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Thermal Enhancement in Storage Silos with Periodic Wall Heating

  • Research Article - Mechanical Engineering
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Abstract

In this paper, unsteady natural convection problem in vertical, open-ended, porous cylinder has been numerically investigated to simulate the transient heat and mass convection in the grain storage in silos. The medium is the seat of a chemical reaction, and the enclosure lateral wall is submitted to a varying temperature profile. Time-dependent boundary temperature is presented as sinusoidal function which can approximate real weather conditions. In the case of constant temperature, a map diagram comprising several characteristic parameters such as Rayleigh number, aspect ratio, buoyancy ratio and lumped effective reaction rate of the two observed flow types, with and without fluid recirculation, was obtained. In order to approve that heat exchanges are dependent of reversal flow and control parameters, the phase diagrams connecting heat transfer (Nu) to the recirculation flow rate (Q r) are proposed. The observed relative difference between sinusoidal and constant wall temperature increases with increasing Rayleigh number (Ra) and dimensionless temperature amplitudes (X A), and it is particularly sensitive to the buoyancy ratio values (N) and the reaction rate (A k). This difference passes from 18.7 % in the only thermal case to 8.15 % in the thermo-solutal case.

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Abbreviations

A :

Aspect ratio, A = R/H

\({A_{\rm k}'}\) :

Lumped effective reaction rate (s−1)

A k :

Scaled lumped effective reaction rate, \({A_{\rm k}=A_{\rm k}' H^{2}/\alpha _{\rm f}}\)

Bi :

Heat transfer Biot number

Bi m :

Mass transfer Biot number

C p :

Specific heat at constant pressure (J kg−1 K−1)

C :

Dimensionless concentration

D :

Species diffusivity (m2 s−1)

G :

Gravitational acceleration (m s−2)

h :

Heat transfer coefficient at the cylinder exit (J m−2 K s−1)

H :

Cylinder height (m)

k :

Thermal conductivity (J m−1 K s−1)

K :

Porous medium permeability (m2)

Le :

Lewis number, \({Le=\alpha _{{\rm f}} /D_{{\rm eff}}}\)

Nu :

Nusselt number

N :

Buoyancy ratio

P :

Dimensionless pressure

r :

Dimensionless radial coordinate

R :

Cylinder radius (m)

Ra :

Thermal Rayleigh number, \({Ra=g\beta_{\rm T} \Delta T_{{\rm ref}}}\) \({{KH}/(\nu \cdot \alpha _{\rm f} )}\)

Ra c :

Solutal Rayleigh number, \({Ra_{\rm C} =g \beta _{\rm C} \Delta C_{{\rm ref}}}\) \({= K\, H/(\nu \cdot \alpha _{\rm f} )}\)

R k :

Conductivity ratio, R k = k eff /k f

T :

Dimensionless temperature

t :

Dimensionless time

U :

Dimensionless longitudinal velocity

V :

Dimensionless radial velocity

x :

Dimensionless axial coordinate

X A :

Dimensionless amplitude

\({\alpha}\) :

Thermal diffusivity (m2 s−1)

\({\beta}\) :

Coefficients (Eq. 3)

\({\beta_{\rm T}}\) :

Thermal expansion coefficient in Eq. (1) (kg m−3 K −1)

\({\beta_{\rm C}}\) :

Solutal expansion coefficient in Eq. (1)

\({\delta}\) :

Dimensionless boundary layer thickness

\({\mu}\) :

Dynamic viscosity (kg m−1 s−1)

\({\rho}\) :

Fluid density (kg m−3)

\({\sigma}\) :

Heat capacity ratio, \({\frac{\left( {\rho C_{{\rm P}} } \right)_{{\rm eff}} }{\left( {\rho C_{{\rm P}} } \right)_{\rm f} }}\)

\({\varepsilon}\) :

Porosity

\({\tau}\) :

Dimensionless period

amb:

Ambient

c:

Cold

eff:

Effective

f:

Fluid

h:

Hot

Ref:

Reference

Max:

Maximum

pm:

Medium

' :

dimensioned values

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Author information

Authors and Affiliations

  1. Laboratory of Multiphase Transport and Porous Media (LTPMP), Faculty of Mechanical and Process Engineering (FGMGP), USTHB, B.P.32, El Alia Bab Ezzouar, 16111, Algiers, Algeria

    N. Himrane, D. E. Ameziani & K. Bouhadef

  2. ENS-Cachan Dpt GC/ LMT, 61, Av du Président Wilson, 94235, Cachan Cedex, France

    R. Bennacer

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  1. N. Himrane
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  2. D. E. Ameziani
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  3. K. Bouhadef
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  4. R. Bennacer
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Correspondence to N. Himrane.

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Himrane, N., Ameziani, D.E., Bouhadef, K. et al. Thermal Enhancement in Storage Silos with Periodic Wall Heating. Arab J Sci Eng 41, 623–637 (2016). https://doi.org/10.1007/s13369-015-1701-2

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