdot U \cdot \left[ T_e(t, l, r_w) - T \right] |
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| \rho_e \, c_e \, \frac{\partial T_e}{\partial t} = \nabla ( \lambda_e \nabla T_e) |
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| T(t=0, l) = T_{e0}(l) |
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| T_e(t=0, l, r) = T_{e0}(l) |
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| T(t, l=0) = T_0(t) |
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| T_e(t, l, r \rightarrow \infty) = T_{e0}(l) |
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| 2 \pi \, \lambda_e \, r_w \, \frac{\partial T_e}{\partial r} \, \bigg|_{r=r_w} = 2 \pi \, r_f \, U \cdot \left( T_e \, \bigg|_{r=r_w} - T \right) |
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Approximations
See also
References
https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae
https://neutrium.net/fluid_flow/pressure-loss-in-pipe/
