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Log Mean Temperature Difference

 

LMTD_CF returns the correction factor needed to determine the log mean temperature difference (LMTD) of a heat exchanger with a flow configuration other than counterflow.  LMTD_CF is 1 by definition for counterflow but it will be less than one for other flow configurations as presented in section 8.2 of Nellis and Klein.

 

Usage:

The general form is:  F=LMTD_CF(TypeHX$,P,R)

 

Inputs:

        

where 

     Ti and To, and ti and to are the temperatures at the inlet and outlet of the two streams respectively.

     TypeHX$ - specifies the heat exchanger flow configuration; applicable heat exchanger geometries are listed below

 

Flow Configurations:

The heat exchanger flow configuration, TypeHX$, must be set to one of the following (case-insensitive) strings:

    'parallelflow'

    'crossflow_both_unmixed'

    'crossflow_one_unmixed'

    '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, .... . }

 

Limitations:

Function LMTD_CF calls HX to determine the NTU of the heat exchanger, which is then used to determine LMTD_CF.  The log mean temperature difference is valid, in general, for all values of R and from 0<P<1.  However, at a particular value of R, it is possible to choose a value of P for which no value for F exists. In this case, the error shown may appear as: 'There is no solution for Ntu given epsilon = ___'.  

 

There is no analytical solution to NTU given epsilon for the 'crossflow_both_mixed' flow configuration.  In this case, a subprogram is internally called to solve for NTU in an iterative manner given the effectiveness.   

 

Example:

$UnitSystem SI K Pa J

TypeHX$='crossflow_both_unmixed'

T_h_i=400 [K]                "unmixed fluid inlet temperature"

T_h_o=330 [K]              "unmixed fluid inlet temperature"

t_c_i=300 [K]                  "mixed fluid inlet temperature"

t_c_o=325 [K]                 "mixed fluid outlet temperature"

P=(t_c_o-t_c_i)/(T_h_i-t_c_i)

R=(T_h_i-T_h_o)/(t_c_o-t_c_i)

F=LMTD_CF(TypeHX$,P,R)

 

{Solution: F=0.9253}

 

Heat Exchangers Index