4. Result and discussion

<sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup>�<sup>1</sup> <sup>¼</sup> <sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup>þ<sup>1</sup>

likewise, Kc n� ð Þ ¼ Kc n<sup>þ</sup> ð Þ

<sup>¼</sup> <sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup> � <sup>6</sup>Δ<sup>t</sup>

The conduction through the surface of the globe-shaped concrete is equal to the convection at

However, this boundary condition cannot be directly represented in finite difference form,

Instead a first law energy balance was utilized to obtain the nodal equation for the surface of

out <sup>þ</sup> <sup>E</sup>\_

in ¼ �KA <sup>∂</sup><sup>T</sup>

out ¼ UCA T � Tg

st <sup>¼</sup> <sup>r</sup>CV <sup>∂</sup><sup>T</sup>

� � <sup>þ</sup> qV\_ <sup>¼</sup> <sup>r</sup>CV <sup>∂</sup><sup>T</sup>

4 3 π r 3 <sup>n</sup> � r 3 n� � �q\_

<sup>n</sup>UC <sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup> � <sup>T</sup><sup>∞</sup> � � <sup>þ</sup>

Representing Eq. (23) in a finite difference form consistent with Eq. (20) and (21) resulted to:

gen <sup>¼</sup> <sup>E</sup>\_

since such formulation requires a volume element and Eq. (22) applies at a point.

E\_

E\_

E\_

<sup>∂</sup><sup>r</sup> � UCA T � Tg

2

E\_

<sup>r</sup>c mð ÞCc mð ÞΔr<sup>2</sup> Kc n<sup>þ</sup> ð Þ !

¼ �UCð Þ Tr¼<sup>R</sup> � T<sup>∞</sup> (22)

st (23)

<sup>∂</sup><sup>r</sup> (24)

<sup>∂</sup><sup>t</sup> (27)

<sup>∂</sup><sup>t</sup> (28)

<sup>n</sup> ¼

(29)

� � (25)

gen ¼ qV\_ (26)

<sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup>þ<sup>1</sup> (21)

∴Eq. (20) simplified to:

This occur at rn = 0.

the surface.

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where,

∴T<sup>Z</sup> <sup>n</sup> þ

Δtq\_<sup>n</sup> rc mð ÞCc mð Þ

This simplified form of Eq. (20) was used to represent the center node.

∴ � K ∂T ∂r at,r¼<sup>R</sup>

the globe-shaped concrete. This energy balance can be written as:

�KA <sup>∂</sup><sup>T</sup>

<sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup> � <sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup>�<sup>1</sup>

<sup>Δ</sup><sup>r</sup> � <sup>4</sup>π<sup>r</sup>

Δt

n

This can be written in finite difference form to give:

�4πr<sup>2</sup>

where, Uc = convection coefficient.

4 3 πrCn r 3 <sup>n</sup> � r 3 n� � � <sup>T</sup><sup>Z</sup>þ<sup>1</sup> <sup>n</sup> � <sup>T</sup><sup>Z</sup>

<sup>n</sup>� Kn�

E\_ in � <sup>E</sup>\_

> The values of Eq. (33) are obtained from the values in Table 1. Since the thermal properties are constant, average temperatures could therefore be used to determine thermal properties of bed materials.

> The following data were obtained from the theoretical/mathematical modeling carried out on thermal performance of packed bed energy storage system as shown in Figure 3.

The following are the definitions of the symbols:

Time = the interval time of measurements, in minutes.

Ts-in = the inlet air temperature to the packed bed storage tank in �C.

Ts-out = the outlet air temperature from the packed bed storage tank in �C.


Tct1, Tct2, Tct3, and Tct4 = the temperatures of the contact made between globe-shaped concrete and imbedded copper tube (�C) through the bed at different heights of the storage tank 117.5,

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Tt1, Tt2, Tt3, and Tt4 = the surface temperatures of the copper tube (�C) through the bed at

Figure 4. Average temperature measurement of charging packed bed storage system for globe-shaped concrete of size

Figure 5. Average temperature measurement of charging packed bed storage system for globe-shaped concrete of size

/s.

/s.

different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

235, 352.5, and 470 cm, respectively.

0.11 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup>

0.08 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup>

Table 1. Modeling parameters.

Figure 3. Schematic of the storage tank systems.

Tt-in = the inlet air temperature to the copper tube in �C.

Tt-out = the outlet air temperature from the copper tube in �C.

