EXPERIMENTAL STUDY ON HEAT TRANSFER COEFFICIENT AND FRICTION FACTOR OF Al 2 O 3 NANOFLUID IN A PACKED BED COLUMN

Transcription

1 Journal o Mechanical Engineering and Sciences (JMES) e-issn: ; Volume 1, pp. 1-15, December 2011 FKM, Universiti Malaysia ahang EXERIMENTAL STUDY ON HEAT TRANSFER COEFFICIENT AND FRICTION FACTOR OF Al 2 O 3 NANOFLUID IN A ACKED BED COLUMN G. Srinivasa Rao 1, K.V. Sharma 2*, S.. Chary 3, R.A. Bakar 2, M. M. Rahman 2, K. Kadirgama 2 and M.M. Noor 4 1 Department o Mechanical Engineering Kakatiya Institute o Technology and Science Warangal, Andhra radesh, India, gsrkits@gmail.com 2 Faculty o Mechanical Engineering, Universiti Malaysia ahang, ekan, ahang, Malaysia 3 Retd. roessor, Andhra University, Visakhapatnam , India 4 Dept. o Mech. & Mechatronic Eng., University o Southern Queensland, Australia * Corresponding author kvsharma@gmail.com ABSTRACT Forced convection heat transer coeicient and riction actor are determined or low o water and nanoluid in a vertical packed bed column. The analysis is undertaken in the laminar and transition Reynolds number range. The column is illed with spherical glass beads as the bed material. The heat transer coeicients with Al 2 O 3 nanoluid increased by 12 to 15% with the increase o volume concentration rom 0.02 to 0.5% compared to water. The experimental values o axial temperature are in good agreement with NTU-ε method proposed by Schumann's model. Keywords: acked bed, Al 2 O 3 nanoluid, convective heat transer, riction actor, heat transer enhancement. INTRODUCTION The process o orced convection in various installations such as boilers, solar collectors, heat exchangers and electronic devices is employed. However, low thermal conductivity o heat transer luids such as water, oil, and ethylene glycol mixture is a serious limitation or improving their perormance. To overcome this disadvantage, there is strong reason to develop advanced heat transer luids with signiicantly higher conductivity. An innovative means o improving the thermal conductivities o luids is to suspend nanosize solid particles in the luid. (Tuckerman and ease, 1982) conducted experiments or laminar low in a channel. The heat transer coeicient estimated is inversely proportional to the width o the channel, since the limiting Nusselt number is a constant. (Mahalingam,1985) conirmed the superiority o micro-channel cooling on a silicon substrate with a surace area o 5cm x 5cm using water and air as coolants. Many studies are directed towards evaluation o heat transer coeicients or luid low in micro-channels. orous structures are also used or heat transer augmentation as these aggravate the mixing o the lowing luid and improve the convection heat transer. Hence, studies are undertaken due to its broad applications. The early works are due to the eect o various parameters through experiments and statistical methods and developed a set o equations based on theoretical models or packed beds in tubular low (Sadri, 1952). 1

