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fluids.Fourier_heat(t=1.5, L=2, rho=1000., Cp=4000., k=0.6))
assert_close(fluids.numba.Graetz_heat(1.5, 0.25, 5, 800., 2200., 0.6),
fluids.Graetz_heat(1.5, 0.25, 5, 800., 2200., 0.6))
assert_close(fluids.numba.Schmidt(D=2E-6, mu=4.61E-6, rho=800),
fluids.Schmidt(D=2E-6, mu=4.61E-6, rho=800))
assert_close(fluids.numba.Lewis(D=22.6E-6, alpha=19.1E-6),
fluids.Lewis(D=22.6E-6, alpha=19.1E-6))
assert_close(fluids.numba.Confinement(0.001, 1077, 76.5, 4.27E-3),
fluids.Confinement(0.001, 1077, 76.5, 4.27E-3))
assert_close(fluids.numba.Prandtl(Cp=1637., k=0.010, nu=6.4E-7, rho=7.1),
fluids.Prandtl(Cp=1637., k=0.010, nu=6.4E-7, rho=7.1))
assert_close(fluids.numba.Grashof(L=0.9144, beta=0.000933, T1=178.2, rho=1.1613, mu=1.9E-5),
fluids.Grashof(L=0.9144, beta=0.000933, T1=178.2, rho=1.1613, mu=1.9E-5))
assert_close(fluids.numba.Froude(1.83, L=2., squared=True),
fluids.Froude(1.83, L=2., squared=True))
assert_close(fluids.numba.nu_mu_converter(998., nu=1.0E-6),
fluids.nu_mu_converter(998., nu=1.0E-6))
assert_close(fluids.numba.gravity(55, 1E4),
fluids.gravity(55, 1E4))
References
----------
.. [1] Kudirka, A. A., R. J. Grosh, and P. W. McFadden. "Heat Transfer in
Two-Phase Flow of Gas-Liquid Mixtures." Industrial & Engineering
Chemistry Fundamentals 4, no. 3 (August 1, 1965): 339-44.
doi:10.1021/i160015a018.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m*x/(rhog*pi/4*D**2)
Vls = m*(1-x)/(rhol*pi/4*D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
Rels = D*Vls*rhol/mu_b
Nu = 125*(Vgs/Vls)**0.125*(mug/mu_b)**0.6*Rels**0.25*Prl**(1/3.)
if mu_w:
Nu *= (mu_b/mu_w)**0.14
return Nu*kl/D
299.3796286459285
References
----------
.. [1] Ravipudi, S., and Godbold, T., The Effect of Mass Transfer on Heat
Transfer Rates for Two-Phase Flow in a Vertical Pipe, Proceedings 6th
International Heat Transfer Conference, Toronto, V. 1, p. 505-510, 1978.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m*x/(rhog*pi/4*D**2)
Vls = m*(1-x)/(rhol*pi/4*D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
Rels = D*Vls*rhol/mu_b
Nu = 0.56*(Vgs/Vls)**0.3*(mug/mu_b)**0.2*Rels**0.6*Prl**(1/3.)
if mu_w is not None:
Nu *= (mu_b/mu_w)**0.14
return Nu*kl/D
References
----------
.. [1] Elamvaluthi, G., and N. S. Srinivas. "Two-Phase Heat Transfer in Two
Component Vertical Flows." International Journal of Multiphase Flow 10,
no. 2 (April 1, 1984): 237-42. doi:10.1016/0301-9322(84)90021-1.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vg = m*x/(rhog*pi/4*D**2)
Vl = m*(1-x)/(rhol*pi/4*D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
ReM = D*Vl*rhol/mu_b + D*Vg*rhog/mug
Nu_TP = 0.5*(mug/mu_b)**0.25*ReM**0.7*Prl**(1/3.)
if mu_w:
Nu_TP *= (mu_b/mu_w)**0.14
return Nu_TP*kl/D
References
----------
.. [1] Groothuis, H., and W. P. Hendal. "Heat Transfer in Two-Phase Flow.:
Chemical Engineering Science 11, no. 3 (November 1, 1959): 212-20.
doi:10.1016/0009-2509(59)80089-0.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vg = m*x/(rhog*pi/4*D**2)
Vl = m*(1-x)/(rhol*pi/4*D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
ReM = D*Vl*rhol/mu_b + D*Vg*rhog/mug
if water:
Nu_TP = 0.029*(ReM)**0.87*(Prl)**(1/3.)
else:
Nu_TP = 2.6*ReM**0.39*Prl**(1/3.)
if mu_w:
Nu_TP *= (mu_b/mu_w)**0.14
return Nu_TP*kl/D
References
----------
.. [1] Aggour, Mohamed A. Hydrodynamics and Heat Transfer in Two-Phase
Two-Component Flows, Ph.D. Thesis, University of Manutoba, Canada
(1978). http://mspace.lib.umanitoba.ca/xmlui/handle/1993/14171.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vls = m*(1-x)/(rhol*pi/4*D**2)
Vl = Vls/(1.-alpha)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mu_b)
if turbulent or (Rel > 2000.0 and turbulent is None):
hl = 0.0155*(kl/D)*Rel**0.83*Prl**0.5
return hl*(1-alpha)**-0.83
else:
hl = 1.615*(kl/D)*(Rel*Prl*D/L)**(1/3.)
if mu_w:
hl *= (mu_b/mu_w)**0.14
return hl*(1.0 - alpha)**(-1/3.)
.. [1] Martin, B. W, and G. E Sims. "Forced Convection Heat Transfer to
Water with Air Injection in a Rectangular Duct." International Journal
of Heat and Mass Transfer 14, no. 8 (August 1, 1971): 1115-34.
doi:10.1016/0017-9310(71)90208-0.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m*x/(rhog*pi/4*D**2)
Vls = m*(1-x)/(rhol*pi/4*D**2)
if hl is None:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re, Pr=Pr, L=L, Di=D, mu=mu_b, mu_w=mu_w)
hl = Nul*kl/D
return hl*(1.0 + 0.64*(Vgs/Vls)**0.5)
.. [1] Knott, R. F., R. N. Anderson, Andreas. Acrivos, and E. E. Petersen.
"An Experimental Study of Heat Transfer to Nitrogen-Oil Mixtures."
Industrial & Engineering Chemistry 51, no. 11 (November 1, 1959):
1369-72. doi:10.1021/ie50599a032.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m*x/(rhog*pi/4*D**2)
Vls = m*(1-x)/(rhol*pi/4*D**2)
if not hl:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re, Pr=Pr, L=L, Di=D, mu=mu_b, mu_w=mu_w)
hl = Nul*kl/D
return hl*(1 + Vgs/Vls)**(1/3.)