Testing heat storage capability of some loose granular materials

Heat Recovery Systems & CHP Vol. 12, No. 2, pp. 181-186, 1992 Printed in Great Britain

08904332/92 $5.00 + .00 Pergamon Press Ltd

TECHNICAL TESTING

HEAT

NOTE

STORAGE CAPABILITY OF SOME GRANULAR MATERIALS

LOOSE

A. K. SHROTRIYA, S. K. JAIN,* L. S. VERMA,'~ R. SINGHand D. R. CHAUDHARY Thermal Physics Laboratory, Department of Physics, University o f Rajasthan, Jaipur-302004, India; *Department of Physics, Engineering College, Kota-324009, India; and ?Department of Physics, M.S.J. College, Bharatapur-321001, India

(Received 3 September 1991) Abstract--The role of the heat storage coefficient of some loose granular materials in determining the amount o f heat retained during the transient state has been investigated. An experimental study has been done in the laboratory for testing the heat storage capability of some loose granular materials such as marble powder, dune sand, ash, high refractory cement, wheat husk and sawdust. For this purpose a wooden box of sides 30.5 × 51 × 53 cm was fabricated. In the middle of this a rectangular plastic box (heat store) of sides 28 × 23 x 6.5 cm, surrounded by loose granular materials, was placed. The upper portion of the wooden box was covered by thermal insulation. Two containers, similar to the one placed in the materials, were lying above the wooden box at a height. Using a battery of electric light bulbs the temperature of water in these containers was raised to about 70°C. The water from one of the containers was transferred to the container lying in the material. A study of heat loss from this container (heat store) and from the other one which was lying in the open, was conducted at time intervals. In the heat store a thermocouple was also placed along the z-axis. It was found that the fall in temperature of the materials surrounding the heat store is determined by the heat storage coefficients of the surrounding materials, which were measured by the plane heat source method. It was observed that for the low-values of heat storage coefficient surrounding materials, the heat dissipation from the heat store was low, whereas for high valued heat storage coefficient material surrounding the store, heat loss increased.

NOMENCLATURE T

t X, y, 2' S q

Q

2 20

(pc)

(pc)~ P 6T/~t ~e

To

Q~ Q~ Bo

temperature [°C] time [s] spatial cartesian coordinates [m] isothermal surface area [m 2] power per unit area [W m -2] total amount of heat passing through any area S during any time interval t [J] thermal diffusivity [m s s - ~] thermal conductivity [W m - ~K - ~] effective thermal conductivity of the material [W m - ~K - ~] volumetric specific heat [J m -3 K -I ] effective volumetric specific heat of the material [J m -3 K -~] numerical constant rate of fall o f temperature due to diffusion of heat [°C s -~] effective thermal diffusivity [m 2 s -~ ] temperature of the surface at z = 0 [°C] heat storage coefficient [W m -2 K - t s I/2] effective heat storage coefficient [W m -2 K -~ s ~/2] heat amounts crossing the levels zj in time t through the material [J] heat amounts crossing the levels z 2 in time t through the material [J] slope of the temperature-time curve in the measurement of heat storage coefficient [ °C s- ~]

1. I N T R O D U C T I O N

In the literature [1-5] one finds very little importance attached to knowledge of the heat storage coefficient of various materials. It has wide applications in thermal engineering from the viewpoint of energy storage [6-11]. It is well known that knowledge of the heat storage coefficient is necessary in calculating the heat-accumulating capability of a medium when the energy flow is transient. A detailed account of the usefulness of knowledge of the heat storage coefficient is given in [11]. The heat storage coefficient characterizes a medium from the viewpoint of its heat storage ability. 181

182

A . K . SHROTRIYAet al.

a good insulating envelope, the amount of heat flowing through it should be small, which implies that the heat storage coefficient should be low. In this work we have measured the values of heat storage coefficients of different loose granular materials, using the plane heat source method [11]. Then, we have designed an experiment for testing heat storage capability of these materials. The measurements were taken for dissipation of heat through all these materials surrounding a heat store.

2. M A T H E M A T I C A L A N A L Y S I S The temperature field T in a given material is a function of position ( x , y , z ) and time (t)

T = f ( x , y , z, t).

