Free convection to immersed bodies (ht.conv_free_immersed)

ht.conv_free_immersed.Nu_vertical_plate_Churchill(Pr, Gr)[source]

Calculates Nusselt number for natural convection around a vertical plate according to the Churchill-Chu [R255305] correlation, also presented in [R256305]. Plate must be isothermal; an alternate expression exists for constant heat flux.

\[Nu_{L}=\left[0.825+\frac{0.387Ra_{L}^{1/6}} {[1+(0.492/Pr)^{9/16}]^{8/27}}\right]^2\]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

Returns:

Nu : float

Nusselt number, [-]

Notes

Although transition from laminar to turbulent is discrete in reality, this equation provides a smooth transition in value from laminar to turbulent. Checked with the original source.

Can be applied to vertical cylinders as well, subject to the criteria below:

\[\frac{D}{L}\ge \frac{35}{Gr_L^{1/4}}\]

References

[R255305](1, 2) Churchill, Stuart W., and Humbert H. S. Chu. “Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate.” International Journal of Heat and Mass Transfer 18, no. 11 (November 1, 1975): 1323-29. doi:10.1016/0017-9310(75)90243-4.
[R256305](1, 2, 3) Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.

Examples

From [R256305], Example 9.2, matches:

>>> Nu_vertical_plate_Churchill(0.69, 2.63E9)
147.16185223770603
ht.conv_free_immersed.Nu_sphere_Churchill(Pr, Gr)[source]

Calculates Nusselt number for natural convection around a sphere according to the Churchill [R257307] correlation. Sphere must be isothermal.

\[Nu_D=2+\frac{0.589Ra_D^{1/4}} {\left[1+(0.469/Pr)^{9/16}\right]^{4/9}} \cdot\left\{1 + \frac{7.44\times 10^{-8}Ra} {[1+(0.469/Pr)^{9/16}]^{16/9}}\right\}^{1/12}\]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

Returns:

Nu : float

Nusselt number, [-]

Notes

Although transition from laminar to turbulent is discrete in reality, this equation provides a smooth transition in value from laminar to turbulent. Checked with the original source.

Good for Ra < 1E13. Limit of Nu is 2 at low Grashof numbers.

References

[R257307](1, 2) Schlunder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

Examples

>>> Nu_sphere_Churchill(.7, 1E7)
25.670869440317578
ht.conv_free_immersed.Nu_vertical_cylinder_Griffiths_Davis_Morgan(Pr, Gr, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R258308] correlated by [R259308], as presented in [R260308] and [R261308].

\[ \begin{align}\begin{aligned}Nu_H = 0.67 Ra_H^{0.25},\; 10^{7} < Ra < 10^{9}\\Nu_H = 0.0782 Ra_H^{0.357}, \; 10^{9} < Ra < 10^{11}\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns:

Nu : float

Nusselt number, [-]

Notes

Cylinder of diameter 17.43 cm, length from 4.65 to 263.5 cm. Air as fluid. Transition between ranges is not smooth. If outside of range, no warning is given.

References

[R258308](1, 2) Griffiths, Ezer, A. H. Davis, and Great Britain. The Transmission of Heat by Radiation and Convection. London: H. M. Stationery off., 1922.
[R259308](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R260308](1, 2) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R261308](1, 2) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Griffiths_Davis_Morgan(.7, 2E10)
327.6230596100138
ht.conv_free_immersed.Nu_vertical_cylinder_Jakob_Linke_Morgan(Pr, Gr, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R262312] correlated by [R263312], as presented in [R264312] and [R265312].

\[ \begin{align}\begin{aligned}Nu_H = 0.555 Ra_H^{0.25},\; 10^{4} < Ra < 10^{8}\\Nu_H = 0.129 Ra_H^{1/3},\; 10^{8} < Ra < 10^{12}\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns:

Nu : float

Nusselt number, [-]

Notes

Cylinder of diameter 3.5 cm, length from L/D = 4.3. Air as fluid. Transition between ranges is not smooth. If outside of range, no warning is given. Results are presented rounded in [R265312], and the second range is not shown in [R264312].

