Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe

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Package Content

NameDescription
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe.kc_laminar kc_laminar  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe.kc_overall kc_overall  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe.kc_turbulent kc_turbulent  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe.kc_twoPhaseOverall kc_twoPhaseOverall  


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


Calculation of mean convective heat transfer coefficient kc of a straight pipe at an uniform wall temperature or uniform heat flux and for a hydrodynamically developed or undeveloped laminar fluid flow.

Functions kc_laminar and kc_laminar_KC

There are basically three differences:

Restriction

Geometry

pic_straightPipe

Calculation

The mean convective heat transfer coefficient kc of a straight pipe in the laminar regime can be calculated for the following four heat transfer boundary conditions through its corresponding Nusselt number Nu :

Uniform wall temperature in developed fluid flow (heatTransferBoundary = 1) according to [VDI 2002, p. Ga 2, eq. 6] :

    Nu_TD = [3.66^3 + 0.7^3 + {1.615*(Re*Pr*d_hyd/L)^1/3 - 0.7}^3]^1/3

Uniform heat flux in developed fluid flow (heatTransferBoundary == 2) according to [VDI 2002, p. Ga 4, eq. 19] :

    Nu_qD = [4.364^3 + 0.6^3 + {1.953*(Re*Pr*d_hyd/L)^1/3 - 0.6}^3]^1/3

Uniform wall temperature in undeveloped fluid flow (heatTransferBoundary = 3) according to [VDI 2002, p. Ga 2, eq. 12] :

    Nu_TU = [3.66^3 + 0.7^3 + {1.615*(Re*Pr*d_hyd/L)^1/3 - 0.7}^3 + {(2/[1+22*Pr])^1/6*(Re*Pr*d_hyd/L)^0.5}^3]^1/3

Uniform heat flux in developed fluid flow (heatTransferBoundary == 4) according to [VDI 2002, p. Ga 5, eq. 25] :

    Nu_qU = [4.364^3 + 0.6^3 + {1.953*(Re*Pr*d_hyd/L)^1/3 - 0.6}^3 + {0.924*Pr^1/3*[Re*d_hyd/L]^0.5}^3]^1/3.

The corresponding mean convective heat transfer coefficient kc is determined w.r.t. the chosen heat transfer boundary by:

    kc =  Nu * lambda / d_hyd

with

d_hyd as hydraulic diameter of straight pipe [m],
kc as mean convective heat transfer coefficient [W/(m2K)],
lambda as heat conductivity of fluid [W/(mK)],
L as length of straight pipe [m],
Nu = kc*d_hyd/lambda as mean Nusselt number [-],
Pr = eta*cp/lambda as Prandtl number [-],
Re = rho*v*d_hyd/eta as Reynolds number [-],
v as mean velocity [m/s].

Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc depending on four different heat transfer boundary conditions is shown in the figures below.

This verification has been done with the fluid properties of Water (Prandtl number Pr = 7) and a diameter to pipe length fraction of 0.1.

fig_straightPipe_kc_laminar

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


Calculation of mean convective heat transfer coefficient kc of a straight pipe at an uniform wall temperature or uniform heat flux and for a hydrodynamically developed or undeveloped laminar or turbulent fluid flow with neglect or consideration of pressure loss influence.

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 2200 ≤ Re ≤ 10000 (see figure below).

Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc is shown for the fluid properties of Water (Prandtl number Pr = 7) and a diameter to pipe length fraction of 0.1 in the figure below.

The following verification considers pressure loss influence (roughness =2).

fig_straightPipe_kc_overall

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


Calculation of mean convective heat transfer coefficient kc of a straight pipe for a hydrodynamically developed turbulent fluid flow at uniform wall temperature or uniform heat flux with neglecting or considering of pressure loss influence.

Functions kc_turbulent and kc_turbulent_KC

There are basically three differences:

Restriction

Geometry

pic_straightPipe

Calculation

Neglect pressure loss influence (roughness == 1):

The mean convective heat transfer coefficient kc for smooth straight pipes is calculated through its corresponding Nusselt number Nu according to [Dittus and Boelter in Bejan 2003, p. 424, eq. 5.76]

    Nu = 0.023 * Re^(4/5) * Pr^(1/3).

Consider pressure loss influence (roughness == 2):

The mean convective heat transfer coefficient kc for rough straight pipes is calculated through its corresponding Nusselt number Nu according to [Gnielinski in VDI 2002, p. Ga 5, eq. 26]

    Nu = (zeta/8)*Re*Pr/(1 + 12.7*(zeta/8)^0.5*(Pr^(2/3)-1))*(1+(d_hyd/L)^(2/3)),

where the influence of the pressure loss on the heat transfer calculation is considered through

    zeta =  (1.8*log10(Re)-1.5)^-2.

The mean convective heat transfer coefficient kc in dependence of the chosen calculation (neglecting or considering of pressure loss influence) results into:

    kc =  Nu * lambda / d_hyd

with

d_hyd as hydraulic diameter of straight pipe [m],
kc as mean convective heat transfer coefficient [W/(m2K)],
lambda as heat conductivity of fluid [W/(mK)],
L as length of straight pipe [m],
Nu = kc*d_hyd/lambda as mean Nusselt number [-],
Pr = eta*cp/lambda as Prandtl number [-],
Re = rho*v*d_hyd/eta as Reynolds number [-],
v as mean velocity [m/s],
zeta as pressure loss coefficient [-].

Note that there is no significant difference for the calculation of the mean Nusselt number Nu at a uniform wall temperature (UWT) or a uniform heat flux (UHF) as heat transfer boundary in the turbulent regime (Bejan 2003, p.303).

Verification

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

fig_straightPipe_kc_turbulent

Note that the higher the Prandtl number Pr there is a higher difference in Nusselt numbers Nu comparing the neglect and consideration of pressure loss.

