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.
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@@ -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}
