Pumping Methods

Pumping coolant friction | darcy_friction_haaland()

The pressure drop is based on the Darcy friction factor, using the Haaland equation, an approximation to the implicit Colebrook–White equation.

$$\frac{1}{\sqrt{f}} = -1.8 \log_{10}{\left[ \left(\frac{\epsilon / D}{3.7}\right)^{1.11} + \frac{6.9}{\text{Re}} \right]}$$

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Reynolds number | calculate_reynolds_number()

$$\mathrm{Re} = \frac{\rho v \left(2r_{\text{channel}}\right)}{\mu}$$

where $\rho$ is the coolant density and $\mu$ is the coolant viscosity.

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Gnielinski heat transfer | gnielinski_heat_transfer_coefficient()

1. Calculate the Reynolds number:

   $$\mathrm{Re} = \frac{\rho v \left(2r_{\text{channel}}\right)}{\mu}$$

   where $\rho$ is the coolant density and $\mu$ is the coolant viscosity.

2. Calculate the Prandtl number:

   $$\mathrm{Pr} = \frac{c_{\text{p}}\mu}{k}$$

   were $c_{\text{p}}$ is the coolant heat capacity and $k$ is the coolant thermal conductivity.

3. Calculate the Darcy friction factor using the darcy_friction_haaland() method:

   $$f = \texttt{darcy_friction_haaland()}$$

4. Calculate the Nusselt number using the Gnielinski correlation:

   $$\mathrm{Nu_D} = \frac{\left(f/8\right)\left(\mathrm{Re}-1000\right)\mathrm{Pr}}{1+12.7\left(f/8\right)^{0.5}\left(\mathrm{Pr}^{2/3}-1\right)}$$

   The relation is valid for:

   $$0.5 \le \mathrm{Pr} \le 2000 \\ 3000 \le \mathrm{Re} \le 5 \times 10^6$$

5. Calculate the heat transfer coefficient with the Nusselt number:

   $$h = \frac{\mathrm{Nu_D}k}{2r_{\text{channel}}}$$