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Equations
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9QRCZbigg(1-c(p) \, \rho_0^2 \, q_0^2}{A^2} \bigg ) \partial T}{\partial t} = \frac{d}{dl} \, \bigg( \lambda \, \frac{ |
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dp=(p)gdz -rho_0^2 \, q_0^2 }{2 A^2 d} \frac{f(p)}{\rho(p)}partial T_e}{\partial t} = \nabla ( \lambda_e \nabla T_e) |
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| T(t=0, l) = T_g(l) |
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| T_e(t=0, l, r) = T_g(l) |
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| T(t, l=0) = T_s(t) |
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1u(l) =T_e(t, l, r \rightarrow \infty) = T_g(l) |
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| 2 \pi \, \lambda_e \, r_w \, \frac{\ |
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rho_0partial T_e}{\partial r} \ |
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cdot q_0}{\rho(p) \cdot A(l)}, \bigg|_{r=r_w} = 2 \pi \, r_f \, U \, \bigg( T_e \, \bigg|_{r=r_w} - T \bigg) |
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1q \frac{\rho_0 \cdot q_0}{\rho(p T_{0e} + \int_{z_0}^{z(l)} G_T(z) dz = T_{0e} + \int_{l_0}^l G_T(z(l)) \sin \theta dl |
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| G_T(z(l)) = \frac{j_e}{\lambda_e(l)} |
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(see Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model )
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