Miscellaneous utilities (ht.core)¶
- ht.core.LMTD(Thi, Tho, Tci, Tco, counterflow=True)[source]¶
Returns the log-mean temperature difference of an ideal counterflow or co-current heat exchanger.
\[\Delta T_{LMTD}=\frac{\Delta T_1-\Delta T_2}{\ln(\Delta T_1/\Delta T_2)} \]\[\text{For countercurrent: } \\ \Delta T_1=T_{h,i}-T_{c,o}\\ \Delta T_2=T_{h,o}-T_{c,i} \]\[\text{Parallel Flow Only:} \\ {\Delta T_1=T_{h,i}-T_{c,i}}\\ {\Delta T_2=T_{h,o}-T_{c,o}} \]- Parameters
- Thifloat
Inlet temperature of hot fluid, [K]
- Thofloat
Outlet temperature of hot fluid, [K]
- Tcifloat
Inlet temperature of cold fluid, [K]
- Tcofloat
Outlet temperature of cold fluid, [K]
- counterflowbool, optional
Whether the exchanger is counterflow or co-current
- Returns
- LMTDfloat
Log-mean temperature difference [K]
Notes
Any consistent set of units produces a consistent output.
For the case where the temperature difference is the same in counterflow, the arithmeric mean difference (either difference in that case) is the correct result following evaluation of the limit.
For the same problem with the co-current case, the limit evaluates to a temperature difference of zero.
References
- 1
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
Examples
Example 11.1 in [1].
>>> LMTD(100., 60., 30., 40.2) 43.200409294131525 >>> LMTD(100., 60., 30., 40.2, counterflow=False) 39.75251118049003 >>> LMTD(100., 60., 20., 60) 40.0 >>> LMTD(100., 60., 20., 60, counterflow=False) 0.0
- ht.core.countercurrent_hx_temperature_check(T0i, T0o, T1i, T1o)[source]¶
Perform a check on two sets of temperatures that could represent a countercurrent heat exchanger, and return whether they are possible or not.
- Parameters
- T0ifloat
Inlet temperature of one fluid, [K]
- T0ofloat
Outlet temperature of one fluid, [K]
- T1ifloat
Inlet temperature of another fluid, [K]
- T1ofloat
Outlet temperature of another fluid, [K]
- Returns
- plausiblebool
Whether the exchange is possilble, [-]
- ht.core.fin_efficiency_Kern_Kraus(Do, D_fin, t_fin, k_fin, h)[source]¶
Returns the efficiency eta_f of a circular fin of constant thickness attached to a circular tube, based on the tube diameter Do, fin diameter D_fin, fin thickness t_fin, fin thermal conductivity k_fin, and heat transfer coefficient h.
\[\eta_f = \frac{2r_o}{m(r_e^2 - r_o^2)} \left[\frac{I_1(mr_e)K_1(mr_o) - K_1(mr_e) I_1(mr_o)} {I_0(mr_o) K_1(mr_e) + I_1(mr_e) K_0(mr_o)}\right] \]\[m = \sqrt{\frac{2h}{k_{fin} t_{fin}}} \]\[r_e = 0.5 D_{fin} \]\[r_o = 0.5 D_{o} \]- Parameters
- Dofloat
Outer diameter of bare pipe (as if there were no fins), [m]
- D_finfloat
Outer diameter of the fin, from the center of the tube to the edge of the fin, [m]
- t_finfloat
Thickness of the fin (for constant thickness fins only), [m]
- k_finfloat
Thermal conductivity of the fin, [W/m/K]
- hfloat
Heat transfer coefficient of the finned pipe, [W/K]
- Returns
- eta_finfloat
Fin efficiency [-]
Notes
I0, I1, K0 and K1 are modified Bessel functions of order 0 and 1, modified Bessel function of the second kind of order 0 and 1 respectively.
A number of assumptions are made in deriving this set of equations [5]:
1-D radial conduction
Steady-state operation
No radiative heat transfer
Temperature-independent fin thermal conductivity
Constant heat transfer coefficient across the whole fin
The fin base temperature is a constant value
There is no constant resistance between the tube material and the added fin
The surrounding fluid is at a constant temperature
References
- 1
Kern, Donald Quentin, and Allan D. Kraus. Extended Surface Heat Transfer. McGraw-Hill, 1972.
