The Forced Heat Transfer Check component models the heat transfer coefficient calculation of forced convection.

Before using HeatConvection component, you can check how to calculate the heat transfer coefficient internally.

Average temperature is:

$T\=\frac{\mathrm{Tin}\left[1\right]-\mathrm{Tin}\left[2\right]}{2}$

Heat transfer coefficient of forced convection is calculated with:

$h\=\mathrm{`HeatTransfer.Properties.Fluid.AirForcedlHeatTransfer}\left(\mathrm{pin}\, \mathrm{Tin}\left[1\right]\,\mathrm{Tin}\left[2\right]\, \mathrm{Vin}\,\mathrm{Convection} \mathrm{Type}\, \mathrm{true}\, 1\,1\,1\,1\right)$

( $h\=\frac{\mathrm{Nu}\cdot k}{X}$ )

Output is:

$\mathrm{out}\=h$

And, Nusselt number $\mathrm{Nu}$ is calculated with the following equation which is selected by the option.

$$If you select this option, the generalized equation is valid.

$$$\mathrm{Nu}\=C_{\mathrm{forced}}\cdot \left({\mathrm{Re}}^{m_{\mathrm{forced}}}-{\mathrm{offset}}_{\mathrm{forced}}\right)\cdot {\mathrm{Pr}}^{n_{\mathrm{forced}}}$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

The default value of the experimental parameters are for the flat plate with the laminar flow.

$\mathrm{Nu}\=0.664\cdot {\mathrm{Re}}^{\frac{1}{2}}\cdot {\mathrm{Pr}}^{\frac{1}{3}}$

For laminar flow, the constant Nusselt number is used in this option, and for turbulent, Dittus-Boetter's equation [1] is used.

$$$\mathrm{Nu}\&equals;$$\&lcub;\begin{array}{cc}3.66& \mathrm{Re}<2300\\ \&lcub;\begin{array}{cc}0.023\cdot {\mathrm{Re}}^{0.8}\cdot {\mathrm{Pr}}^{0.4}& T\left[1\right]<T\left[2\right]\\ 0.023\cdot {\mathrm{Re}}^{0.8}\cdot {\mathrm{Pr}}^{0.3}& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

$\mathrm{Nu}\&equals;0.664\cdot {\mathrm{Re}}^{\frac{1}{2}}\cdot {\mathrm{Pr}}^{\frac{1}{3}}$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )$$

This equation is given by Churchill and Bernstein [2], which is valid for the range ${\mathit{10}}^{\mathit{2}}\mathit{<}\mathrm{Re}\mathit{<}{\mathit{10}}^{\mathit{7}}$, $\mathrm{Re}\cdot \mathrm{Pr}\&gt;0.2$.

$\mathrm{Nu}\&equals;0.3\&plus;\frac{0.62\cdot {\mathrm{Re}}^{\frac{1}{2}}\cdot {\mathrm{Pr}}^{\frac{1}{3}}}{{\left(1\&plus;{\left(0.4\cdot \mathrm{Pr}\right)}^{\frac{2}{3}}\right)}^{\frac{1}{4}}}\cdot {\left(1\&plus;{\left(\frac{\mathrm{Re}}{282000}\right)}^{\frac{5}{8}}\right)}^{\frac{4}{5}}$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

This equation is developed by Whitaker [3], which is valid for the range $3.5<\mathrm{Re}<8\cdot {10}^4$, $0.7<\mathrm{Pr}<380$.

$\mathrm{Nu}\&equals;2\&plus;\left(0.4\cdot {\mathrm{Re}}^{\frac{1}{2}}\&plus;0.06\cdot {\mathrm{Re}}^{\frac{2}{3}}\right)\cdot {\mathrm{Pr}}^{0.4}\cdot {\left(\frac{\mathrm{\&eta;\_\_f}}{\mathrm{\&eta;\_\_s}}\right)}^{\frac{1}{4}}$

$$$\mathrm{\&eta;\_\_f}\&equals;\mathrm{`HeatTransfer.Properties.Fluid.AirViscosity\_pT`}\left(p\&comma; \mathrm{T\_\_f}\right)$

$\mathrm{\&eta;\_\_s}\&equals;\mathrm{`HeatTransfer.Properties.Fluid.AirViscosity\_pT`}\left(p\&comma; \mathrm{T\_\_s}\right)$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

For information on the calculation of Fluid properties, see Fluid Properties Check.

References

[1] : Dittus, F. W. and L. M. K. Boelter, Univ. Calif. (Berkeley) Pub. Eng. vol. 2, p.443, 1930.

[2] : Churchill, S. W., and M. Bernstein. "A Correlating Equation for Forced Convection from Gases and Liquids to a Circular Cylinder in Crossflow", J. Heat Transfer, vol.99, pp.300-306, 1977.

[3] : Whitake, S. "Forced Convection Heat-Transfer Correlations for Flow in Pipes, Past Flat Plates, Single Cylinders, Single Spheres, and Flow in Packed Bids and Tube Bundles", AIChE J., vol.18 p361, 1972.

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