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

Package Content

Name	Description
kc_laminar
kc_overall
kc_turbulent

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:

• The function kc_laminar is using kc_laminar_KC but offers additional output variables like e.g. Reynolds number or Nusselt number and failure status (an output of 1 means that the function is not valid for the inputs).
• Generally the function kc_laminar_KC is numerically best used for the calculation of the mean convective heat transfer coefficient kc at known mass flow rate.
• You can perform an inverse calculation from kc_laminar_KC, where an unknown mass flow rate is calculated out of a given mean convective heat transfer coefficient kc

Restriction

• laminar regime (Reynolds number ≤ 1e5)
• Prandtl number 0.6 ≤ Pr ≤ 2000

Geometry

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.

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.

Extends from Modelica.Icons.Information (Icon for general information packages).

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:

• The function kc_overall is using kc_overall_KC but offers additional output variables like e.g. Reynolds number or Nusselt number and failure status (an output of 1 means that the function is not valid for the inputs).
• Generally the function kc_overall_KC is numerically best used for the calculation of the mean convective heat transfer coefficient kc at known mass flow rate.
• You can perform an inverse calculation from kc_overall_KC, where an unknown mass flow rate is calculated out of a given mean convective heat transfer coefficient kc

Restriction

• constant wall temperature
• overall regime (Reynolds number 1e1 < Re < 1e7)
• Prandtl number 0.6 ≤ Pr ≤ 2000

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.

References

VDI:

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

Extends from Modelica.Icons.Information (Icon for general information packages).

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:

• The function kc_turbulent is using kc_turbulent_KC but offers additional output variables like e.g. Reynolds number or Nusselt number and failure status (an output of 1 means that the function is not valid for the inputs).
• Generally the function kc_turbulent_KC is numerically best used for the calculation of the mean convective heat transfer coefficient kc at known mass flow rate.
• You can perform an inverse calculation from kc_turbulent_KC, where an unknown mass flow rate is calculated out of a given mean convective heat transfer coefficient kc

Restriction

• constant wall temperature
• turbulent regime (Reynolds number 5e5 < Re < 1e7)
• Prandtl number 0.6 ≤ Pr ≤ 2000

Geometry

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.

References

VDI:

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

Extends from Modelica.Icons.Information (Icon for general information packages).