References

[R262312](1, 2) Jakob, M., and Linke, W., Warmeubergang beim Verdampfen von Flussigkeiten an senkrechten und waagerechten Flaschen, Phys. Z., vol. 36, pp. 267-280, 1935.
[R263312](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R264312](1, 2, 3) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R265312](1, 2, 3) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Jakob_Linke_Morgan(.7, 2E10)
310.90835207860454
ht.conv_free_immersed.Nu_vertical_cylinder_Carne_Morgan(Pr, Gr, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R266316] correlated by [R267316], as presented in [R268316] and [R269316].

\[ \begin{align}\begin{aligned}Nu_H = 1.07 Ra_H^{0.28},\; 2\times 10^{6} < Ra < 2\times 10^{8}\\Nu_H = 0.152 Ra_H^{0.38},\; 2\times 10^{8} < Ra < 2\times 10^{11}\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns:

Nu : float

Nusselt number, [-]

Notes

Cylinder of diameters 0.475 cm to 7.62 cm, L/D from 8 to 127. Isothermal boundary condition was assumed, but not verified. Transition between ranges is not smooth. If outside of range, no warning is given. The higher range of [R266316] is not shown in [R268316], and the formula for the first is actually for the second in [R268316].

References

[R266316](1, 2, 3) J. B. Carne. “LIX. Heat Loss by Natural Convection from Vertical Cylinders.” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 24, no. 162 (October 1, 1937): 634-53. doi:10.1080/14786443708565140.
[R267316](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R268316](1, 2, 3, 4) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R269316](1, 2) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Carne_Morgan(.7, 2E8)
204.31470629065677
ht.conv_free_immersed.Nu_vertical_cylinder_Eigenson_Morgan(Pr, Gr, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R271321] correlated by [R272321], presented in [R273321] and in more detail in [R274321].

\[ \begin{align}\begin{aligned}Nu_H = 0.48 Ra_H^{0.25},\; 10^{9} < Ra\\Nu_H = 51.5 + 0.0000726 Ra_H^{0.63},\; 10^{9} < Ra < 1.69 \times 10^{10}\\Nu_H = 0.148 Ra_H^{1/3} - 127.6 ,\; 1.69 \times 10^{10} < Ra\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns:

Nu : float

Nusselt number, [-]

Notes

Author presents results as appropriate for both flat plates and cylinders. Height of 2.5 m with diameters of 2.4, 7.55, 15, 35, and 50 mm. Another experiment of diameter 58 mm and length of 6.5 m was considered. Cylinder of diameters 0.475 cm to 7.62 cm, L/D from 8 to 127.Transition between ranges is not smooth. If outside of range, no warning is given. Formulas are presented similarly in [R273321] and [R274321], but only [R274321] shows the transition formula.

References

[R271321](1, 2) Eigenson L (1940). Les lois gouvernant la transmission de la chaleur aux gaz biatomiques par les parois des cylindres verticaux dans le cas de convection naturelle. Dokl Akad Nauk SSSR 26:440-444
[R272321](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R273321](1, 2, 3) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R274321](1, 2, 3, 4) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Eigenson_Morgan(0.7, 2E10)
230.55946525499715
ht.conv_free_immersed.Nu_vertical_cylinder_Touloukian_Morgan(Pr, Gr, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R275325] correlated by [R276325], as presented in [R277325] and [R278325].

\[ \begin{align}\begin{aligned}Nu_H = 0.726 Ra_H^{0.25},\; 2\times 10^{8} < Ra < 4\times 10^{10}\\Nu_H = 0.0674 (Gr_H Pr^{1.29})^{1/3},\; 4\times 10^{10} < Ra < 9\times 10^{11}\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns:

Nu : float

Nusselt number, [-]

Notes

Cylinder of diameters 2.75 inch, with heights of 6, 18, and 36.25 inch. Temperature was controlled via multiple separately controlled heating sections. Fluids were water and ethylene-glycol. Transition between ranges is not smooth. If outside of range, no warning is given. [R276325], [R277325], and [R278325] are in complete agreement about this formulation.

References

[R275325](1, 2) Touloukian, Y. S, George A Hawkins, and Max Jakob. Heat Transfer by Free Convection from Heated Vertical Surfaces to Liquids. Trans. ASME 70, 13-18 (1948).
[R276325](1, 2, 3) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R277325](1, 2, 3) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R278325](1, 2, 3) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Touloukian_Morgan(.7, 2E10)
249.72879961097854
ht.conv_free_immersed.Nu_vertical_cylinder_McAdams_Weiss_Saunders(Pr, Gr, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R279329] and [R280329] correlated by [R281329], as presented in [R282329], [R283329], and [R284329].

\[ \begin{align}\begin{aligned}Nu_H = 0.59 Ra_H^{0.25},\; 10^{4} < Ra < 10^{9}\\Nu_H = 0.13 Ra_H^{1/3.},\; 10^{9} < Ra < 10^{12}\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns

——-

Nu : float

Nusselt number, [-]

Notes

Transition between ranges is not smooth. If outside of range, no warning is given. For ranges under 10^4, a graph is provided, not included here.

