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Heat transfer characteristics of the fluidized bed through the annulus

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Abstract

The annular fluidized bed can be regarded as a promising technique for waste heat recovery applications. This study investigates on the determination of steady state values of the average heat transfer on the surface of the inner tube under different operating conditions that include: (1) input heat flux ranging from 557 to 1671 W/m2, (2) superficial air velocity ranging between 0.12 and 0.36 m/s, (3) initial bed height ranging from 25 to 55 cm, (4) ratio of the inner to the outer diameters ranging from 1/6 to 1/2 and Kaolin particle diameters ranging between 282 and 550 µm. The average values of the heat transfer coefficient along the inner tube (consisting of the fluidized and free board sections) are also deduced. An empirical correlation for calculating the Nusselt number is obtained for the given parameters and ranges.

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Abbreviations

Ac :

Cross section area (annulus area) (m2)

Ap :

Peripheral area (m2)

Ar:

Archimedes number

Cp,g :

Gas specific heat (J/kg K)

dh :

Hydraulic diameter (M)

di :

Inner cylinder diameter (M)

do :

Outer cylinder diameter (M)

dp :

Particle diameter (M)

g:

Acceleration due to gravity (m/s2)

h:

Heat transfer coefficient (W/m2 K)

havg :

Average heat transfer coefficient (W/m2 K)

hi :

Local heat transfer coefficient (W/m2 K)

H:

Static bed height (m)

Ho :

Cylinder height (m)

I:

Electric Current (A)

k:

Gas thermal conductivity (W/mK)

l:

Fluidized bed column length (m)

\({\dot{\text{m}}}_{\text{g}}\) :

Gas mass flow rate (kg/s)

N:

Number of temperature points (=5)

Nu:

Nusselt number based on hydraulic diameter

NuP :

Nusselt number based on particle diameter

q:

Heat flux (W/m2)

Q:

Heating load = q × A (W)

Re:

Reynolds number

tf,i :

Local gas temperature (°C)

tg,i :

Gas inlet temperature (°C)

tg,o :

Gas outlet temperature (°C)

ts,i :

Local surface temperature (°C)

Uo :

Superficial gas velocity (m/s)

V:

Voltage difference (V)

\({\dot{\text{V}}}_{\text{g}}\) :

Gas volume flow rate (m3/s)

µg :

Gas viscosity (kg/sm)

ρg :

Gas density (kg/m3)

ρp :

Particle density (kg/m3)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering at El-Mattaria, Helwan University, Cairo, Egypt

    Mohamed H. Shedid & M. A. M. Hassan

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  1. Mohamed H. Shedid
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  2. M. A. M. Hassan
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Correspondence to Mohamed H. Shedid.

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Shedid, M.H., Hassan, M.A.M. Heat transfer characteristics of the fluidized bed through the annulus. Heat Mass Transfer 52, 1943–1952 (2016). https://doi.org/10.1007/s00231-015-1722-0

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