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Heat Transfer

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Circulating Fluidized Bed Boilers

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Abstract

The magnitude and locations of heating surfaces in a boiler greatly influence its thermal efficiency and output. For example, if less than required heat-absorbing surfaces are provided in the furnace, the steam generation would reduce, and if that is to be retained, the combustion temperature would have to rise adversely affecting the sulfur capture and increase corrosion potential of downstream tubes.

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Abbreviations

A :

Surface area of wall receiving radiation, m2

A f :

Area of fin, m2

A 0 :

Outer surface area of tubes in external heat exchanger, m2

A w :

Boiler surface areas exposed to the upper furnace, m2

B :

Constant in Eq. (3.20)

C c , C p, C f , C g :

Specific heat of cluster, solid, steam, and gas, respectively, kJ/kg K

D b :

Equivalent diameter of bed, m

D c :

Equivalent diameter of cluster, m

d cp :

Diameter of coarser particles, m

d p :

Diameter of average bed particles, m

e b, e c, e d, e g, e p, e s :

Emissivity of bubbling bed, cluster, dispersed phase, gas, particle and wall surface, respectively

\(e^{\prime}_{\text{p}}\) :

Effective emissivity of particle cloud

g :

Acceleration due to gravity, 9.81 m/s2

h :

Overall heat transfer coefficient, kW/m2 K

h c :

Convective heat transfer coefficient due to clusters, kW/m2 K

h cr :

Radiative heat transfer coefficient due to clusters, kW/m2 K

h conv :

Total convective heat transfer coefficient, kW/m2 K

h d :

Convective heat transfer coefficient due to dilute phase, kW/m2 K

h dr :

Radiative heat transfer coefficient due to dilute phase, kW/m2 K

h gp :

Gas-particle heat transfer coefficient, kW/m2 K

h o , h i :

Heat transfer coefficients for the external, and internal surface of the tube, respectively, kW/m2 K

h r :

Total radiative heat transfer coefficient, kW/m2 K

h t :

Heat transfer coefficient on a cluster after residing for a time, t on the wall, kW/m2 K

h tube :

Overall heat transfer coefficient on the tube, kW/m2 K

J :

Thermal time constant, kW/m K

K g, K gf, K c :

Thermal conductivity of gas, gas film, and cluster, respectively, kW/m K

K m, K p :

Thermal conductivity of tube metal and particles, respectively, kW/m K

K :

Constant in Eq. (3.7)

K c , K r :

Empirical constants in Eq. (3.30)

L :

Vertical length of the heat transferring surface, m

L b :

Fin efficiency

n 1, n 2 :

Empirical constants in Eq. (3.30)

Q f :

Heat absorbed by the furnace wall, kW

Q a :

Heat absorbed by the furnace wall, kW

Q fbhe :

Heat absorbed in external heat exchanger, kW

R :

Radius of the bed, m

r :

Radial distance from the center of the bed, m

r o, r i :

Outer and inner radius of heat transferring tube, m

S :

Surface area of particles per unit weight of particles, m2/kg

T b, T g, T s , T p :

Temperatures of the bed, gas, heat transferring wall, and bed particle, respectively, K

T ehe :

Temperature of the external heat exchanger, K

T po :

Initial temperature of the particles, K

T go :

Temperature of the gas entering the bed, K

T w :

Temperature of the boiler wall in upper furnace, K

T 99% :

Limit in Eq. (3.5) expressed as T go + 0.99 (T p  − T go), K

t :

Time, s

t 99% :

Time required for gas-particle temperature difference to reduce to 1 % of its original value, s

t c :

Mean residence time of cluster on wall, s

U :

Superficial gas velocity through fast bed, m/s

U ehe :

Superficial velocity through external heat exchanger, m/s

U c :

Velocity of cluster on wall, m/s

U cp :

Average velocity of coarser particle, m/s

U m :

Maximum fall velocity of clusters, m/s

U mf :

Minimum fluidization velocity, m/s

U p :

Solid velocity, m/s

U t :

Terminal velocity of a single particle, m/s

V :

Volume of the bed, m3/s

V i :

Velocity of steam in tube, m/s

W :

Solid circulation rate, kg/m2 s

X 99% :

Distance required for gas to reach 99 % of the overall bed temperature, m

x :

Distance along the height of the fast bed, m

Y :

Volume fraction of solid in the dispersed phase

Y′:

Volume fraction of solids in the interior of the furnace

ε :

Cross-sectional average voidage

ε c :

Voidage in cluster

ε w :

Voidage near the wall

ε(r):

Voidage at a radius r from the center

η f :

Heat absorbed by fin, kW

ρ avg :

Cross-sectional average bed density, kg/m3

ρ c :

Density of cluster, kg/m3

ρ f :

Density of steam, kg/m3

ρ b :

Bulk density of the bed, kg/m

ρ dis :

Density of dispersed phase, kg/m3

ρ g :

Density of gas, kg/m3

ρ p :

Density of bed material, kg/m3

μ g :

Viscosity of gas, N s/m2

μ f , μ fw :

Viscosity of steam at bulk temperature and wall temperature, respectively, N s/m2

δ c :

Time-averaged fraction of wall area covered by cluster

σ :

Stefan–Boltzman constant (5.67 × 10−11 kW/m2 K4)

Ar :

Archimedes number

Pr, Pr f :

Prandtl number of the gas and steam, respectively

Re, Re f :

Reynolds number of gas and steam, respectively

Re cp :

Reynolds number of coarse particles based on gas-particle slip velocity

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Authors and Affiliations

  1. Greenfield Research Incorporated, Halifax, NS, Canada

    Prabir Basu

  2. Dalhousie University, Halifax, NS, Canada

    Prabir Basu

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Basu, P. (2015). Heat Transfer. In: Circulating Fluidized Bed Boilers. Springer, Cham. https://doi.org/10.1007/978-3-319-06173-3_3

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  • DOI: https://doi.org/10.1007/978-3-319-06173-3_3

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