A MODEL OF HEAT TRANSFER IN A CIRCULATING FLUIDIZED BED COMBUSTOR.
Technical knowledge about design and operation of CFB (circulating fluidized bed) combustor is widely available but little has been done in the field of mathematical modeling of heat transfer in CFBC's. In order to explain heat transfer in circulating fluidized beds and predict heat transfer coefficient, several models have been proposed. However, In order to improve the optimization and control of CFB combustor and to predict heat transfer coefficient precisely, accurate real time model is required to describe it clearly .
Several mechanistic models have been proposed to explain this heat transfer in CFBC.  and  have presented complete reviews on heat transfer studies. A simple and reliable prediction of heat transfer to the wall of a CFBC, based on dimensional analysis has also been looked by many other researchers [14,18,15].
 has presented a model for suspension to wall heat transfer coefficient based on simplified cluster renewal including the effects of radiative heat transfer. Therefore, f this model has been modified and tested for the present research to increase the accuracy of the model by the development of empirical correlations.
2. GENERAL ASSUMPTIONS OF THE MODEL
The following assumptions were made during the development of suspension-to-wall heat transfer in a CFB .
1. Riser of CFB consists of clusters and disperse phase.
2. Heat transfer from suspension-to-wall takes place by renewed contact of clusters and the dispersed phase on the wall;
3. Particles flow downward along the riser wall for a distance 'L' which has been named as thermal contact length of clusters at the wall;
4. The velocity of a cluster is constant;
5. Temperature gradient in the axial direction is negligible.
6. Temperature varies in the radial direction.
3. MODEL FORMULATION As per assumption of the model, mathematically it can be presented as follows:
Above equations are similar to the expressions of .
In the present model, particle convective and radiative heat transfer coefficient consisted of the clusters and dispersed phase so the above equation can be written as: h = fhwc + (1-f) hd + f (hwcr + (1-f) hdr (2)
In the above co relations, "f" is the fraction of the wall covered by the clusters in contact with heat transfer surface and (1-f) be that of dispersed phase contacting with heat transfer surface.
In order to estimate "f" the following correlation  was used: f = 3.5 c 0.37
Where "c" is the average volume fraction of the solid.
 has shown that radiative heat transfer due to clusters and the dispersed phase are the same i.e. hwcr = hdr = hr.
h = fhwc + (1 - f) hd + hr (4)
A description of the individual heat transfer components in equation (4) is given below:
a. CONVECTIVE HEAT TRANSFER COEFFICIENT OF PARTICLE CLUSTERS
A number of models have been proposed to describe the particles convective heat transfer coefficient in details. These models can be classified as: (1) the single particle model (2) the gas solid homogenous model (3) cluster renewable model.
 considered a gas resistance between the wall and clusters in calculating the convective heat transfer coefficient:
Where "hw" is the effective heat transfer coefficient for unsteady state heat transfer in the homogenous semi-infinite medium. "Rw" is the resistance offered by the gas.
"Cpp" and "Cpg" are the heat capacities of the particles and the fluidizing gas respectively. from :
"eav" is the average cross- sectional voidage estimated fromb the measured pressure drop along CFB column .
Where "[?]P" is the differential pressure and "[?]L" is the The effective thermal conductivity of the clusters ke was estimated by :
Where "kg" and "kp" are thermal conductivity of gas and particles.
The contact time or residence time of cluster (tr) on the wall can be calculated by the following relation:
However, this expression does not clearly predict characteristics length. A good approximate value of ''L" has been taken by the researchers.  found a good correlation of measured values with the predicted ones when the value of L was 10 times then calculated from the above equation.
It is assumed that clusters move downward on the wall for a distance ''L" before leaving the heat transfer surface.  correlated their results using two instantaneous heat transfer probes in a smooth wall column and suggested there existed a characteristic residence length at the wall for clusters. They estimated that at room temperature, in a smoothed wall column (0.152m i.d), the characteristic length was proportional to cross sectional average suspension density. The clusters after traveling a certain distance dissolve or The contact resistance between the cluster and the riser wall "Rw"can also be expressed as a resistance offered by a gas gap of thickness dp/n as Hence the particle convective component in equation 5 becomes:
CONVECTIVE HEAT TRANSFER COEFFICIENT OF
THE DISPERSED PHASE
From earlier observations, it is clear that in the furnace of CFB the wall surface is in contact with either a dispersed phase or clusters. So, in these observations the correlation of  can be used for estimating heat transfer coefficient in the dilute phase as follows. The radiative heat transfer coefficient can be calculated by the following general expression. detached from the wall of the heat transfer surface.
