Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel

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Package Content

NameDescription
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapLaminar kc_evenGapLaminar  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapOverall kc_evenGapOverall  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapTurbulent kc_evenGapTurbulent  

Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapLaminar Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapLaminar


Calculation of the mean convective heat transfer coefficient kc for a laminar fluid flow through an even gap at different fluid flow and heat transfer situations.

Functions kc_evenGapLaminar and kc_evenGapLaminar_KC

There are basically three differences:

Restriction

Geometry

pic_gap

Calculation

The mean convective heat transfer coefficient kc for an even gap is calculated through the corresponding Nusselt number Nu_lam according to [VDI 2002, p. Gb 7, eq. 43] :

    Nu_lam = [(Nu_1)^3 + (Nu_2)^3 + (Nu_3)^3]^(1/3)

with the corresponding mean convective heat transfer coefficient kc :

    kc =  Nu_lam * lambda / d_hyd

with

cp as specific heat capacity at constant pressure [J/(kg.K)],
d_hyd = 2*s as hydraulic diameter of gap [m],
eta as dynamic viscosity of fluid [Pa.s],
h as height of cross sectional area in gap [m],
kc as mean convective heat transfer coefficient [W/(m2.K)],
lambda as heat conductivity of fluid [W/(m.K)],
L as overflowed length of gap (normal to cross sectional area) [m] ,
Nu_lam as mean Nusselt number [-],
Pr = eta*cp/lambda as Prandtl number [-],
rho as fluid density [kg/m3],
s as distance between parallel plates of cross sectional area [m],
Re = rho*v*d_hyd/eta as Reynolds number [-],
v as mean velocity in gap [m/s].

The summands for the mean Nusselt number Nu_lam at a chosen fluid flow and heat transfer situation are calculated as follows:

Note that the fluid properties shall be calculated with an arithmetic mean temperature out of the fluid flow temperatures at the entrance and the exit of the gap.

Verification

The mean Nusselt number Nu_lam representing the mean convective heat transfer coefficient kc in dependence of the chosen fluid flow and heat transfer situations (targets) is shown in the figure below.

fig_channel_kc_evenGapLamina

References

Bejan,A.:
Heat transfer handbook. Wiley, 2003.
VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.

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Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapOverall Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapOverall


Calculation of the mean convective heat transfer coefficient kc for an laminar or turbulent fluid flow through an even gap at different fluid flow and heat transfer situations.

Functions kc_evenGapOverall and kc_evenGapOverall_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_evenGapLaminar and kc_evenGapTurbulent.

The calculation conditions for laminar and turbulent flow is equal to the calculation in kc_evenGapLaminar and kc_evenGapTurbulent. A smooth transition between both functions is carried out between 2200 ≤ Re ≤ 30000 (see figure below).

Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc for Prandtl numbers of different fluids in dependence of the chosen fluid flow and heat transfer situations (targets) is shown in the figures below.

The verification for all targets is shown in the following figure w.r.t. the reference:

fig_channel_kc_evenGapOverall

References

Bejan,A.:
Heat transfer handbook. Wiley, 2003.
VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.

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Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapTurbulent Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapTurbulent


Calculation of the mean convective heat transfer coefficient kc for a developed turbulent fluid flow through an even gap at heat transfer from both sides.

Functions kc_evenGapTurbulent and kc_evenGapTurbulent_KC

There are basically three differences:

Restriction

Geometry

pic_gap

Calculation

The mean convective heat transfer coefficient kc for an even gap is calculated through the corresponding Nusselt number Nu_turb according to Gnielinski in [VDI 2002, p. Gb 7, sec. 2.4]

    Nu_turb =(zeta/8)*Re*Pr/{1+12.7*[zeta/8]^(0.5)*[Pr^(2/3) -1]}*{1+[d_hyd/L]^(2/3)}

where the pressure loss coefficient zeta according to Konakov in [VDI 2002, p. Ga 5, eq. 27] is determined by

    zeta =  1/[1.8*log10(Re) - 1.5]^2

resulting to the corresponding mean convective heat transfer coefficient kc

    kc =  Nu_turb * lambda / d_hyd

with

cp as specific heat capacity at constant pressure [J/(kg.K)],
d_hyd = 2*s as hydraulic diameter of gap [m],
eta as dynamic viscosity of fluid [Pa.s],
h as height of cross sectional area in gap [m],
kc as mean convective heat transfer coefficient [W/(m2.K)],
lambda as heat conductivity of fluid [W/(m.K)],
L as overflowed length of gap (normal to cross sectional area) [m] ,
Nu_turb as mean Nusselt number for turbulent regime [-],
Pr = eta*cp/lambda as Prandtl number [-],
rho as fluid density [kg/m3],
s as distance between parallel plates of cross sectional area [m],
Re = rho*v*d_hyd/eta as Reynolds number [-],
v as mean velocity in gap [m/s],
zeta as pressure loss coefficient [-].

Note that the fluid flow properties shall be calculated with an arithmetic mean temperature out of the fluid flow temperatures at the entrance and the exit of the gap.

Verification

The mean Nusselt number Nu_turb representing the mean convective heat transfer coefficient kc in dependence of the chosen fluid flow and heat transfer situations (targets) is shown in the figure below.

fig_channel_kc_evenGapTurbulent

References

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

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