This type is for Natural convection, and there are 4 options including the default setting.

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

$$$\mathrm{Nu}\&equals;\&lcub;\begin{array}{cc}\mathrm{C\_\_lam}\cdot {\mathrm{Ra}}^{\mathrm{n\_\_lam}}& \mathrm{Ra}<\mathrm{Threshold}\\ \mathrm{C\_\_tur}\cdot {\mathrm{Ra}}^{\mathrm{n\_\_tur}}& \mathrm{otherwise}\end{array}$

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

The default value of the experimental parameters are for the vertical plate.

$$$\mathrm{Nu}\&equals;\&lcub;\begin{array}{cc}0.59\cdot {\mathrm{Ra}}^{\frac{1}{4}}& \mathrm{Ra}<{10}^9\\ 0.1\cdot {\mathrm{Ra}}^{\frac{1}{3}}& \mathrm{otherwise}\end{array}$$$

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

And, several thermophysics properties are calculated with Modelica functions which call Maple's built-in library CoolProp.

For more information, see Fluid Properties Check.

$\mathrm{Gr}\&equals;\mathrm{`HeatTransfer.Properties.Fluids.AirGrashof\_pT`}\left(p\&comma; \mathrm{T\_\_s}\&comma; \mathrm{T\_\_f}\&comma; g\&comma; X\right)$

$\mathrm{Pr}\&equals;\mathrm{`HeatTransfer.Properties.Fluids.AirPrandtl\_pT`}\left(p\&comma; \mathrm{T\_\_s}\&comma; \mathrm{T\_\_f}\&comma; X\right)$

$\mathrm{Ra}\&equals;\mathrm{Gr}\cdot \mathrm{Pr}$

$k\&equals;\mathrm{`HeatTransfer.Properties.Fluids.AirConductivity\_pT`}\left(p\&comma; \frac{\mathrm{T\_\_s+T\_\_f}}{2}\right)$

$g$ is gravity force and its value is 9.81.

Parameter values for this case is referred from [1].

$\mathrm{Nu}\&equals;\&lcub;\begin{array}{cc}0.59\cdot {\mathrm{Ra}}^{\frac{1}{4}}& \mathrm{Ra}<{10}^9\\ 0.1\cdot {\mathrm{Ra}}^{\frac{1}{3}}& \mathrm{otherwise}\end{array}$

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

The calculation for thermophysics properties is same as Default : Use references for Natural = false.

Parameter values for this case is referred from [1].

$\mathrm{Nu}\&equals;\&lcub;\begin{array}{cc}0.54\cdot {\mathrm{Ra}}^{\frac{1}{4}}& \mathrm{Ra}<{10}^7\\ 0.15\cdot {\mathrm{Ra}}^{\frac{1}{3}}& \mathrm{otherwise}\end{array}$

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

The calculation for thermophysics properties is same as Default : Use references for Natural = false.

Parameter values for this case is referred from [1].

$\mathrm{Nu}\&equals;\&lcub;\begin{array}{cc}0.27\cdot {\mathrm{Ra}}^{\frac{1}{4}}& \mathrm{Ra}<{10}^5\\ 0.27\cdot {\mathrm{Ra}}^{\frac{1}{4}}& \mathrm{otherwise}\end{array}$

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

The calculation for thermophysics properties is same as Default : Use references for Natural = false.

This type is for Forced convection, and there are 5 options including the default setting.

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

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

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

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

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

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

And, several thermophysics properties are calculated with Modelica functions which is to call Maple's built-in library CoolProp.

Please see more in Fluid Properties Check.

$\mathrm{Re}\&equals;\mathrm{`HeatTransfer.Properties.Fluids.AirReynolds\_pT`}\left(p\&comma; \mathrm{T\_\_s}\&comma; \mathrm{T\_\_f}\&comma; X\&comma; v\right)$

$\mathrm{Pr}\&equals;\mathrm{`HeatTransfer.Properties.Fluids.AirPrandtl\_pT`}\left(p\&comma; \mathrm{T\_\_s}\&comma; \mathrm{T\_\_f}\&comma; X\right)$

$k\&equals;\mathrm{`HeatTransfer.Properties.Fluids.AirConductivity\_pT`}\left(p\&comma; \frac{\mathrm{T\_\_s+T\_\_f}}{2}\right)$

For laminar flow, the constant Nusselt number is used in this option, and for turbulent, Dittus-Boetter's equation [2] 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}& \mathrm{T\_\_s}<\mathrm{T\_\_f}\\ 0.023\cdot {\mathrm{Re}}^{0.8}\cdot {\mathrm{Pr}}^{0.3}& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}$

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

The calculation for thermophysics properties is same as Default : Use references for Forced = false.

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

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

The calculation for thermophysics properties is same as Default : Use references for Forced = false.

This equation is given by Churchill and Bernstein [3], which is valid for the range ${\mathit{10}}^{\mathit{2}}\mathit{<}\mathrm{Re}\mathit{<}{\mathit{10}}^{\mathit{7}}$, $\mathrm{Re}\cdot \mathrm{Pr}\&gt;0.2$.

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

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

The calculation for thermophysics properties is same as Default : Use references for Forced = false.

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

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

$\mathrm{h\_act}\&equals; \bar{h} \&equals;\mathrm{Nu} \cdot \frac{k}{X}$

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

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

The calculation for the other thermophysics properties is same as Default : Use references for Forced = false.

	Convection type: Constant
	With this type, the heat transfer coefficient is specified by the value of parameter $h$. $\mathrm{h\_act}\=h$

	Convection type: External input
	If using this type, the heat transfer coefficient is specified by the signal input $h_{\mathit{in}}$. $\mathrm{h\_act}\=\mathrm{h\_\_in}$

[1] : J. P. Holman. "Heat Transfer Ninth Edition", McGraw-Hill Higher Education.

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

[3] : 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.

[4] : 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.