def Yun_Heo_Kim(m, x, D, rhol, mul, Hvap, sigma, q=None, Te=None): r'''Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as shown in [1]_ and [2]_, and also reviewed in [3]_. Either the heat flux or excess temperature is required for the calculation of heat transfer coefficient. Uses liquid Reynolds number, Weber number, and Boiling number. Weber number is defined in terms of the velocity if all fluid were liquid. .. math:: h_{tp} = 136876(Bg\cdot We_l)^{0.1993} Re_l^{-0.1626} .. math:: Re_l = \frac{G D (1-x)}{\mu_l} .. math:: We_l = \frac{G^2 D}{\rho_l \sigma} Parameters ---------- m : float Mass flow rate [kg/s] x : float Quality at the specific tube interval [] D : float Diameter of the tube [m] rhol : float Density of the liquid [kg/m^3] mul : float Viscosity of liquid [Pa*s] Hvap : float Heat of vaporization of liquid [J/kg] sigma : float Surface tension of liquid [N/m] q : float, optional Heat flux to wall [W/m^2] Te : float, optional Excess temperature of wall, [K] Returns ------- h : float Heat transfer coefficient [W/m^2/K] Notes ----- [1]_ has been reviewed. Examples -------- >>> Yun_Heo_Kim(m=1, x=0.4, D=0.3, rhol=567., mul=156E-6, sigma=0.02, Hvap=9E5, q=1E4) 9479.313988550184 References ---------- .. [1] Yun, Rin, Jae Hyeok Heo, and Yongchan Kim. "Evaporative Heat Transfer and Pressure Drop of R410A in Microchannels." International Journal of Refrigeration 29, no. 1 (January 2006): 92-100. doi:10.1016/j.ijrefrig.2005.08.005. .. [2] Yun, Rin, Jae Hyeok Heo, and Yongchan Kim. "Erratum to 'Evaporative Heat Transfer and Pressure Drop of R410A in Microchannels; [Int. J. Refrigeration 29 (2006) 92-100]." International Journal of Refrigeration 30, no. 8 (December 2007): 1468. doi:10.1016/j.ijrefrig.2007.08.003. .. [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) V = G/rhol Rel = G*D*(1-x)/mul We = Weber(V=V, L=D, rho=rhol, sigma=sigma) if q is not None: Bg = Boiling(G=G, q=q, Hvap=Hvap) return 136876*(Bg*We)**0.1993*Rel**-0.1626 elif Te is not None: A = 136876*(We)**0.1993*Rel**-0.1626*(Te/G/Hvap)**0.1993 return A**(10000/8007.) else: raise ValueError('Either q or Te is needed for this correlation')
def Sun_Mishima(m, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None): r'''Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as shown in [1]_, and also reviewed in [2]_. Either the heat flux or excess temperature is required for the calculation of heat transfer coefficient. Uses liquid-only Reynolds number, Weber number, and Boiling number. Weber number is defined in terms of the velocity if all fluid were liquid. .. math:: h_{tp} = \frac{ 6 Re_{lo}^{1.05} Bg^{0.54}} {We_l^{0.191}(\rho_l/\rho_g)^{0.142}}\frac{k_l}{D} .. math:: Re_{lo} = \frac{G_{tp}D}{\mu_l} Parameters ---------- m : float Mass flow rate [kg/s] D : float Diameter of the tube [m] rhol : float Density of the liquid [kg/m^3] rhog : float Density of the gas [kg/m^3] mul : float Viscosity of liquid [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of liquid [J/kg] sigma : float Surface tension of liquid [N/m] q : float, optional Heat flux to wall [W/m^2] Te : float, optional Excess temperature of wall, [K] Returns ------- h : float Heat transfer coefficient [W/m^2/K] Notes ----- [1]_ has been reviewed. [1]_ used 2501 data points to derive the results, covering hydraulic diameters from 0.21 to 6.05 mm and 11 different fluids. Examples -------- >>> Sun_Mishima(m=1, D=0.3, rhol=567., rhog=18.09, kl=0.086, mul=156E-6, sigma=0.02, Hvap=9E5, Te=10) 507.6709168372167 References ---------- .. [1] Sun, Licheng, and Kaichiro Mishima. "An Evaluation of Prediction Methods for Saturated Flow Boiling Heat Transfer in Mini-Channels." International Journal of Heat and Mass Transfer 52, no. 23-24 (November 2009): 5323-29. doi:10.1016/j.ijheatmasstransfer.2009.06.041. .. [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. ''' G = m/(pi/4*D**2) V = G/rhol Relo = G*D/mul We = Weber(V=V, L=D, rho=rhol, sigma=sigma) if q is not None: Bg = Boiling(G=G, q=q, Hvap=Hvap) return 6*Relo**1.05*Bg**0.54/(We**0.191*(rhol/rhog)**0.142)*kl/D elif Te is not None: A = 6*Relo**1.05/(We**0.191*(rhol/rhog)**0.142)*kl/D return A**(50/23.)*Te**(27/23.)/(G**(27/23.)*Hvap**(27/23.)) else: raise ValueError('Either q or Te is needed for this correlation')