- 2
Thulukkanam, Kuppan. Heat Exchanger Design Handbook, Second Edition. CRC Press, 2013.
- 3
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
- 4
Kraus, Allan D., Abdul Aziz, and James Welty. Extended Surface Heat Transfer. 1st edition. New York: Wiley-Interscience, 2001.
- 5
Perrotin, Thomas, and Denis Clodic. “Fin Efficiency Calculation in Enhanced Fin-and-Tube Heat Exchangers in Dry Conditions.” In Proc. Int. Congress of Refrigeration 2003, 2003.
Examples
>>> fin_efficiency_Kern_Kraus(0.0254, 0.05715, 3.8E-4, 200, 58) 0.8412588620231153
- ht.core.is_heating_property(prop, prop_wall)[source]¶
Checks whether or not a fluid side is being heated or cooled, from a property of the fluid at the wall and the bulk temperature. Returns True for heating the bulk fluid, and False for cooling the bulk fluid.
- Parameters
- propfloat
Viscosity (or Prandtl number) of flowing fluid away from the heat transfer surface, [Pa*s]
- prop_wallfloat
Viscosity (or Prandtl number) of the fluid at the wall, [Pa*s]
- Returns
- is_heatingbool
Whether or not the flow is being heated up by the wall, [-]
Examples
>>> is_heating_property(1E-3, 1.2E-3) False
- ht.core.is_heating_temperature(T, T_wall)[source]¶
Checks whether or not a fluid side is being heated or cooled, from the temperature of the wall and the bulk temperature. Returns True for heating the bulk fluid, and False for cooling the bulk fluid.
- Parameters
- Tfloat
Temperature of flowing fluid away from the heat transfer surface, [K]
- T_wallfloat
Temperature of the fluid at the wall, [K]
- Returns
- is_heatingbool
Whether or not the flow is being heated up by the wall, [-]
Examples
>>> is_heating_temperature(298.15, 350) True
- ht.core.wall_factor(mu=None, mu_wall=None, Pr=None, Pr_wall=None, T=None, T_wall=None, mu_heating_coeff=0.11, mu_cooling_coeff=0.25, Pr_heating_coeff=0.11, Pr_cooling_coeff=0.25, T_heating_coeff=0.11, T_cooling_coeff=0.25, property_option='Prandtl')[source]¶
Computes the wall correction factor for heat transfer, mass transfer, or momentum transfer between a fluid and a wall. Utility function; the coefficients for the phenomenon must be provided to this method. The default coefficients are for heat transfer of a turbulent liquid.
The general formula is as follows; substitute the property desired and the phenomenon desired into the equation for things other than heat transfer.
\[\frac{Nu}{Nu_{\text{constant properties}}} = \left(\frac{\mu}{\mu_{wall}}\right)^n \]- Parameters
- mufloat, optional
Viscosity of flowing fluid away from the surface, [Pa*s]
- mu_wallfloat, optional
Viscosity of the fluid at the wall, [Pa*s]
- Prfloat, optional
Prandtl number of flowing fluid away from the surface, [-]
- Pr_wallfloat, optional
Prandtl number of the fluid at the wall, [-]
- Tfloat, optional
Temperature of flowing fluid away from the surface, [K]
- T_wallfloat, optional
Temperature of the fluid at the wall, [K]
- mu_heating_coefffloat, optional
Coefficient for viscosity - surface providing heating, [-]
- mu_cooling_coefffloat, optional
Coefficient for viscosity - surface providing cooling, [-]
- Pr_heating_coefffloat, optional
Coefficient for Prandtl number - surface providing heating, [-]
- Pr_cooling_coefffloat, optional
Coefficient for Prandtl number - surface providing cooling, [-]
- T_heating_coefffloat, optional
Coefficient for temperature - surface providing heating, [-]
- T_cooling_coefffloat, optional
Coefficient for temperature - surface providing cooling, [-]
- property_optionstr, optional
Which property to use for computing the correction factor; one of ‘Viscosity’, ‘Prandtl’, or ‘Temperature’.
