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					Heat Transfer & Fluid Flow 1 (2009)                                                               www.journal.boilersdesign.info




                               BIO Electronic Journal of Heat Transfer & Fluid Flow



          THERMO-PHYSICAL PROPERTIES OF COMBUSTION PRODUCTS

                                                     M.Sc. / R. K. Nsaif (Insayif)
                                                              HEES. Com.
                                              Ministry of Industry and Minerals in Iraq 
                                                E-Mail/ rashid@boilersdesign.info

Introduction:
        The calculation of combustion gases physical properties, (density, dynamic viscosity, thermal
conductivity, specific heat) is the first step in calculating the amount of heat released from the combustion
gases flow inside heat exchanger tubes. Least squares method (polynomial regression) was used in
(Graphing Advantage Plus-Curve Fitting Program) in order to convert the gases physical properties tables
data to equations that will be need in the program that build in Microsoft Excel 2003 to perform all the
calculation and graphs.
        The chemical composition of light oil is (C, S, H2 , O2 , N2). The complete combustion process
produces a mixture of gases, (Carbon dioxide, Water vapor, Nitrogen, Sulfur dioxide). The weight
percentage of these components depends on the weight percentage of the fuel chemical composition
(Chattopadhyay, 1998).

C + O2 = CO2 + heat (408.8 kJ/mol) .................................................... (1)
1mole    1 mole      1 mole


S + O2 = SO2 + heat (292.2 kJ/mol) .................................................... (2)
1mole   1 mole       1 mole


H2 + 0.5O2 = H2O + heat (242 kJ/mol) ................................................... (3)
1mole   0.5 mole      1 mole


Calculation Procedure:
1- Density:
        The combustion gases is a mixture of several gases, thus, its density can be calculated according to
the following formula (TEMA, 1988):
                 n

ρ mixture =   ∑
              i =1
                       ρi Xi ................................................................................. (4)

where n = number of gases content in the flue gases,
       X i = is the mass fraction (X i = W i / W t),
       W i = mass of one gas in kg,
       W t = total mass of the mixture gases in kg.
The individual gas density (ρi) is evaluated from the ideal gas equation
(P`V = NROT) ........................................................................................... (5)
where, P` = partial gas pressure in Pa (N/m2),
        N= moles number of the gas,
        V= gas volume in m3,
        RO= Universal gas constant = 8.314 J/mol.K.
        T = absolute gas temperature in K.

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Heat Transfer & Fluid Flow 1 (2009)                                                                   www.journal.boilersdesign.info

2- Dynamic Viscosity:
      Dynamic viscosity of the combustion gases can be calculated by using this formula (TEMA, 1988):
                 n

               ∑i =1
                             µi Υi(Mwi)1/2

µ mixture =                                               ....................................................... (6)
                       n

                      ∑
                      i =1
                               Υi(Mwi)1/2


Where Yi is the mole fraction (Yi = Ni / N t ),
Ni= number of moles of one gas,
N t = total moles number of mixture gases.
        The viscosity of N2, O2, CO2, H2O are taken from physical properties tables (Kays and Crawford,
1980), while dynamic viscosity of SO2 is taken from (McAdams, 1954). All these data are formulated to
equations that calculate the dynamic viscosity for each gas at different temperatures.
µm = (a+bT´+cT´2)/d            ........................................................................ (7)
where (m) is the type of gas, and ( a, b, c, and d) are constants evaluated from table (1) .


3- Specific Heat:
       Combustion gases specific heat can be calculated by using this formula (Doolittle and Hale, 1983):
                n

Cp mixture =   ∑
               i =1
                             Υi Cpi    ........................................................................... (8)

       The specific heat of the combustion gases components, CO2, H2O vapor, and N2 is calculated from
(Doolittle, and Hale, 1983) formulas:
CpCO2 = [a- (b/ T´) + (c / T´2)] ................................................................... (8a)
CpH2O = [a – (b/ T´0.5) + (c/T´)].................................................................. (8b)
Cp N2 = [ a – (b/ T´) + (c/ T´2)]................................................................... (8c)
CpO2 = [ a – (b/T´0.5) + (c/ T´)] ................................................................ (8d)
while specific heat SO2 is calculated from (McAdams, 1954) such that:
CpSO2 = (a + bT´ + cT´2 + dT´3)* 0.064 .................................................... (8e)
where a, b, c, and d are constant taken from table (2) .