2 Experimental study on heat transer coeicient and riction actor o Al 2 O 3 nanoluid in a packed bed column Jeigarnik et al. (1991) experimentally investigated convection heat transer o water on lat plates and in channels packed with sintered spherical particles, nets, porous metal and elt. The majority o the experiments is or the evaluation o heat transer coeicients with dierent thickness (0.86 to 3.9 mm) and particle diameters (0.1 to 0.6 mm). They ound that the porous media increased the heat transer coeicient 5-10 times, although the hydraulic resistance increase is even more. Experiment to study the percolation behavior o luids through a packed bed is undertaken by (Yagi et al., 1964), (Gunn et al., 1987; Lamine et al., 1992a). Analysis or heat transer coeicients by Weekman and Myers (1995); Silveira (1991) and Lamine et al. (1992a) on gas-liquid low, however, presented with limited results. Adeyanju (2009) experimentally determined the velocity variations with in a porous medium or packed beds. He concluded that the pressure drop across the porous medium was due to various actors, which included orm drag, viscous drag, rom bounding wall and inertia orce. The results rom this study conirmed that the pressure drop is a linear and quadratic unction o low velocity, at low and high Reynolds number respectively. (You et al., 2010) analyzed the thermal characteristics o an N 2 O catalytic igniter as a hybrid system or small satellites. The authors analyzed the problem theoretically to determine the thermal perormance o the catalytic igniter results on porosity, pumping capacity and the ratio o length to diameter. Carlos et al. (2008) predicted a generalised equation or radial velocity distribution in a packed bed having low tube to particle diameter ratio rom six hydrodynamic models. Their calculations show that the use o an eective viscosity parameter to predict experimental data can be avoided, i the magnitude o the two parameters in Ergun s equation, related to viscous and inertial energy losses, are reestimated rom velocity measurements or the packed beds. Maxwell (1904) showed the potential or increasing the thermal conductivity o a solution by mixing with solid particles. Fluids containing small quantities o nanosized particles are nanoluids. The particles are less than 100nm dispersed in a liquid uniormly. The dispersion o nanoparticles in normal luids enhances heat transer even when added in small quantities. The nanoluids show greater potential or increasing heat transer rates in a variety o cases. Lee et al. (1999) demonstrated CuO or Al 2 O 3 nanoparticles in water and ethylene glycol exhibit enhanced thermal conductivity. The thermal conductivity increased by 20% at 4.0% concentration, when 35nm size CuO nanoparticles are mixed in ethylene glycol. (Mansour et al., 2007) used Al 2 O 3 particles with a mean diameter o 13 nm at volume concentration o 4.3% and reported an increase in thermal conductivity by 30%.(Xuan and Roetzel, 2000) presented a relation or the evaluation o orced convection heat transer coeicient or low in tubes with Cu nanoluid. Various concepts are proposed to explain the reasons or enhancement in heat transer.xuan (2003) and Xuan et al. (2004) have identiied two causes or improvement in heat transer with nanoluids; the increased dispersion due to the chaotic motion o nanoparticles that accelerates energy exchanges in the luid and the enhanced conductivity o nanoluids considered by Choi (1995). Thermal conductivity o Al 2 O 3 nanoluid has been evaluated by (Das et al., 2003) in the temperature range o o C. They observed 2 to 4 old enhancement o thermal conductivity in the range o concentration tested. (Wen and Ding, 2004) evaluated the heat transer o nanoluid in the laminar region through experiments. They used equations available in the literature to determine viscosity at bulk temperature. (Maiga et al., 2005) investigated water- Al 2 O 3 and Ethylene glycol - Al 2 O 3 nanoluids observed adverse eects o wall shear when tested with the later. The heat transer enhancement o the nanoluids can be 2

3 Srinivasa Rao et al. / Journal o Mechanical Engineering and Sciences 1(2011) 1-15 expected due to intensiication o turbulence, suppression o the boundary layer as well as dispersion or back mixing o the suspended particles, a large enhancement in the surace area o nanoparticles and a signiicant increase in the thermo physical properties o the luid. Thereore, the convective heat transer coeicient with nanoluid is a unction o the physical properties o the constituents, dimension and volume raction o suspended nanoparticles, and low velocity. (Sarma et al., 2003) developed a theoretical model or the estimation o heat transer coeicient under laminar low in a tube with twisted tape inserts. (Syam Sundar et al., 2007) investigated heat transer enhancement or nanoluid low in a circular tube with twisted tape insets. The impact o operating parameters on nanoluid low in a packed bed on heat transer has not been attempted. The inluence o nanoluid concentration on parameters aecting orced convection heat transer in a vertical tube illed with packing materials is undertaken. The temperatures are measured at dierent axial positions with p-type thermocouples as shown in Figure 1. Al 2 O 3 nanoluid at 0.02, 0.1 and 0.5% volume concentration is pumped through the test section against gravity at dierent low rates and inlet temperatures. The Nusselt number, riction actor and heat transer coeicients are evaluated next. Figure 1. Experimental test rig or packed bed MODELS FOR REDICTING THERMAL ANALYSIS OF ACKED BED In order to determine the heat transer o a packed bed system, several theoretical models have been reported in literature based on experimental investigations. A bed is o height LB, diameter D p and cross sectional area A and packed with material having a void raction ε as shown in Figure 2. It is assumed that the temperature o the bed is uniorm at an initial value T Bi. The luid enters at ' T i with a mass low rate m and leaves the bed at T 0. The bed height L B is divided into a certain number o elements o thickness x. The temperature at the entry o the element is T m and exits at T m+1. 3

