Question 12.5: A CFB combustion boiler has an evaporator in the form of a m......
A CFB combustion boiler has an evaporator in the form of a membrane tube wall of the furnace. It is operating under the following conditions:
• Fluidized-bed pressure p = 1 bar, temperature T = 850°C = 1123 K, bed porosity \varepsilon = 0.83, and effective emissivity of the fluidized-bed–wall system \varepsilon_\mathrm{fb–w} = 0.88
• Particle diameter d = 1 mm and density \rho_{p} = 2300 kg/m³
• Tube wall surface temperature T_{w}= 490°C = 763 K, wall surface area A = 960 m²
• Air properties at 1 bar and 850°C: thermal conductivity k = 0.075 W/mK, density ρ = 0.31 kg/m³, kinematic viscosity \nu =151\times10^{-6}\,\mathrm{m^{2}/s}, and Prandtl number Pr = 0.72
• Stefan–Boltzmann constant: \sigma=5.67\times10^{-8}\:\mathrm{W/m^{2}K^{4}}
Calculate (i) the heat-transfer coefficient between fluidized-bed and tube wall surface h_\mathrm{fb–w} and (ii) the rate of transfer from fluidized-bed-to-tube wall surface Q_\mathrm{fb–w}.
1. Heat transfer between fluidized-bed and tube wall surface occurs by radiation and gas and solid particle convection.
Radiation heat-transfer coefficient from fluidized-bed-to-tube wall
=0.88\times5.67\times10^{-8}\times(1123^{4}-763^{4})/(1123-763)
= 173.5 Wm²K
2. Archimedes number
\mathrm{Ar}\,=\,g\ d^{3}(\mathbf{r}_{\mathrm{p}}\,-\,\mathbf{r})/(\mathbf{r}\,\nu^{2})=9.81\times0.001^{3}\times(2300-0.31)/[0.31\times(151\times10^{-6})^{2}]=3192
3. Heat-transfer coefficient by fluid (gas) convection from fluidized-bed-to-tube wall surface
h_\mathrm{f}\,=\,0.009\,\,\mathrm{Pr}^{0.33}\,\mathrm{Ar}^{0.5}k/d=0.009\times0.72^{0.33}\times3\,192^{0.5}\times0.075\,/0.00\mathbf{1}= 34.2 W/m²K
4. The heat-transfer coefficient h_{p} by particle convection from fluidized-bed-to-tube wall may be calculated as empirical formulae 12.15 through 12.17.
For the given data, Equation 12.15 may be replaced by the following simplified formula:
h_{\mathrm{p}}=Z\left(1-\varepsilon\right)\left[1-\exp\left(-N\right)\right]k/d\quad\mathrm{W/m^{2}K} (12.15)
h_{\mathrm{p}}=12(1-e)(k/d)=12\times(1-0.83)\times(0.075/0.001)=153{\mathrm{~W/m^{2}K}}5. Total heat-transfer coefficient from fluidized-bed-to-tube wall surface
h_\mathrm{fb-w}=h_{r}+h_\mathrm{f}+h_{{\mathrm{p}}}=173.5+34.2+153=360.7~\mathrm{W/m^{2}~K}6. Rate of heat transfer from fluidized-bed-to-tube wall surface
Q_{\mathrm{fb-w}}=h_{\mathrm{fb-w}}A\ (t_{\mathrm{fb}}-t_{\mathrm{w}})=360.7\times960\times(850-490)= 124,657,920 W ≈ 124.66 MW