def Lazarek_Black(m, D, mul, kl, Hvap, q=None, Te=None): r'''Calculates heat transfer coefficient for film boiling of saturated fluid in vertical tubes for either upward or downward flow. Correlation is as shown in [1]_, and also reviewed in [2]_ and [3]_. Either the heat flux or excess temperature is required for the calculation of heat transfer coefficient. Quality independent. Requires no properties of the gas. Uses a Reynolds number assuming all the flow is liquid. .. math:: h_{tp} = 30 Re_{lo}^{0.857} Bg^{0.714} \frac{k_l}{D} .. math:: Re_{lo} = \frac{G_{tp}D}{\mu_l} Parameters ---------- m : float Mass flow rate [kg/s] D : float Diameter of the channel [m] mul : float Viscosity of liquid [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of liquid [J/kg] q : float, optional Heat flux to wall [W/m^2] Te : float, optional Excess temperature of wall, [K] Returns ------- h : float Heat transfer coefficient [W/m^2/K] Notes ----- [1]_ has been reviewed. [2]_ claims it was developed for a range of quality 0-0.6, Relo 860-5500, mass flux 125-750 kg/m^2/s, q of 1.4-38 W/cm^2, and with a pipe diameter of 3.1 mm. Developed with data for R113 only. Examples -------- >>> Lazarek_Black(m=10, D=0.3, mul=1E-3, kl=0.6, Hvap=2E6, Te=100) 9501.932636079293 References ---------- .. [1] Lazarek, G. M., and S. H. Black. "Evaporative Heat Transfer, Pressure Drop and Critical Heat Flux in a Small Vertical Tube with R-113." International Journal of Heat and Mass Transfer 25, no. 7 (July 1982): 945-60. doi:10.1016/0017-9310(82)90070-9. .. [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) Relo = G*D/mul if q is not None: Bg = Boiling(G=G, q=q, Hvap=Hvap) return 30*Relo**0.857*Bg**0.714*kl/D elif Te is not None: # Solved with sympy return 27000*30**(71/143)*(1./(G*Hvap))**(357/143)*Relo**(857/286)*Te**(357/143)*kl**(500/143)/D**(500/143) else: raise ValueError('Either q or Te is needed for this correlation')
def Li_Wu(m, x, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None): r'''Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as shown in [1]_, and also reviewed in [2]_ and [3]_. Either the heat flux or excess temperature is required for the calculation of heat transfer coefficient. Uses liquid Reynolds number, Bond number, and Boiling number. .. math:: h_{tp} = 334 Bg^{0.3}(Bo\cdot Re_l^{0.36})^{0.4}\frac{k_l}{D} .. math:: Re_{l} = \frac{G(1-x)D}{\mu_l} Parameters ---------- m : float Mass flow rate [kg/s] x : float Quality at the specific tube interval [] D : float Diameter of the tube [m] rhol : float Density of the liquid [kg/m^3] rhog : float Density of the gas [kg/m^3] mul : float Viscosity of liquid [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of liquid [J/kg] sigma : float Surface tension of liquid [N/m] q : float, optional Heat flux to wall [W/m^2] Te : float, optional Excess temperature of wall, [K] Returns ------- h : float Heat transfer coefficient [W/m^2/K] Notes ----- [1]_ has been reviewed. [1]_ used 18 sets of experimental data to derive the results, covering hydraulic diameters from 0.19 to 3.1 mm and 12 different fluids. Examples -------- >>> Li_Wu(m=1, x=0.2, D=0.3, rhol=567., rhog=18.09, kl=0.086, mul=156E-6, sigma=0.02, Hvap=9E5, q=1E5) 5345.409399239492 References ---------- .. [1] Li, Wei, and Zan Wu. "A General Correlation for Evaporative Heat Transfer in Micro/mini-Channels." International Journal of Heat and Mass Transfer 53, no. 9-10 (April 2010): 1778-87. doi:10.1016/j.ijheatmasstransfer.2010.01.012. .. [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] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and Predictive Methods for Pressure Drop in Adiabatic, Condensing and Boiling Mini/micro-Channel Flows." International Journal of Heat and Mass Transfer 77 (October 2014): 74-97. doi:10.1016/j.ijheatmasstransfer.2014.04.035. ''' G = m/(pi/4*D**2) Rel = G*D*(1-x)/mul Bo = Bond(rhol=rhol, rhog=rhog, sigma=sigma, L=D) if q is not None: Bg = Boiling(G=G, q=q, Hvap=Hvap) return 334*Bg**0.3*(Bo*Rel**0.36)**0.4*kl/D elif Te is not None: A = 334*(Bo*Rel**0.36)**0.4*kl/D return A**(10/7.)*Te**(3/7.)/(G**(3/7.)*Hvap**(3/7.)) else: raise ValueError('Either q or Te is needed for this correlation')