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.StraightPipe.kc_twoPhaseOverall Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe.kc_twoPhaseOverall


Calculation of local two phase heat transfer coefficient kc_2ph for (horizontal/vertical) boiling or (horizontal) condensation for an overall flow regime.

Restriction

Geometry

Calculation

Boiling in a horizontal pipe (target = 1):

The local two phase heat transfer coefficient kc_2ph during boiling in a horizontal straight pipe for an overall regime is calculated according to [Gungor/Winterton 1986, p.354, eq. 2] :

    kc_2ph = E_fc*E_fc_hor*kc_fc+S_nb+S_nb_hor*kc_nb

with

Bo=qdot_A/(mdot_A*dh_lv) as boiling number [-],
dh_lv as evaporation enthalpy [J/kg],
E_fc=f(Bo,Fr_l,X_tt) as forced convection enhancement factor [-],
E_fc_hor =f(Fr_l) as forced convection enhancement factor for horizontal straight pipes [-],
Fr_l as Froude number assuming total mass flow rate flowing as liquid [-],
kc_2ph as local two phase heat transfer coefficient [W/(m2K)],
kc_fc as heat transfer coefficient considering forced convection [W/(m2K)],
kc_nb as heat transfer coefficient considering nucleate boiling [W/(m2K)],
mdot_A as total mass flow rate density [kg/(m2s)],
qdot_A as heat flow rate density [W/m2],
Re_l as Reynolds number assuming liquid mass flow rate flowing alone [-],
S_nb =f(E_fc,Re_l) as suppression factor of nucleate boiling [-],
S_nb_hor =f(Fr_l) as suppression factor of nucleate boiling for horizontal straight pipes [-],
x_flow as mass flow rate quality [-],
X_tt = f(x_flow) as Martinelli parameter [-].

Boiling in a vertical pipe (target = 2):

The local two phase heat transfer coefficient kc_2ph during boiling in a vertical straight pipe for an overall regime is calculated out of the correlations for boiling in a horizontal straight pipe, where the horizontal correction factors E_fc_hor,S_nb_hor are unity.

Please note that the correlations named above are not valid for subcooled boiling due to a different driving temperature for nucleate boiling and forced convection. At subcooled boiling there is no enhancement factor (no vapour generation) but the suppression factor remains effective.

Condensation in a horizontal pipe (target = 3):

The local two phase heat transfer coefficient kc_2ph during condensation in a horizontal straight pipe for an overall regime is calculated according to [Shah 1979, p.548, eq. 8] :

  kc_2ph = kc_1ph*[(1 - x_flow)^0.8 + 3.8*x_flow^0.76*(1 - x_flow)^0.04/p_red^0.38]

where the convective heat transfer coefficient kc_1ph assuming the total mass flow rate is flowing as liquid according to [Shah 1979, p.548, eq. 5] :

  kc_1ph = 0.023*Re_l^0.8*Pr_l^0.4*lambda_l/d_hyd
 

with

d_hyd as hydraulic diameter [m],
kc_2ph as local two phase heat transfer coefficient [W/(m2K)],
kc_1ph as convective heat transfer coefficient assuming total mass flow rate is flowing as liquid [W/(m2K)],
lambda_l as thermal conductivity of fluid [W/(mK)],
pressure as thermodynamic pressure of fluid [Pa],
p_crit as critical pressure of fluid [Pa],
p_red = pressure/p_crit as reduced pressure [-],
Pr_l as Prandtl number assuming [-],
Re_l as Reynolds number assuming total mass flow rate is flowing as liquid [-],
x_flow as mass flow rate quality [-],

Verification

The local two phase heat transfer coefficient kc_2ph during for horizontal and vertical boiling as well as for horizontal condensation is shown for a straight pipe in the figures below.

Boiling in a horizontal pipe (target = 1):

Here the validation of the two phase heat transfer coefficient is shown for boiling in a horizontal straight pipe.

fig_kc_twoPhaseOverall

The two phase heat transfer coefficient (kc_2ph ) w.r.t. Gungor/Winterton is shown in dependence of the mass flow rate quality (x_flow ) for different mass flow rate densities (mdot_A ). The validation has been done with measurement results from Kattan/Thome for R134a as medium.

The two phase heat transfer coefficient increases with increasing mass flow rate quality up to a maximum value. After that there is a rapid decrease of (kc_2ph ) with increasing (x_flow ). This can be explained with a partial dryout of the pipe wall for a high mass flow rate quality.

Condensation in a horizontal pipe (target = 3):

Here the validation of the two phase heat transfer coefficient is shown for condensation in a horizontal straight pipe.

fig_kc_twoPhaseOverall

The two phase heat transfer coefficient (kc_2ph ) w.r.t. Shah is shown in dependence of the mass flow rate quality (x_flow ) for different mass flow rate densities (mdot_A ). The validation has been done with measurement results from Dobson/Chato for R134a as medium.

References

Bejan,A.:
Heat transfer handbook. Wiley, 2003.
M.K. Dobson and J.C. Chato:
Condensation in smooth horizontal tubes. Journal of HeatTransfer, Vol.120, p.193-213, 1998.
Gungor, K.E. and R.H.S. Winterton:
A general correlation for flow boiling in tubes and annuli, Int.J. Heat Mass Transfer, Vol.29, p.351-358, 1986.
N. Kattan and J.R. Thome:
Flow boiling in horizontal pipes: Part 2 - new heat transfer data for five refrigerants.. Journal of Heat Transfer, Vol.120. p.148-155, 1998.
Shah, M.M.:
A general correlation for heat transfer during film condensation inside pipes. Int. J. Heat Mass Transfer, Vol.22, p.547-556, 1979.


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