- Returns
- factorfloat
Correction factor for heat transfer; to be multiplied by the Nusselt number or heat transfer coefficient or friction factor or pressure drop to obtain the actual result, [-]
Examples
>>> wall_factor(mu=8E-4, mu_wall=3E-4, Pr=1.2, Pr_wall=1.1, T=300, ... T_wall=350, property_option='Prandtl') 1.0096172023817749
- ht.core.wall_factor_Nu(mu, mu_wall, turbulent=True, liquid=False)[source]¶
Computes the wall correction factor for heat transfer between a fluid and a wall. These coefficients were derived for internal flow inside a pipe, but can be used elsewhere where appropriate data is missing. It is also useful to compare these results with the coefficients used in various heat transfer coefficients.
\[\frac{Nu}{Nu_{\text{constant properties}}} = \left(\frac{\mu}{\mu_{wall}}\right)^n \]- Parameters
- mufloat
Viscosity (or Prandtl number) of flowing fluid away from the heat transfer surface, [Pa*s]
- mu_wallfloat
Viscosity (or Prandtl number) of the fluid at the wall, [Pa*s]
- turbulentbool
Whether or not to use the turbulent coefficient, [-]
- liquidbool
Whether or not to use the liquid phase coefficient; otherwise the gas coefficient is used, [-]
- Returns
- factorfloat
Correction factor for heat transfer; to be multiplied by the Nusselt number, or heat transfer coefficient to obtain the actual result, [-]
Notes
The exponents are determined as follows:
Regime
Phase
Heating
Cooling
Turbulent
Liquid
0.11
0.25
Turbulent
Gas
0.5
0
Laminar
Liquid
0.14
0.14
Laminar
Gas
0
0
References
- 1
Kays, William M., and Michael E. Crawford. Convective Heat and Mass Transfer. 3rd edition. New York: McGraw-Hill Science/Engineering/Math, 1993.
Examples
>>> wall_factor_Nu(mu=8E-4, mu_wall=3E-4, turbulent=True, liquid=True) 1.1139265634480144
>>> wall_factor_Nu(mu=8E-4, mu_wall=3E-4, turbulent=False, liquid=True) 1.147190712947014
>>> wall_factor_Nu(mu=1.5E-5, mu_wall=1.3E-5, turbulent=True, liquid=False) 1.0741723110591495
>>> wall_factor_Nu(mu=1.5E-5, mu_wall=1.3E-5, turbulent=False, liquid=False) 1.0
- ht.core.wall_factor_fd(mu, mu_wall, turbulent=True, liquid=False)[source]¶
Computes the wall correction factor for pressure drop due to friction between a fluid and a wall. These coefficients were derived for internal flow inside a pipe, but can be used elsewhere where appropriate data is missing.
\[\frac{f_d}{f_{d,\text{constant properties}}} = \left(\frac{\mu}{\mu_{wall}}\right)^n \]- Parameters
- mufloat
Viscosity (or Prandtl number) of flowing fluid away from the wall, [Pa*s]
- mu_wallfloat
Viscosity (or Prandtl number) of the fluid at the wall, [Pa*s]
- turbulentbool
Whether or not to use the turbulent coefficient, [-]
- liquidbool
Whether or not to use the liquid phase coefficient; otherwise the gas coefficient is used, [-]
- Returns
- factorfloat
Correction factor for pressure loss; to be multiplied by the friction factor, or pressure drop to obtain the actual result, [-]
Notes
The exponents are determined as follows:
Regime
Phase
Heating
Cooling
Turbulent
Liquid
-0.25
-0.25
Turbulent
Gas
0.1
0.1
Laminar
Liquid
-0.58
-0.5
Laminar
Gas
-1
-1
References
- 1
Kays, William M., and Michael E. Crawford. Convective Heat and Mass Transfer. 3rd edition. New York: McGraw-Hill Science/Engineering/Math, 1993.
Examples
>>> wall_factor_fd(mu=8E-4, mu_wall=3E-4, turbulent=True, liquid=True) 0.7825422900366437