TA1, TA2, TA3, and TA4 = the air stream temperatures (�C) through the bed at different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

Tci1, Tci2, Tci3, and Tci4 = the core temperatures of the globe-shaped concrete (�C) through the bed at different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

Tti1, Tti2, Tti3, and Tti4 = the temperatures of air flowing inside the copper tube (�C) through the bed at different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

Tct1, Tct2, Tct3, and Tct4 = the temperatures of the contact made between globe-shaped concrete and imbedded copper tube (�C) through the bed at different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

Tt1, Tt2, Tt3, and Tt4 = the surface temperatures of the copper tube (�C) through the bed at different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

Figure 4. Average temperature measurement of charging packed bed storage system for globe-shaped concrete of size 0.11 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.

Tt-in = the inlet air temperature to the copper tube in �C.

Figure 3. Schematic of the storage tank systems.

Table 1. Modeling parameters.

152 HVAC System

Tt-out = the outlet air temperature from the copper tube in �C.

of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

TA1, TA2, TA3, and TA4 = the air stream temperatures (�C) through the bed at different heights

Tci1, Tci2, Tci3, and Tci4 = the core temperatures of the globe-shaped concrete (�C) through the

Tti1, Tti2, Tti3, and Tti4 = the temperatures of air flowing inside the copper tube (�C) through the

bed at different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

Parameters Values Airflow rate 0.01316 m<sup>3</sup>

Air—density 1.07154 Kg/m3 Air—specific heat capacity 1008 J/Kg K Concrete—density 2400 Kg/m<sup>3</sup> Concrete—specific heat capacity 1130 J/Kg K Copper tube—density 8900 Kg/m<sup>3</sup> Copper tube—specific heat capacity 384 J/Kg K Area of globe-shaped concrete 0.013 m<sup>2</sup> Area of copper tube + header 0.664 m<sup>2</sup> Volumetric heat transfer coefficient 106.5 W/m3 K

/s (28 cfm)

bed at different heights of the storage tank 117.5, 235, 352.5, and 470 cm, respectively.

Figure 5. Average temperature measurement of charging packed bed storage system for globe-shaped concrete of size 0.08 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.

The results of the experimentation were shown in Figures 4–6 for globe-shaped concrete of size 0.11; 0.08 and 0.065 m diameter respectively while the discharging only temperature measurements were shown in Figures 7–9 respectively for air flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.

Figure 6. Average temperature measurement of charging packed bed storage system for globe-shaped concrete of size 0.065 m diameter and flow rate of 0.0094, 0.013, and 0.019 m3 /s.

Figure 7. Average temperature measurement of discharging packed bed storage system for globe-shaped concrete of size 0.11 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.

Figure 10 presents the comparison of the temperature variations with time at Ts-in, Ts-out, Tt-in, Tt-out, TA1, TA2, TA3, TA4, Tci1, Tci2, Tci3, Tci4, Tti1, Tti2, Tti3, Tti4, Tct1, Tct2, Tct3, Tct4, Tt1, Tt2, Tt3, and Tt4 during the simultaneous charging and discharging while Figure 11 presents for discharging

Figure 9. Average temperature measurement of discharging packed bed storage system for globe-shaped concrete of size

Figure 8. Average temperature measurement of discharging packed bed storage system for globe-shaped concrete of size

/s.

/s.

/s.

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only. The comparisons were presented for air flow rates of 0.0094, 0.013, and 0.019 m3

0.065 m diameter and flow rate of 0.0094, 0.013, and 0.019 m3

0.08 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup>

The results of the experimentation were shown in Figures 4–6 for globe-shaped concrete of size 0.11; 0.08 and 0.065 m diameter respectively while the discharging only temperature measurements were shown in Figures 7–9 respectively for air flow rate of 0.0094, 0.013, and

Figure 6. Average temperature measurement of charging packed bed storage system for globe-shaped concrete of size

Figure 7. Average temperature measurement of discharging packed bed storage system for globe-shaped concrete of size

/s.

/s.

0.065 m diameter and flow rate of 0.0094, 0.013, and 0.019 m3

0.11 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup>

0.019 m<sup>3</sup>

154 HVAC System

/s.

Figure 8. Average temperature measurement of discharging packed bed storage system for globe-shaped concrete of size 0.08 m diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.

Figure 9. Average temperature measurement of discharging packed bed storage system for globe-shaped concrete of size 0.065 m diameter and flow rate of 0.0094, 0.013, and 0.019 m3 /s.

