diff --git a/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md b/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md index 8ef34ae9e78831386394fe63090527d89143ea25..ac656a0b8d3e2b7de71d91a95b11c8bd6c9d8644 100644 --- a/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md +++ b/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md @@ -123,11 +123,11 @@ def time_function(t_D): The Prandtl and Reynolds number can be calculated as follows $$ - Pr = \frac{\mu_f c_{p,f}}{\lambda_f} + \mathrm{Pr} = \frac{\mu_f c_{p,f}}{\lambda_f} $$ $$ - Re = \frac{\rho_f v d_{pi}}{\mu_f} + \mathrm{Re} = \frac{\rho_f v d_{pi}}{\mu_f} $$ where, $\mu_f, \rho_f$ and $\lambda_f$ is the fluid viscosity, density and thermal conductivity. @@ -145,15 +145,17 @@ Re = rho_f * v * (2 * r_pi) / mu_f The Nusselt number can be determined by the following equation (Diersch, 2013): $$ - Nu = 4.364,\ Re < 2300 + \mathrm{Nu} = 4.364,\ \mathrm{Re} < 2300 $$ $$ - Nu = \frac{(\xi_{k}/8)\ \mathrm{Re}_{k}\ \mathrm{Pr}}{1+12.7\sqrt{\xi_{k}/8}(\mathrm{Pr}^{2/3}-1)} \left[ 1+\left(\frac{d_{k}^{i}}{L}\right)^{2/3} \right],\ Re \geq 10^4 + \mathrm{Nu} = \frac{(\xi_{k}/8)\ \mathrm{Re}_{k}\ \mathrm{Pr}}{1+12.7\sqrt{{\xi_k}/8}(\mathrm{Pr}^{2/3}-1)} [ 1+(\frac{{d_k}^{i}}{L})^{2/3}], Re \geq 10^4 $$ $$ - Nu = (1-\gamma_{k})\ 4.364 + \gamma_{k} ( \frac{(0.0308/8)10^{4}\mathrm{Pr}}{1+12.7\ \sqrt{0.0308/8}(\mathrm{Pr}^{2/3}-1)} \left[ 1+\left(\frac{d_{k}^{i}}{L}\right)^{2/3} \right] ), 2 300 \leq Re < 10^{4} + +$$ + \mathrm{Nu} = (1-\gamma_{k})\ 4.364 + \gamma_{k} ( \frac{(0.0308/8)10^{4}\mathrm{Pr}}{1+12.7\ \sqrt{0.0308/8}(\mathrm{Pr}^{2/3}-1)} \left[ 1+\left(\frac{d_{k}^{i}}{L}\right)^{2/3} \right] ), 2 300 \leq \mathrm{Re} < 10^{4} $$ with