References

[R279329](1, 2) Weise, Rudolf. “Warmeubergang durch freie Konvektion an quadratischen Platten.” Forschung auf dem Gebiet des Ingenieurwesens A 6, no. 6 (November 1935): 281-92. doi:10.1007/BF02592565.
[R280329](1, 2) Saunders, O. A. “The Effect of Pressure Upon Natural Convection in Air.” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 157, no. 891 (November 2, 1936): 278-91. doi:10.1098/rspa.1936.0194.
[R281329](1, 2) McAdams, William Henry. Heat Transmission. 3E. Malabar, Fla: Krieger Pub Co, 1985.
[R282329](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R283329](1, 2) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R284329](1, 2) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_McAdams_Weiss_Saunders(.7, 2E10)
313.31849434277973
ht.conv_free_immersed.Nu_vertical_cylinder_Kreith_Eckert(Pr, Gr, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R285335] correlated by [R286335], also as presented in [R287335], [R288335], and [R289335].

\[ \begin{align}\begin{aligned}Nu_H = 0.555 Ra_H^{0.25},\; 10^{5} < Ra < 10^{9}\\Nu_H = 0.021 Ra_H^{0.4},\; 10^{9} < Ra < 10^{12}\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns:

Nu : float

Nusselt number, [-]

Notes

Transition between ranges is not smooth. If outside of range, no warning is given.

References

[R285335](1, 2) Eckert, E. R. G., Thomas W. Jackson, and United States. Analysis of Turbulent Free-Convection Boundary Layer on Flat Plate. National Advisory Committee for Aeronautics, no. 2207. Washington, D.C.: National Advisoty Committee for Aeronautics, 1950.
[R286335](1, 2) Kreith, Frank, Raj Manglik, and Mark Bohn. Principles of Heat Transfer. Cengage, 2010.
[R287335](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R288335](1, 2) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R289335](1, 2) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Kreith_Eckert(.7, 2E10)
240.25393473033196
ht.conv_free_immersed.Nu_vertical_cylinder_Hanesian_Kalish_Morgan(Pr, Gr)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to the results of [R290340] correlated by [R291340], also as presented in [R292340] and [R293340].

\[Nu_H = 0.48 Ra_H^{0.23},\; 10^{6} < Ra < 10^{8}\]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

Returns:

Nu : float

Nusselt number, [-]

Notes

For air and fluoro-carbons. If outside of range, no warning is given. Laminar range only!

References

[R290340](1, 2) Hanesian, D. and Kalish, R. “Heat Transfer by Natural Convection with Fluorocarbon Gases.” IEEE Transactions on Parts, Materials and Packaging 6, no. 4 (December 1970): 147-148. doi:10.1109/TPMP.1970.1136270.
[R291340](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R292340](1, 2) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R293340](1, 2) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Hanesian_Kalish_Morgan(.7, 1E7)
18.014150492696604
ht.conv_free_immersed.Nu_vertical_cylinder_Al_Arabi_Khamis(Pr, Gr, L, D, turbulent=None)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to [R294344], also as presented in [R295344] and [R296344].

\[ \begin{align}\begin{aligned}Nu_H = 2.9Ra_H^{0.25}/Gr_D^{1/12},\; 9.88 \times 10^7 \le Ra_H \le 2.7\times10^{9}\\Nu_H = 0.47 Ra_H^{0.333}/Gr_D^{1/12},\; 2.7 \times 10^9 \le Ra_H \le 2.95\times10^{10}\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number with respect to cylinder height [-]

L : float

Length of vertical cylinder, [m]

D : float

Diameter of cylinder, [m]

turbulent : bool or None, optional

Whether or not to force the correlation to return the turbulent

result; will return the laminar regime if False; leave as None for

automatic selection

Returns:

Nu : float

Nusselt number, [-]

Notes

For air. Local Nusselt number results also given in [R294344]. D from 12.75 to 51 mm; H from 300 to 2000 mm. Temperature kept constant by steam condensing.