4- Thermal Conductivity:
       From (TEMA, 1988) thermal conductivity of the combustion gases can be calculated as:
                 n

               ∑i =1
                             Ki Υi(Mwi)1/3

K mixture =                                    .................................................................. (9)
                       n

                      ∑
                      i =1
                               Υi(Mwi)1/3


        Temperature dependent thermal conductivity of N2, O2, CO2, H2O is taken from physical properties
tables by (Kays and Crawford, 1980), and formulated in equations such that:
Km = (a+bT´+cT´2)/d ............................................................................. (10a)
where the constants a, b, c, and d are taken from table (3). Thermal conductivity of sulfur dioxide is
calculated for temperature range (200 to 800°C) depending on:
kSO2 = (µ * CP/Pr) .................................................................................... (10b)
where values of µ, and CP are calculated from equations (7), and (8e). Prandtl number is extracted from
(McAdams, 1954).

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Heat Transfer & Fluid Flow 1 (2009)                                                                     www.journal.boilersdesign.info

5- Mean Combustion Gases Physical Properties:
        Mean combustion gases physical properties that flowing inside tubes can be calculated by integrating
the local physical properties such that:
                    L

ρmean. = (1/L) *    ∫
                    0
                                ρx . dx     ........................................................................ (11)

                        L

µ. mean = (1/L) *       ∫
                        0
                                µx . dx     ........................................................................ (12)

                            L

Cpmean. = (1/L) *           ∫
                            0
                                 Cpx . dx .................................................................... (13)

                    L

kmean = (1/L) *     ∫
                    0
                                kx . dx    ......................................................................... (14)



Discussion:

The Effect of Combustion Gases Temperature Gradient on Its Physical Properties:
        Figure (1) shows physical properties variation with temperature, for combustion gases flow inside
empty and inserted test tube for different fuel consumptions rates. In this figure clarify the density
proportional inversely with combustion gases temperature, while the dynamic viscosity, thermal
conductivity, and specific heat proportional approximately linear with combustion gases temperature
(Insayif,2008) .



                                          Tables of Constants Physicals Properties Equations.

              Table (1): Constants for Gases Dynamic Viscosity Physical Properties Equations.
                                  For temperature range (300 – 500 )K
              µm (N.s/m2).             m = N2               M = O2                m = CO2
                   a             1.873714285721       1.557142857138         -0.568857142854
                   b             0.061188571429       0.072385714286          0.057525714286
                   c            -0.000026285714       -0.000028857143 -0.000018857143
                   d                  1000000             1000000                 1000000
                                  For temperature range (500 - 1400)K
              µm (N.s/m2).             m = N2               M = O2                m = CO2
                   a             7.75789393939        8.038666666662          3.149151515148
                   b             0.040440378788       0.050102424242          0.045127575758
                   c            -0.000007799242       -0.000009606061 -0.000008530303
                   d                  1000000             1000000                 1000000
                                  For temperature range (380 – 850)K
                         µm (N.s/m2)                               m = H2O vapor
                              a                                  -0.989222642985
                              b                                   0.036063630361
                              c                                   0.000000011647
                              d                                       1000000
                                                  For temperature range (373 - 1273)K

                                     µm (N.s/m2).                                                      m = SO2

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Heat Transfer & Fluid Flow 1 (2009)                                     www.journal.boilersdesign.info

                                  a                                0.252591176471
                                  b                                0.003673017839
                                  c                               -0.000000664898

                                  d                                     100000


              Table (2): Constants for Gases Specific Heat Physical Properties Equations.
    Temp. range       (300-          (300-           (300-           (300-        (366.3 – 1144.1)K
                     5000)K         2800)K          3500)K          2800)K
    Cp (J/mol.K)        N2             O2             CO2        H2O vapor                SO2
         a            39.65         48.211           67.83           83.15       356.973209950214
         b         8.07*1000         536.7       15.19*1000          1863          1.189510329057
         c        1.499*10^6         3558        1.822*10^6         17450         -0.000976612179
         d                                                                         0.000000269776

Note/ Constants (a, b, and c) was taken from Doolittle and Hale (1983), while (d) is from (Graphing
Advantage Plus-Curve Fitting Program).


             Table (3): Constants for Gases Thermal Conductivity Physical Properties Equations.
                                   For temperature range (300 – 500 )K
             Km (W/m.K)               m = N2               m = O2                 m = CO2
                   a            3.502285714299        1.777714285718          -6.27799999999
                   b            0.082111428571        0.089948571429              0.07512
                   c            -0.000023714286       -0.000022285714             0.000004
                   d                    1000                1000                    1000
                                  For temperature range (500 - 1400)K
             Km (W/m.K)               m = N2               m = O2                 m = CO2
                   a            10.374878787874       5.390454545448 -17.639030303035
                   b            0.061298636364        0.077658333333              0.11432
                   c            -0.000008583333       -0.000011325758        -0.000028606061
                   d                    1000                1000                    1000
                                   For temperature range (380 – 850)K
                         Km (W/m/K)                                 M = H2O vapor
                              a                                   -2.673622983012
                              b                                    0.066349945745
                              c                                    0.00001381515
                              d                                         1000


                                                     .