Then they are replaced by new ones. So, detailed measurements of cluster velocities, their voidage and characteristics length of travel "L" are necessary. , by using two heat transfer probes showed that this "L" may be correlated with the cross sectional average suspension density rs in a 0.152 m ID CFB Where s =Stefan-Boltzmann constant, Temperature of the gas - particle suspension, K Riser wall temperature of the wall, K Emissivity of riser wall surface, the value was assumed to equal to 0.73  has approximated the emissivity of the gas-particle by the following correlations by using multiple reflection of particle.
Where "ep" is the emissivity of particles.
This method of heat transfer was also proposed by  with different methods of estimating the suspension and surface wall emissivity.
4. MODEL COMPARISON WITH THE PRESENT EXPERIMENTAL DATA
The model formulated has been tested with present findings at different operating conditions and for 0.61 m heat transfer surface length and is shown in the figures (1-8) respectively. Model predictions and experimental results of the variation of heat transfer coefficient with suspension density at temperature of 600degC and 750degC. It can be noticed that in both cases, the predicted and measured heat transfer coefficients increased with suspension density. Agreement between model prediction and experimental results is very encouraging. Results shown in figures (3) and (4) give the comparison of model prediction and experimental results of the variation in heat transfer coefficient with high bed temperature. It is obvious from the results that there is a direct relationship between model prediction and measurement of heat transfer coefficients.
5. DEVELOPMENT OF EMPIRICAL CORRELATION
Suspension density is established as the most important factor influencing the heat transfer coefficient in CFBC. Particle size, bed temperature and varying heat transfer surface length are other important parameters to be considered in the heat transfer studies. Suspension density is again related to other key-parameters like superficial gas velocity, solid circulation rate, particle density, particle size distribution, gas density and viscosity. Therefore, many investigators [8,2,6,13] have taken suspension density as the most important parameters in their studies and in there correlations.
In present study, the same approach has been employed to develop an empirical correlation by correlating the parameters h, rsusp , and kg in a fundamental relationship as follows.
Where h = heat transfer coefficient, W/m2 K rsusp = Suspension density, kg/m3 kg = Thermal conductivity of fluidizing gas, W/m k a, a and b are constants For radial heat transfer coefficient the correlation can be written as same as that of :
However, the deviation is about 4 - 7% in the present model.
Using the present experimental data of heat transfer coefficient variation with suspension density and temperature, the average value of slopes 'a' and 'b' were computed to be 0.5 of 0.163 respectively. The value of a was found to be 93.52 and for axial heat transfer coefficient the modified relation can be written as:
The predicted results from equations (20-21) were compared with the experimental results and were found to be in good agreement. The applicable range of this correlation was found to be: T = 600 -7500C, U = 4.6 - 5.2 m/s and particle diameter of 125 um. The results are shown in figures (9-14).
The modified model was based on the cluster renewal concept. It was consisted of contribution of convective and radiative heat transfer by clusters as well as dispersed phase. The present experimental results were tested in this modified model. Model predictions were found to be in good agreement with the heat transfer coefficient measurements in CFB system for various ranges of suspension density, bed temperature, particle size at the heat transfer surface length of 0.61m.
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NFC IEFR, Faisalabad, Pakistan, Centre for Coal Technology, University of the Punjab, Lahore, Pakistan, Biomass Conversion Research Centre, Department of Chemical Engineering, COMSATS Institute of Information Technology, Lahore-Pakistan, NFC IET, Multan, Pakistan, NTU, Faisalabad, Pakistan. Corresponding Author: email@example.com
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|Author:||Khana, Waqar Ali; Shahzadb, Khurram; Akhtarb, Javaid; Ghauric, Moinuddin; Alid, Najaf; Akhtare, Niaz|
|Date:||Dec 31, 2013|
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