If outside of range, no warning is given. Applies for range of:

\[1.08 \times 10^4 \le Gr_D \le 6.9 \times 10^5\]

References

[R294344](1, 2, 3) Al-Arabi, M., and M. Khamis. “Natural Convection Heat Transfer from Inclined Cylinders.” International Journal of Heat and Mass Transfer 25, no. 1 (January 1982): 3-15. doi:10.1016/0017-9310(82)90229-0.
[R295344](1, 2) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R296344](1, 2) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Al_Arabi_Khamis(.71, 2E10, 10, 1)
280.39793209114765
ht.conv_free_immersed.Nu_vertical_cylinder_Popiel_Churchill(Pr, Gr, L, D, Nu_vertical_plate_correlation=<function Nu_vertical_plate_Churchill>)[source]

Calculates Nusselt number for natural convection around a vertical isothermal cylinder according to [R297347], also presented in [R298347].

\[ \begin{align}\begin{aligned}\frac{Nu}{Nu_{L,fp}} = 1 + B\left[32^{0.5}Gr_L^{-0.25}\frac{L}{D}\right]^C\\B = 0.0571322 + 0.20305 Pr^{-0.43}\\C = 0.9165 - 0.0043Pr^{0.5} + 0.01333\ln Pr + 0.0004809/Pr\end{aligned}\end{align} \]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number with respect to cylinder height [-]

L : float

Length of vertical cylinder, [m]

D : float

Diameter of cylinder, [m]

Nu_vertical_plate_correlation : function, optional

Correlation for vertical plate heat transfer

Returns:

Nu : float

Nusselt number, [-]

Notes

For 0.01 < Pr < 100. Requires a vertical flat plate correlation. Both [2], [3] present a power of 2 instead of 0.5 on the 32 in the equation, but the original has the correct form.

References

[R297347](1, 2) Popiel, C. O., J. Wojtkowiak, and K. Bober. “Laminar Free Convective Heat Transfer from Isothermal Vertical Slender Cylinder.” Experimental Thermal and Fluid Science 32, no. 2 (November 2007): 607-613. doi:10.1016/j.expthermflusci.2007.07.003.
[R298347](1, 2) Popiel, Czeslaw O. “Free Convection Heat Transfer from Vertical Slender Cylinders: A Review.” Heat Transfer Engineering 29, no. 6 (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
[R299347]Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_vertical_cylinder_Popiel_Churchill(0.7, 1E10, 2.5, 1)
228.8979005514989
ht.conv_free_immersed.Nu_vertical_cylinder(Pr, Gr, L=None, D=None, Method=None, AvailableMethods=False)[source]

This function handles choosing which vertical cylinder free convection correlation is used. Generally this is used by a helper class, but can be used directly. Will automatically select the correlation to use if none is provided; returns None if insufficient information is provided.

Preferred functions are ‘Popiel & Churchill’ for fully defined geometries, and ‘McAdams, Weiss & Saunders’ otherwise.

Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number with respect to cylinder height [-]

L : float, optional

Length of vertical cylinder, [m]

D : float, optional

Diameter of cylinder, [m]

Returns:

Nu : float

Nusselt number, [-]

methods : list, only returned if AvailableMethods == True

List of methods which can be used to calculate Nu with the given inputs

Other Parameters:
 

Method : string, optional

A string of the function name to use, as in the dictionary vertical_cylinder_correlations

AvailableMethods : bool, optional

If True, function will consider which methods which can be used to calculate Nu with the given inputs

Examples

>>> Nu_vertical_cylinder(0.72, 1E7)
30.562236756513943
ht.conv_free_immersed.Nu_horizontal_cylinder_Churchill_Chu(Pr, Gr)[source]

Calculates Nusselt number for natural convection around a horizontal cylinder according to the Churchill-Chu [R300350] correlation, also presented in [R301350]. Cylinder must be isothermal; an alternate expression exists for constant heat flux.

\[Nu_{D}=\left[0.60+\frac{0.387Ra_{D}^{1/6}} {[1+(0.559/Pr)^{9/16}]^{8/27}}\right]^2\]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

Returns:

Nu : float

Nusselt number, [-]

Notes

Although transition from laminar to turbulent is discrete in reality, this equation provides a smooth transition in value from laminar to turbulent. Checked with the original source, which has its powers unsimplified but is equivalent.