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Heat Transfer & Fluid Flow 1 (2009)                                                               www.journal.boilersdesign.info


                                 900                                                                           (a)
                                 800                                                                      7 kg/h, twisted
                                 700                                                                      7 kg/h, empty
              Temperature in C


                                 600                                                                      6.16 kg/h, twisted
                                 500                                                                      6.16 kg/h, empty
                                 400                                                                      4.5 kg/h, twisted
                                 300                                                                      4.5 kg/h, empty
                                 200                                                                      3.24 kg/h, twisted
                                 100                                                                      3.24 kg/h, empty
                                   0                                                                      1.6 kg/h, twisted
                                    0.15     0.2        0.25       0.3      0.35        0.4       0.45    1.6 kg/h, empty
                                                           Density (kg/m^3)


   Figure (1) Physical Properties Variation with Temperature for Combustion Gases Flow
        inside Empty and Inserted Test Tube for Different Fuel Consumptions Rates.



                                 900                                                                           (b)
                                                                                                          7 kg/h, twisted
                                 800
                                 700                                                                      7 kg/h, empty
              Temperature in C




                                 600                                                                      6.16 kg/h, twisted

                                 500                                                                      6.16 kg/h, empty

                                 400                                                                      4.5 kg/h, twisted

                                 300                                                                      4.5 kg/h, empty

                                 200                                                                      3.24 kg/h, twisted
                                 100                                                                      3.24 kg/h, empty
                                   0                                                                      1.6 kg/h, twisted
                                  0.00002   0.000025     0.00003    0.000035       0.00004    0.000045    1.6 kg/h, empty
                                                     Dynamic viscosity ( N.s/m^2)


                                                               Figure (1) Continued


                                 900                                                                          (c)
                                 800                                                                      7 kg/h, twisted
                                 700                                                                      7 kg/h, empty
              Temperature in C




                                 600                                                                      6.16 kg/h, twisted
                                 500                                                                      6.16 kg/h, empty
                                 400                                                                      4.5 kg/h, twisted
                                 300                                                                      4.5 kg/h, empty
                                 200                                                                      3.24 kg/h, twisted
                                 100                                                                      3.24 kg/h, empty
                                   0                                                                      1.6kg/h, twisted
                                    0.03      0.04          0.05         0.06         0.07        0.08    1.6 kg/h, empty
                                                     Thermal condictivity (W/m.K)


                                                               Figure (1) Continued
                                                                                                                                   5
Heat Transfer & Fluid Flow 1 (2009)                                              www.journal.boilersdesign.info


                                 900                                                         (d)
                                 800                                                     7 kg/h, twisted
                                 700                                                     7 kg/h, empty
              Temperature in C


                                 600                                                     6.16 kg/h, twisted
                                 500                                                     6.16 kg/h, empty
                                 400                                                     4.5 kg/h, twisted
                                 300                                                     4.5 kg/h, empty
                                 200                                                     3.24 kg/h, twisted
                                 100                                                     3.24 kg/h, empty
                                  0                                                      1.6 kg/h, twisted
                                  1050   1100     1150        1200       1250   1300     1.6 kg/h, empty
                                                Specific heat (J/kg.K)



                                                     Figure (1) Continued

References
          -Chattopadhyay, P. 1998. “Boiler Operation Engineering”. Tata Mc     Graw – Hill, New Delhi.
          -Doolittle, J. and Hale, F.J. 1983. “Thermodynamics for engineers”. John Wiley and Sons. New
          York.
          -Insayif, R. K. 2008. “An investigation of thermal behavior of fire tube boiler utilizing
          unconventional tubes”. M.Sc. thesis, College of Engineering, Baghdad University.
          -Kays, W.M. and Crawford, M.E. 1980. “Convective heat and mass transfer ”. McGraw- Hill, New
          York.
          -McAdams, W.H. 1954. “Heat transmission”. McGraw- Hill, New York.
          -Standards of the tubular exchanger manufacturers association (TEMA). 1988. Seventh edition.
          New York.




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Description: The calculation of combustion gases physical properties, (density, dynamic viscosity, thermal conductivity, specific heat) is the first step in calculating the amount of heat released from the combustion gases flow inside heat exchanger tubes. Least squares method (polynomial regression) was used in (Graphing Advantage Plus-Curve Fitting Program) in order to convert the gases physical properties tables data to equations that will be need in the program that build in Microsoft Excel 2003 to perform all the calculation and graphs. The chemical composition of light oil is (C, S, H2 , O2 , N2). The complete combustion process produces a mixture of gases, (Carbon dioxide, Water vapor, Nitrogen, Sulfur dioxide). The weight percentage of these components depends on the weight percentage of the fuel chemical composition (Chattopadhyay, 1998).