Figure 10 presents the comparison of the temperature variations with time at Ts-in, Ts-out, Tt-in, Tt-out, TA1, TA2, TA3, TA4, Tci1, Tci2, Tci3, Tci4, Tti1, Tti2, Tti3, Tti4, Tct1, Tct2, Tct3, Tct4, Tt1, Tt2, Tt3, and Tt4 during the simultaneous charging and discharging while Figure 11 presents for discharging only. The comparisons were presented for air flow rates of 0.0094, 0.013, and 0.019 m3 /s.

Figure 10. Comparison of average temperature measurement of charging packed bed storage system for globe-shaped concrete of size 0.065, 0.08, 0.11 m in diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.

i. Storage efficiency at air flow rates of 0.0094 m3

concrete of size 0.065, 0.08, 0.11 m in diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup>

ii. Storage efficiency at air flow rates of 0.013 m3

iii. Storage efficiency at air flow rates of 0.019 m3

i. Storage efficiency at air flow rates of 0.0094 m3

ii. Storage efficiency at air flow rates of 0.013 m3

iii. Storage efficiency at air flow rates of 0.019 m3

i. Storage efficiency at air flow rates of 0.0094 m3

ii. Storage efficiency at air flow rates of 0.013 m3

iii. Storage efficiency at air flow rates of 0.019 m3

For 0.065 m diameter globe-shaped concrete:

For 0.08 m diameter globe-shaped concrete:

/s = 40.7%

/s.

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/s = 60.5%

Figure 11. Comparison of average temperature measurement of discharging packed bed storage system for globe-shaped

/s = 57.5%

/s = 23.5%

/s = 51.3%

/s = 50.2%

/s = 14.8%

/s = 35.06%

/s = 40.3%

These figures show that the difference of the temperature response between the charging and fluid to solid heat transfer process at the initial period (<30 min) of the packed bed was large (large inlet–outlet temperature difference means large heat supply), and the heat recovered by the cool air (approximately 27�C) flowing inside the copper tube was fairly high (larger inlet–outlet temperature difference compared with the later period indicates larger heat recovery).

Therefore, a relatively large part of the heat supplied by the simulated air heater was used to heat the air flowing inside the copper tube through conduction and convection and also stores the rest for continuous usage.

The following are the storage efficiency for globe-shaped concrete of size 0.11 m, 0.08 m and 0.065 m diameter at airflow rate of 0.0094, 0.013 and 0.019 m<sup>3</sup> /s (Figure 12):

For 0.11 m diameter globe-shaped concrete:

Figure 11. Comparison of average temperature measurement of discharging packed bed storage system for globe-shaped concrete of size 0.065, 0.08, 0.11 m in diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.


For 0.08 m diameter globe-shaped concrete:

These figures show that the difference of the temperature response between the charging and fluid to solid heat transfer process at the initial period (<30 min) of the packed bed was large (large inlet–outlet temperature difference means large heat supply), and the heat recovered by the cool air (approximately 27�C) flowing inside the copper tube was fairly high (larger inlet–outlet temperature difference compared with the later period indicates larger heat

Figure 10. Comparison of average temperature measurement of charging packed bed storage system for globe-shaped

concrete of size 0.065, 0.08, 0.11 m in diameter and flow rate of 0.0094, 0.013, and 0.019 m<sup>3</sup>

Therefore, a relatively large part of the heat supplied by the simulated air heater was used to heat the air flowing inside the copper tube through conduction and convection and also stores

The following are the storage efficiency for globe-shaped concrete of size 0.11 m, 0.08 m and

/s (Figure 12):

/s.

0.065 m diameter at airflow rate of 0.0094, 0.013 and 0.019 m<sup>3</sup>

recovery).

156 HVAC System

the rest for continuous usage.

For 0.11 m diameter globe-shaped concrete:


For 0.065 m diameter globe-shaped concrete:


Author details

References

Adeyanju Anthony Ademola

1974. pp. 441-446

Transfer. 1929;5:208-212

Engineering. 1930;22:26-721

St. Augustine, Trinidad and Tobago

Address all correspondence to: anthony.adeyanju@sta.uwi.edu

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[1] Adeyanju AA, Manohar K. Theoretical and experimental investigation of heat transfer in

[2] Balakrishnan AR, Pei DCT. Heat transfer in fixed bed. In: Industrial and Engineering Chemical Process Design Development. Vol. 13. Washington DC, USA: ACS Publication;

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packed beds. Research Journal of Applied Sciences. 2009;4(5):166-177

Figure 12. Storage efficiency of simultaneous charging and discharging packed bed storage system for globe-shaped concrete of diameter 0.065, 0.08, 0.11 m and air flow rate 0.0094, 0.013, and 0.019 m<sup>3</sup> /s.