(1)

In investigating the temperature field it is assumed that the material is isotropic, and horizontal surfaces parallel to the top surface (z = 0) are isothermal. It means that temperature T varies only with the depth z and time t. The temperature gradient causes a heat flux dQ of flux density q, which is the amount of heat passing per unit time through unit area of an isothermal surface area S, and can be expressed as dO q = dtS"

(2)

We consider such loose materials in which heat propagates only through the modes of heat conduction (under steady state) and diffusion (under non-steady state). Therefore, Fourier's law dT q = - Ae d~

(3)

holds, where 2~ is the effective thermal conductivity of the material. Using relations (2) and (3) it follows that the heat flowing through an area element dS from the surface towards the depth is

dQ = - 2~ ~ dS dt.

(4)

Therefore, the total amount of heat passing through any area S during any time interval t is

f' d T dt

Q = - 2~ J0 dz

dS.

(5)

Under a transient process, the one-dimensional flow of heat relation [3] for the material is represented as

62T

c gT

;,e ~yz2 = (p)¢ ~ - ,

(6)

where (pc)~ is the effective volumetric specific heat of the material and 6T/6t is the rate of fall of temperature due to the diffusion of heat. The solution of relation (6) is T = fl(z) f2(t)

(7)

T = To e P' e -~Ip/~o)'~,

(8)

or

where p = numerical constant, ~e = 2e/(pc)~ effective thermal diffusivity, and To is the temperature of the surface at z = 0. Differentiating relation (8) w.r.t, z and testing the boundary condition that as z ~ oo, 6T/6z ~ 0, we obtain

6T gz

_

{p/ote}1/2To e -p' e -z~/~°l~12.

(9)

Testing heat storage capability

183

In neighbouring layers to the z --*0 surface where z < 1 e -'{"/~0~'/2 ,~ [1 -

z(pl~o)'2].

Thus, relation (9) becomes fiT tS----z.= -- {plate },/2 To e-pt [1 - z(p/~te)'/2].

(10)

Since the total amount of heat passing through any area S of a sample during any interval of time t is

Q = -~.o

;0;s

--d-~zdtdS,

(ll)

for the surface z ---,0, the total heat loss Q by the material of surface area S in t sec towards the depth of the material is [using equation (lO)]

Q= ~

Stpl/2e -pt.

(12)

The factor (2e/~t~/2) is called the heat storage coefficient for the material which characterizes the loose material from the viewpoint of its heat storage qualities, and is numerically equal to the thermal conductivity of the material whose thermal diffusivity is equal to unity. In terms of heat flow, it may be defined as the amount of flux flowing under unit temperature difference at an instant of 1 / x / ~ . If we consider a section of the medium, then some of the heat entering is retained by it and the rest is transferred to subsequent layers. When the steady state is reached no heat is retained and all is transferred to the subsequent layers. It can be seen that during the transient state the heat retained by a particular layer is a function of its storage coefficient (fl). It is evident from relation (12) that the amount of heat Q transported is determined by storage parameter fl of the system. In both the processes of heat storing and heat conduction, the restriction lies on the quantity of heat involved. For insulation purposes one requires that the amount of heat passing through any material in time t should be as low as possible, and for storage purposes also one should have the same condition. Specifically, for storage purposes, if Q~ and Q2 are respective heat amounts crossing the levels z~ and z2 in time t, through the material, one should have Q1 - Q2 to be a maximum. To obtain the best benefits from an insulation one requires the same condition. On the other hand, for conduction purposes, the conditions reverse and one requires that Q1 - Q2 should be a minimum. In all such estimations the parameter fl plays a decisive role. 3. E X P E R I M E N T A L A R R A N G E M E N T

