Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate

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Package Content

NameDescription
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_laminar kc_laminar  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_overall kc_overall  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_turbulent kc_turbulent  

Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_laminar Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_laminar


Calculation of the mean convective heat transfer coefficient kc for a laminar fluid flow over an even surface.

Functions kc_laminar and kc_laminar_KC

There are basically three differences:

Restriction

Geometry

pic_plate

Calculation

The mean convective heat transfer coefficient kc for flat plate is calculated through the corresponding Nusselt number Nu_lam according to [VDI 2002, p. Gd 1, eq. 1] :

    Nu_lam = 0.664 * Re^(0.5) * (Pr)^(1/3)

and the corresponding mean convective heat transfer coefficient kc :

    kc =  Nu_lam * lambda / L

with

cp as specific heat capacity at constant pressure [J/(kg.K)],
eta as dynamic viscosity of fluid [Pa.s],
kc as mean convective heat transfer coefficient [W/(m2.K)],
lambda as heat conductivity of fluid [W/(m.K)],
L as length of plate [m],
Nu_lam as mean Nusselt number for laminar regime [-],
Pr = eta*cp/lambda as Prandtl number [-],
rho as fluid density [kg/m3],
Re = rho*v*L/eta as Reynolds number [-].

Verification

The mean Nusselt number Nu in the laminar regime representing the mean convective heat transfer coefficient kc for Prandtl numbers of different fluids is shown in the figure below.

fig_plate_kc_laminar

Note that this function is best used in the laminar regime up to a Reynolds number Re smaller than 2300. There is a deviation w.r.t. literature due to the neglect of the turbulence influence in the transition regime even though this function is used inside its cited restrictions for a higher Reynolds number. The function kc_overall is recommended for the simulation of a Reynolds number higher than 2300.

References

VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.

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Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_overall Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_overall


Calculation of the mean convective heat transfer coefficient kc for a laminar or turbulent fluid flow over an even surface.

Functions kc_overall and kc_overall_KC

There are basically three differences:

Restriction

Geometry and Calculation

This heat transfer function enables a calculation of heat transfer coefficient for laminar and turbulent flow regime. The geometry, constant and fluid parameters of the function are the same as for kc_laminar and kc_turbulent.

The calculation conditions for laminar and turbulent flow is equal to the calculation in kc_laminar and kc_turbulent. A smooth transition between both functions is carried out between 1e5 ≤ Re ≤ 5e5 (see figure below).

Verification

The mean Nusselt number Nu = sqrt(Nu_lam^2 + Nu_turb^2) representing the mean convective heat transfer coefficient kc for Prandtl numbers of different fluids is shown in the figure below.

fig_plate_kc_overall

References

VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.

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Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_turbulent Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_turbulent


Calculation of the mean convective heat transfer coefficient kc for a hydrodynamically developed turbulent fluid flow over an even surface.

Functions kc_turbulent and kc_turbulent_KC

There are basically three differences:

Restriction

Geometry

pic_plate

Calculation

The mean convective heat transfer coefficient kc for flat plate is calculated through the corresponding Nusselt number Nu_turb according to [VDI 2002, p. Gd 1, eq. 2]:

    Nu_turb = (0.037 * Re^0.8 * Pr) / (1 + 2.443/Re^0.1 * (Pr^(2/3)-1))

and the corresponding mean convective heat transfer coefficient kc :

    kc =  Nu_turb * lambda / L

with

cp as specific heat capacity at constant pressure [J/(kg.K)],
eta as dynamic viscosity of fluid [Pa.s],
kc as mean convective heat transfer coefficient [W/(m2.K)],
lambda as heat conductivity of fluid [W/(m.K)],
L as length of plate [m],
Nu_turb as mean Nusselt number for turbulent regime [-],
Pr = eta*cp/lambda as Prandtl number [-],
rho as fluid density [kg/m3],
Re = v*rho*L/eta as Reynolds number [-].

Verification

The mean Nusselt number in turbulent regime Nu representing the mean convective heat transfer coefficient kc for Prandtl numbers of different fluids is shown in the figure below.

fig_plate_kc_turbulent

References

VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.

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