How to use the fluids.core.Prandtl function in fluids

t_dry_film = rhol*Hvap/q*(delta0 - C_delta0)
    if t_dry_film > tv:
        t_film = tv
        delta_end = delta0 - q/rhol/Hvap*tv # what could time possibly be?
        t_dry = 0
    else:
        t_film = t_dry_film
        delta_end = C_delta0
        t_dry = tv-t_film
    Ll = tau*G/rhol*(1-x)
    Ldry = t_dry*vp


    Prg = Prandtl(Cp=Cpg, k=kg, mu=mug)
    Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
    fg = (1.82*log10(Reg) - 1.64)**-2
    fl = (1.82*log10(Rel) - 1.64)**-2
    
    Nu_lam_Zl = 2*0.455*(Prl)**(1/3.)*(D*Rel/Ll)**0.5
    Nu_trans_Zl = turbulent_Gnielinski(Re=Rel, Pr=Prl, fd=fl)*(1 + (D/Ll)**(2/3.))
    if Ldry == 0:
        Nu_lam_Zg, Nu_trans_Zg = 0, 0
    else:
        Nu_lam_Zg = 2*0.455*(Prg)**(1/3.)*(D*Reg/Ldry)**0.5
        Nu_trans_Zg = turbulent_Gnielinski(Re=Reg, Pr=Prg, fd=fg)*(1 + (D/Ldry)**(2/3.))
        
    h_Zg = kg/D*(Nu_lam_Zg**4 + Nu_trans_Zg**4)**0.25
    h_Zl = kl/D*(Nu_lam_Zl**4 + Nu_trans_Zl**4)**0.25
        
    h_film = 2*kl/(delta0 + C_delta0)
    return tl/tau*h_Zl + t_film/tau*h_film + t_dry/tau*h_Zg

tv = tau/(1 ++ rhog/rhol*((1.-x)/x))

    t_dry_film = rhol*Hvap/q*(delta0 - C_delta0)
    if t_dry_film > tv:
        t_film = tv
        delta_end = delta0 - q/rhol/Hvap*tv # what could time possibly be?
        t_dry = 0
    else:
        t_film = t_dry_film
        delta_end = C_delta0
        t_dry = tv-t_film
    Ll = tau*G/rhol*(1-x)
    Ldry = t_dry*vp


    Prg = Prandtl(Cp=Cpg, k=kg, mu=mug)
    Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
    fg = (1.82*log10(Reg) - 1.64)**-2
    fl = (1.82*log10(Rel) - 1.64)**-2
    
    Nu_lam_Zl = 2*0.455*(Prl)**(1/3.)*(D*Rel/Ll)**0.5
    Nu_trans_Zl = turbulent_Gnielinski(Re=Rel, Pr=Prl, fd=fl)*(1 + (D/Ll)**(2/3.))
    if Ldry == 0:
        Nu_lam_Zg, Nu_trans_Zg = 0, 0
    else:
        Nu_lam_Zg = 2*0.455*(Prg)**(1/3.)*(D*Reg/Ldry)**0.5
        Nu_trans_Zg = turbulent_Gnielinski(Re=Reg, Pr=Prg, fd=fg)*(1 + (D/Ldry)**(2/3.))
        
    h_Zg = kg/D*(Nu_lam_Zg**4 + Nu_trans_Zg**4)**0.25
    h_Zl = kl/D*(Nu_lam_Zl**4 + Nu_trans_Zl**4)**0.25
        
    h_film = 2*kl/(delta0 + C_delta0)

----------
    .. [1] Bennett, Douglas L., and John C. Chen. "Forced Convective Boiling in
       Vertical Tubes for Saturated Pure Components and Binary Mixtures." 
       AIChE Journal 26, no. 3 (May 1, 1980): 454-61. doi:10.1002/aic.690260317.
    .. [2] Bennett, Douglas L., M.W. Davies and B.L. Hertzler, The Suppression 
       of Saturated Nucleate Boiling by Forced Convective Flow, American 
       Institute of Chemical Engineers Symposium Series, vol. 76, no. 199. 
       91-103, 1980.
    .. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella. 
       "Review and Comparative Analysis of Studies on Saturated Flow Boiling in
       Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
       no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
    '''
    G = m/(pi/4*D**2)
    Rel = D*G*(1-x)/mul
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl)*kl/D
    Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
    F = ((Prl+1)/2.)**0.444*(1 + Xtt**-0.5)**1.78
    X0 = 0.041*(sigma/(g*(rhol-rhog)))**0.5
    S = (1 - exp(-F*hl*X0/kl))/(F*hl*X0/kl)
    
    hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma,
                       Hvap=Hvap, rhol=rhol, rhog=rhog)
    return hnb*S + hl*F