AND M E A S U R E M E N T S

The experimental arrangement is shown in Fig. 1. For this study we used a wooden box of sides 51 x 53 cm and height 31.5 cm. The box was filled with loose granular material. The upper portion of the wooden box was covered after filling the sample. In the centre of the box we placed a rectangular container of plastic (heat store). Two containers similar to the one placed in the test material were lying above the wooden box at certain heights. All three plastic boxes A, B and C were of the sizes 28 x 23 x 6.5 cm. In the plastic box, there was an arrangement for transferring the water between inlet and outlet. Using a battery of electric light bulbs and an electric heater, the temperature of the water in these containers was raised to about 70°C. The heating was then stopped and the water from one of the containers was transferred to the container lying in the material. A study of heat loss from this container, which may be termed as a heat store, and the other one lying above in the open was conducted at time intervals. The loose materials used in the experiment were marble powder, dune sand, ash, high refractory cement, wheat husk and sawdust. In the middle of the heat store a needle of stainless steel with thermocouples was placed along the z-axis. The ends of thermocouple were attached to the temperature measuring unit (Fig. 2). The voltage was registered by a digital micro-voltmeter with an accuracy of 0.1 #V. After transferring the water at about 70°C into the heat store, measurements of temperature at time HRS 12/2-43

A.K. SHROTRIYAet al.

184

Battery of bulbs

~ /3 /3 ~ /3 /3 /3 u (5 /3 /3 i3

for hootingwire Top glass sheet

~ ~ z / ~ ~

4 ~ - ~

s~"hWat Pleaestirtc~ ) - ~ Supl~rting

II , ~,~__~A, B, C=Rectangularbox of plastic ][

rodsto hold heat store

of the same size

L

.......

~

:

__

__

ItOI

.

npl -- Ironstand

: ~:.;..:..:..'....'..; i

I

Leadsof

'1

I

i

i

Fig. 1. Experimentalarrangement for the study of heat storage capability test. intervals of 30 min were taken. A similar process was repeated for all the materials surrounding the container. We also measured the values of the heat storage coefficient of all the loose granular materials which were used in this study, using the plane heat source method [11]. The effective heat storage coefficient fie of the material, in which the plane heat source is placed, is calculated by the relation [11, 12]

T=~

/~,

(13)

where q is the power per unit area, T is the rise in temperature and t is the time (sec). A graph of T vs ~ will be a straight line and its slope Bo will be Bo = ~ q

(14)

Hence

fie--

(15)

q

Thus, knowing the values of q and Bo, the heat storage coefficient can be determined.

o,

I Blas EMFI Digital

1,

V

2,

V

3=

V

microvoltmeter

Reference junction O, 1, 2, 3 leeds of thermocouples

Fig. 2. Temperaturemeasuringunit.

Testing heat storage capability

185

Table 1. Heat storagecoefficientand porosityof the materials S.N. I. 2. 3. 4. 5. 6. 7.

Sample

Porosity (Wm-z K-I sI/2)

Marble powder Marble powder High refractory cement Ash Wheat husk Sawdust Dune sand

0.406 0.390 0.700 0.686 0.800 0.823 0.420

552.9 585.1 349.2 367.0 251.7 248.2 561.0

4. R E S U L T S A N D D I S C U S S I O N The heat storage coefficients of all the materials were determined at room temperature (30 _ 5°C). The porosity values of the materials were also measured. As the thermal coefficients of loose materials depend upon the degree of compactness, care was taken to ensure the same degree of packing during the measurements. This was done by tapping the container gently until no more material settled down. The heat storage coefficient values so obtained are reported here in Table 1, along with the corresponding values of porosity. F r o m the time-temperature history of water inside and outside the material we obtained some interesting results. This study was conducted for 10 h, where the observation interval was kept 30 min. However, for the first hour the time interval was 10 min. The behaviour of all the materials surrounding the container is shown in Fig. 3. It can be seen that the change in temperature of the water with time depends upon the heat storage coefficient of the surrounding materials. F r o m Fig. 3, it can also be concluded that if the value of heat storage coefficient of the surrounding material is low, then the rate of heat loss by the water is low; whereas for higher value of heat storage coefficient heat losses increase. For example, the temperature of water decreased from 70°C to 48°C in 10 h, if the surrounding material was wheat husk. And if the surrounding material was dune sand, then the temperature becomes 40°C from 70°C in the same time period of 10 h. This is because the value of the heat storage coefficient for dune sand is higher than that

- : •"='=-e-e•o-o60

•o-o-

?

