Effectiveness-NTU
HX returns either the heat exchanger effectiveness (epsilon) given the number of transfer units (Ntu) or it returns Ntu given the effectiveness..
The general form is either:
epsilon=HX(TypeHX$, Ntu, C_1, C_2 , Return$)
or
Ntu=HX(TypeHX$, epsilon, C_1, C_2 , Return$)
depending upon the value of the text string Return$. If Return$ is set to 'epsilon' then the HX returns the effectiveness but if Return$ is set to 'Ntu' then HX returns Ntu. Note that all strings are case-insenstive in EES.
If epsilon is known, then it is more efficient to set Return$='Ntu'. If Ntu is known, then it is more efficient to set Return$='epsilon'.
There is always a solution for epsilon given any valid Ntu but there may not be a solution for Ntu given any valid epsilon.
The heat exchanger flow configuration is specified with the parameter TypeHX$. The following are acceptable values (case-insensitive) for TypeHX$:
'parallelflow'
'counterflow'
'crossflow_both_unmixed'
'crossflow_both_mixed'
'crossflow_one_unmixed' {C_1 must be the unmixed fluid.}
'shell&tube_N' {where N is an integer between 1 and 9, specifying the number of shell pass. The number of tube passes is then, 2N, 4N, 6N, .... . }
'regenerator' {balanced flow is assumed; HX cannot solve for Ntu given epsilon for this case.}
Number of Transfer Units, NTU:
The ratio of the overall conductance to the minimum capacitance rate is the number of transfer units. For a regenerator, NTU is the product of the surface area of the matrix and the heat transfer coefficient experienced during one blow period (both periods are assumed to have the same value) divided by the capacitance rate of the fluid.
Capacitance rates, C_1 and C_2 :
The product of the mass flow rate (e.g., kg/s or lbm/hr) and the fluid specific heat (e.g., J/kg-K or Btu/lbm-R) is the capacitance rate. The two capacitance rates are C_1 and C_2. In most cases it does not matter which fluid is C_1 or C_2. However, for a cross-flow heat exchanger with one fluid mixed, C_1 must be the unmixed fluid. If one fluid is at a constant temperature (e.g., an evaporator or condenser), that fluid capacitance rate should be set to a large number compared to the other fluid (e.g., 1000 times bigger is usually sufficient). For a regenerator, C_1 is the product of the mass flow rate and specific heat of the fluid during the hot or cold flow period. The flow is assumed to be balanced so the capacitance rates and flow duration during the hot and cold flow periods are equal. C_2 is the thermal capacity of the regenerator divided by the duration of the hot or cold flow process.
"Find the outlet temperature for the cold stream and the length of a concentric tube HX."
$UnitSystem SI C J Pa
$VarInfo A units=m^2
$VarInfo C_dot_c units=W/K
$VarInfo C_dot_h units=W/K
$VarInfo C_dot_min units=W/K
$VarInfo L units=m
$VarInfo q units=W
$VarInfo q_max units=W
$VarInfo T_c_o units=K
"knowns:"
T_h_i=100 [C]
T_h_o=60 [C]
T_c_i=30 [C]
m_dot_h=0.1 [kg/s]
m_dot_c=0.1 [kg/s]
U=60 [W/m^2-K]
D=0.025 [m]
c_p_oil=1900 [J/kg-K]
c_p_water=4200 [J/kg-K]
"a) What is the heat transfer and the water outlet temperature?"
C_dot_h=m_dot_h*c_p_oil
C_dot_c=m_dot_c*c_p_water
q=C_dot_h * (T_h_i-T_h_o)
q=C_dot_c * (T_c_o-T_c_i)
"b) What is the HX length?"
C_dot_min=min(C_dot_h, C_dot_c)
TypeHX$='counterflow'
q_max=C_dot_min * (T_h_i-T_c_i)
epsilon=q/q_max
Ntu=hx(TypeHX$, epsilon, C_dot_h, C_dot_c, 'Ntu')
Ntu=(U*A)/C_dot_min
A=pi*D*L
{Solution:
L=40.36 [m]
q=7600 [W]
T_c_o=48.1 [K]
}
Equations used for recuperative heat exchangers in this function are taken from Tables 8-1 of Nellis and Klein. Note that for the crossflow both fluids unmixed case, it is not possible to analytically determine NTU given epsilon. In this case, NTU is determined numerically using a Subprogram in the HX library file.
The regenerator effectiveness is determined from a lookup table as a function of the NTU and utilizilation using the tabular data presented in G. D. Dragutinovic and B. S. Baclic, Operation of Counterflow Regenerators, Computational Mechanics Publications, Billerica, 1998