2012): 325-35. doi:10.1016/j.ijrefrig.2011.11.002.
    .. [2] Huang, Jianchang. "Performance Analysis of Plate Heat Exchangers 
       Used as Refrigerant Evaporators," 2011. Thesis.
       http://wiredspace.wits.ac.za/handle/10539/9779
    .. [3] Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. 
       "Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers.
       Part 1: Review and Experimental Database." International Journal of 
       Refrigeration 61 (January 2016): 166-84.
       doi:10.1016/j.ijrefrig.2015.07.010.
    .. [4] Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. "A Survey of
       Correlations for Heat Transfer and Pressure Drop for Evaporation and 
       Condensation in Plate Heat Exchangers." International Journal of 
       Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.
    '''
    do = 0.0146*angle*(2.*sigma/(g*(rhol - rhog)))**0.5
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    alpha_l = thermal_diffusivity(k=kl, rho=rhol, Cp=Cpl)
    h = 1.87E-3*(kl/do)*(q*do/(kl*Tsat))**0.56*(Hvap*do**2/alpha_l**2)**0.31*Prl**0.33
    return h

----------
    .. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
       R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press, 
       1994.
    .. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
       Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986). 
    .. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
       Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
       in Cross Flow."  Heat Transfer Engineering 8, no. 2 (January 1987): 
       49-62.
    '''
    fin_height = 0.5*(fin_diameter - tube_diameter)

    V_max = m/(A_min*rho)
    Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
    Pr = Prandtl(Cp=Cp, mu=mu, k=k)
    Nu = (0.183*Re**0.7*(bare_length/fin_height)**0.36
          *(pitch_normal/fin_diameter)**0.06
          *(fin_height/fin_diameter)**0.11*Pr**0.36)
    
    staggered = abs(1 - pitch_normal/pitch_parallel) > 0.05
    F2 = ESDU_tube_row_correction(tube_rows=tube_rows, staggered=staggered)
    Nu *= F2
    if Pr_wall is not None:
        F1 = wall_factor(Pr=Pr, Pr_wall=Pr_wall, Pr_heating_coeff=0.26, 
                         Pr_cooling_coeff=0.26, 
                         property_option=WALL_FACTOR_PRANDTL)
        Nu *= F1
    
    h = k/tube_diameter*Nu
    efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter, 
                                           D_fin=fin_diameter,

Pressure Drop of Air Flowing across Triangular Banks of Finned Tubes",
       Chemical Engineering Progress Symp., Series 41, No. 59. Chem. Eng. Prog.
       Symp. Series No. 41, "Heat Transfer - Houston".
    .. [2] Mukherjee, R., and Geoffrey Hewitt. Practical Thermal Design of 
       Air-Cooled Heat Exchangers. New York: Begell House Publishers Inc.,U.S.,
       2007.
    .. [3] Kroger, Detlev. Air-Cooled Heat Exchangers and Cooling Towers: 
       Thermal-Flow Performance Evaluation and Design, Vol. 1. Tulsa, Okl:
       PennWell Corp., 2004.
    '''
    fin_height = 0.5*(fin_diameter - tube_diameter)
    
    V_max = m/(A_min*rho)
    
    Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
    Pr = Prandtl(Cp=Cp, mu=mu, k=k)

    Nu = 0.134*Re**0.681*Pr**(1/3.)*(bare_length/fin_height)**0.2*(bare_length/fin_thickness)**0.1134

    h = k/tube_diameter*Nu
    efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter, D_fin=fin_diameter,
                                           t_fin=fin_thickness, k_fin=k_fin, h=h)
    h_total_area_basis = (efficiency*A_fin + A_tube_showing)/A*h
    h_bare_tube_basis = h_total_area_basis*A_increase
        