Sawdust W h e a t husk High refractory c e m e n t Ash Marble p o w d e r (@=0.406) Marble p o w d e r (~p=0.39) Dune sand Air

55

50 (9 ~L

E 45

40

35

0

50

100

150

200

250

300

350

400

450

500

550

600

"lime in minutes

Fig. 3. Decrease in temperature of water from 70°C with time, embedded in different loose granular materials.

186

A.K. SHROTRIYAet al.

for wheat husk (Table 1). W h e a t husk is a better insulator t h a n m a r b l e powder a n d high refractory cement is a much insulator then ash. F r o m Fig. 3, one can say that the shape of the decreasing trend of temperature is almost identical. Initially, the temperature decreases rapidly, then the rate of decrease slows as expected. 5. C O N C L U S I O N S It is concluded from this experimental study that, with the knowledge of a single parameter heat storage coefficient of materials, one can select them for the purpose of a heat store. The results o b t a i n e d show that sawdust a n d wheat husk are the best insulating materials a n d both have the lowest values of heat storage coefficients. I f by k n o w i n g either the effective thermal conductivity (2e) or effective thermal diffusivity (~o) of a material, one makes decisions a b o u t the i n s u l a t i o n / c o n d u c t i o n envelope a r o u n d a heat store, one m a y have misleading results. However, if materials are restricted to the type which should n o t decay in time a m o n g s t c o m m o n l y available loose g r a n u l a r materials, then one should go for ash rather t h a n marble powder a n d d u n e sand. Acknowledgements--We are thankful to Dr (Mrs) Usha Singh for her valuable suggestions and discussions. Financial assistance from Department of Non-Conventional Energy Sources, New Delhi and Council of Scientific Industrial Research, New Delhi and equipment support from the Third World Academy of Science, Trieste, Italy, are gratefully acknowledged.

REFERENCES 1. A. A. Babnov, Methods for calculation of thermal conduction coefficientsof capillary porous materials, Soy. Phy.-Tech. Phys. 2, 476~84 (1957). 2. A. M. Luc and D. L. Balageas, Non-stationary thermal behaviour of reinforced composites. A better evaluation of wall energy balance for convective conduction, ONERA T.P. 1-23 (1981). 3. S. V. Nerpin and A. F. Chudnovski, Physics of the Soil, pp. 187, 194. Israel Program for ScientificTransactions (1970). 4. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd Edn, pp. 261-262. Clarendon, Oxford (1959). 5. A. E. Weshler, P. E. Glaser and J. A. Fountain, Thermal properties of granulated materials, in Progress in Astronautics and Aeronautics, Vol. 28, Chapter 3a, pp. 215-241. MIT Press, Cambridge, MA (1972). 6. R.G. Sharma, R. N. Pandey and D. R. Chaudhary, Thermal characteristics of two-phase granular materials at varying interstitial air pressures, Ind. J. Pure Appl. Phys. 24, 11-14 (1986). 7. A. K. Shrotriya, L. S. Verma, R. Singh and D. R. Chaudhary, Prediction of heat storage coefficient of some loose granular materials on the basis of structure and packing of the grains. Heat Recovery Systems & CHP 11, 423~,30 (1991). 8. A. K. Shrotriya, L. S. Verma, R. Singh and D. R. Chaudhary, Prediction of the heat storage coefficientof a two-phase system. J. Phys. D: Appl. Phys. 24, 849-853 (1991). 9. A. K. Shrotriya, L. S. Verma, R. Singh and D. R. Chaudhary, Prediction of the heat storage coefficientof a three-phase system. J. Phys. D: Appl. Phys. 24, 1527-1532 (1991). 10. A. K. Shrotriya, L. S. Verma, R. Singh and D. R. Chaudhary, Effect of temperature and moisture on the heat storage coefficient of loose granular systems. Heat Recovery Systems & CHP 11, 483~194 (1991). 11. L. S. Verma, A. K. Shrotriya, U. Singh and D. R. Chaudhary, Heat storage coefficient--an important thermophysical parameter and its experimental determination. J. Phys. D: Appl. Phys. 23, 1405-1410 (1990). 12. L. R. Ingersoll, O. J. Zobel and A. C. Ingersoll, Heat Conduction (Indian Edn) pp. 91, 156. Oxford University Press and IBH, Oxford (1969).