[R300350] recommends 1E-5 as the lower limit for Ra, but no upper limit. [R301350] suggests an upper limit of 1E12.

References

[R300350](1, 2, 3) Churchill, Stuart W., and Humbert H. S. Chu. “Correlating Equations for Laminar and Turbulent Free Convection from a Horizontal Cylinder.” International Journal of Heat and Mass Transfer 18, no. 9 (September 1975): 1049-53. doi:10.1016/0017-9310(75)90222-7.
[R301350](1, 2, 3, 4) Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.

Examples

From [R301350], Example 9.2, matches:

>>> Nu_horizontal_cylinder_Churchill_Chu(0.69, 2.63E9)
139.13493970073597
ht.conv_free_immersed.Nu_horizontal_cylinder_Kuehn_Goldstein(Pr, Gr)[source]

Calculates Nusselt number for natural convection around a horizontal cylinder according to the Kuehn-Goldstein [R302352] correlation, also shown in [R303352]. Cylinder must be isothermal.

\[\frac{2}{Nu_D} = \ln\left[1 + \frac{2}{\left[\left\{0.518Ra_D^{0.25} \left[1 + \left(\frac{0.559}{Pr}\right)^{3/5}\right]^{-5/12} \right\}^{15} + (0.1Ra_D^{1/3})^{15}\right]^{1/15}}\right]\]
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

Returns:

Nu : float

Nusselt number, [-]

Notes

[R302352] suggests this expression is valid for all cases except low-Pr fluids. [R303352] suggests no restrictions.

References

[R302352](1, 2, 3) Kuehn, T. H., and R. J. Goldstein. “Correlating Equations for Natural Convection Heat Transfer between Horizontal Circular Cylinders.” International Journal of Heat and Mass Transfer 19, no. 10 (October 1976): 1127-34. doi:10.1016/0017-9310(76)90145-9
[R303352](1, 2, 3) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_horizontal_cylinder_Kuehn_Goldstein(0.69, 2.63E9)
122.99323525628186
ht.conv_free_immersed.Nu_horizontal_cylinder_Morgan(Pr, Gr)[source]

Calculates Nusselt number for natural convection around a horizontal cylinder according to the Morgan [R304354] correlations, a product of a very large review of the literature. Sufficiently common as to be shown in [R305354]. Cylinder must be isothermal.

\[Nu_D = C Ra_D^n\]
Gr min Gr max C n
10E-10 10E-2 0.675 0.058
10E-2 10E2 1.02 0.148
10E2 10E4 0.850 0.188
10E4 10E7 0.480 0.250
10E7 10E12 0.125 0.333
Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

Returns:

Nu : float

Nusselt number, [-]

Notes

Most comprehensive review with a new proposed equation to date. Discontinuous among the jumps in range. Blindly runs outside if upper and lower limits without warning.

References

[R304354](1, 2) Morgan, V.T., The Overall Convective Heat Transfer from Smooth Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and J.P. Hartnett, V 11, 199-264, 1975.
[R305354](1, 2) Boetcher, Sandra K. S. “Natural Convection Heat Transfer From Vertical Cylinders.” In Natural Convection from Circular Cylinders, 23-42. Springer, 2014.

Examples

>>> Nu_horizontal_cylinder_Morgan(0.69, 2.63E9)
151.3881997228419
ht.conv_free_immersed.Nu_horizontal_cylinder(Pr, Gr, Method=None, AvailableMethods=False)[source]

This function handles choosing which horizontal cylinder free convection correlation is used. Generally this is used by a helper class, but can be used directly. Will automatically select the correlation to use if none is provided; returns None if insufficient information is provided.

Prefered functions are ‘Morgan’ when discontinuous results are acceptable and ‘Churchill-Chu’ otherwise.

Parameters:

Pr : float

Prandtl number [-]

Gr : float

Grashof number [-]

Returns:

Nu : float

Nusselt number, [-]

methods : list, only returned if AvailableMethods == True

List of methods which can be used to calculate Nu with the given inputs

Other Parameters:
 

Method : string, optional

A string of the function name to use, as in the dictionary horizontal_cylinder_correlations

AvailableMethods : bool, optional

If True, function will consider which methods which can be used to calculate Nu with the given inputs

Examples

>>> Nu_horizontal_cylinder(0.72, 1E7)
24.864192615468973