    return h_bare_tube_basis

References
    ----------
    .. [1] A. Cavallini, J. R. Smith and R. Zecchin, A dimensionless correlation
       for heat transfer in forced convection condensation, 6th International 
       Heat Transfer Conference., Tokyo, Japan (1974) 309-313. 
    .. [2] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st. 
       Wiley-Interscience, 1991.
    .. [3] Balcılar, Muhammet, Ahmet Selim Dalkılıç, Berna Bolat, and Somchai 
       Wongwises. "Investigation of Empirical Correlations on the Determination
       of Condensation Heat Transfer Characteristics during Downward Annular 
       Flow of R134a inside a Vertical Smooth Tube Using Artificial 
       Intelligence Algorithms." Journal of Mechanical Science and Technology 
       25, no. 10 (October 12, 2011): 2683-2701. doi:10.1007/s12206-011-0618-2.
    '''
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    Vl = m*(1-x)/(rhol*pi/4*D**2)
    Vg = m*x/(rhog*pi/4*D**2)
    Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mul)    
    Reg = Reynolds(V=Vg, D=D, rho=rhog, mu=mug)
    '''The following was coded, and may be used instead of the above lines,
    to check that the definitions of parameters here provide the same results
    as those defined in [1]_.
    G = m/(pi/4*D**2)
    Re = G*D/mul
    Rel = Re*(1-x)
    Reg = Re*x/(mug/mul)'''
    Reeq = Reg*(mug/mul)*(rhol/rhog)**0.5 + Rel
    Nul = 0.05*Reeq**0.8*Prl**0.33
    return Nul*kl/D # confirmed to be with respect to the liquid

Saturated and Subcooled Flow Boiling in Tubes and Annuli, Based on a 
       Nucleate Pool Boiling Equation." International Journal of Heat and Mass 
       Transfer 34, no. 11 (November 1991): 2759-66. 
       doi:10.1016/0017-9310(91)90234-6. 
    .. [2] Fang, Xiande, Zhanru Zhou, and Dingkun Li. "Review of Correlations 
       of Flow Boiling Heat Transfer Coefficients for Carbon Dioxide." 
       International Journal of Refrigeration 36, no. 8 (December 2013): 
       2017-39. doi:10.1016/j.ijrefrig.2013.05.015.
    .. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella. 
       "Review and Comparative Analysis of Studies on Saturated Flow Boiling in
       Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
       no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
    '''
    G = m/(pi/4*D**2)
    ReL = D*G/mul
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    hl = turbulent_Dittus_Boelter(Re=ReL, Pr=Prl)*kl/D
    F = (1 + x*Prl*(rhol/rhog - 1))**0.35
    S = (1 + 0.055*F**0.1*ReL**0.16)**-1
#    if horizontal:
#        Fr = Froude(V=G/rhol, L=D, squared=True)
#        if Fr < 0.05:
#            ef = Fr**(0.1 - 2*Fr)
#            es = Fr**0.5
#            F *= ef
#            S *= es
    h_nb = Cooper(Te=Te, P=P, Pc=Pc, MW=MW)
    return ((F*hl)**2 + (S*h_nb)**2)**0.5

----------
    .. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
       R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press, 
       1994.
    .. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
       Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986). 
    .. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
       Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
       in Cross Flow."  Heat Transfer Engineering 8, no. 2 (January 1987): 
       49-62.
    '''
    fin_height = 0.5*(fin_diameter - tube_diameter)

    V_max = m/(A_min*rho)
    Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
    Pr = Prandtl(Cp=Cp, mu=mu, k=k)
    Nu = 0.242*Re**0.658*(bare_length/fin_height)**0.297*(pitch_normal/pitch_parallel)**-0.091*Pr**(1/3.)

    if tube_rows < 2:
        F2 = 0.76
    elif tube_rows < 3:
        F2 = 0.84
    elif tube_rows < 4:
        F2 = 0.92
    else:
        F2 = 1.0

    Nu *= F2
    if Pr_wall is not None:
        F1 = wall_factor(Pr=Pr, Pr_wall=Pr_wall, Pr_heating_coeff=0.26, 
                         Pr_cooling_coeff=0.26, 
                         property_option=WALL_FACTOR_PRANDTL)

References
    ----------
    .. [1] Shah, M. M. "A General Correlation for Heat Transfer during Film 
       Condensation inside Pipes." International Journal of Heat and Mass 
       Transfer 22, no. 4 (April 1, 1979): 547-56. 
       doi:10.1016/0017-9310(79)90058-9. 
    .. [2] Shah, M. M., Heat Transfer During Film Condensation in Tubes and 
       Annuli: A Review of the Literature, ASHRAE Transactions, vol. 87, no. 
       3, pp. 1086-1100, 1981.
    .. [3] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st. 
       Wiley-Interscience, 1991.
    '''
    VL = m/(rhol*pi/4*D**2)
    ReL = Reynolds(V=VL, D=D, rho=rhol, mu=mul)
    Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
    hL = turbulent_Dittus_Boelter(ReL, Prl)*kl/D
    Pr = P/Pc
    return hL*((1-x)**0.8 + 3.8*x**0.76*(1-x)**0.04/Pr**0.38)