4 Experimental study on heat transer coeicient and riction actor o Al 2 O 3 nanoluid in a packed bed column 2.1 Schumann Model Schumann (1929) has modeled the thermal behaviour o packed beds which is extended by Sagara and Nakahara (1991). The model estimates the mean luid and solid material temperatures at a given cross section as a unction o time and axial position. The assumptions made by Schumann according to (Duie and Beckman, 1991) are: 1. The bed material has ininite thermal conductivity in the radial direction with plug low i.e. no temperature gradient in the radial direction. 2. Bed material has zero thermal conductivity in the axial direction. 3. Thermal and physical properties o the sold and luid are constant. 4. The heat transer coeicient does not vary with time and position inside the bed. 5. No mass transer occurs. 6. No heat loss to environment. 7. No phase change o the luid in the axial direction. 8. The low is steady and uniorm. Fluid out X L B Fluid in Figure 2. Elemental representation o packed bed domain The energy balance equation or the luid and solid components in Schumann model or packed bed can be written as Energy in luid at entry to bed = (Energy transerred to bed) + (Energy with the luid in the bed) + (Energy with the luid leaving the bed) + (Energy loss to environment) T T i m Cp T i = hv( T Tb) Adx + ρ C pεadx + m C p T i + dx + Ul x( T T mb) (1) t Energy with the luid in the bed and energy loss to the environment can be neglected as per the assumptions. Based on the assumptions stated, Eq. (1) becomes T hv AL B (2) X = m& C p [ T T ] S x 4

5 Srinivasa Rao et al. / Journal o Mechanical Engineering and Sciences 1(2011) 1-15 The above equation can be also written as where, X = L B T X hv AL = m& C x, NTU (Number o transer units) = B p [ T T ] = NTU ( T T ) S h V AL m C Energy transerred to the material = Energy stored by the material Ts hv( T Ts) Acs dx = ρ sc ps ( 1 ε )Acs dx (4) t The above equation can be expressed as; T s (5) = NTU τ ( T where τ (dimensionless time) = m& C t ( ρ C ps )( 1 ε ) A cs L B ) The equations (3) and (5) give the thermal perormance o the packed bed. The exit luid temperature rom the bed is obtained by integrating the equation (3) and can be written as NTU N θ Th = 1 e (6) The rate o heat transer rom luid to bed element o thickness x is given by; Q = m& C p ( T,m+1 T,m) (7) Eq. (7) with the aid o Eq. (6) can be written to obtain to determine the exit temperature o the luid m& C p ( T,m+1 T,m) = NTU / N m& Cp ( T,m TS,m)( 1 e ) (8) Similarly Eq. (8) can be modiied to calculate the mean temperature o bed elements m as given below T s ) ( T T ) dts, m = CN, m S, m dτ (9) N where C is a constant and equal to1 e NTU /. Eq. (9) permits energy loss to environment at temperature T amb and can be written as dt U m A S,m CS,m = CN( T,m TS,m) + ( Tatm TS,m) dτ m C (10) FABRICATION OF THE EXERIMENTAL SETU The experimental setup consists o 4.0 cm diameter 50 cm height o a packed bed column. Figure3 shows the process and instrumentation diagram o the experimental setup. An immersion heater heats the water which is in connection with a eed water storage tank o 50 liter capacity. A pump with low control and bypass valves supply a regulated low o circulating working luid through the test section. The low rate o working luid, the pressure drop across the bed and the variation o axial temperature are measured and recorded using suitable instrumentation. The working luid lows through a helical coil immersed in the hot water tank with the aid o a pump. It achieves the desired temperature beore it enters the test section. The interaction between the cold bed and the hot luid takes place. As a result, the luid temperature at bed outlet decreases. The luid recirculates in a closed circuit. When the bed reaches steady state, the pressure drop across the bed and temperatures along the bed length are obtained rom personal computer through a data loger or two dierent glass beads o sizes 6 mm and 14.6 mm diameter. B p S (3) 5

6 Experimental study on heat transer coeicient and riction actor o Al 2 O 3 nanoluid in a packed bed column ESTIMATION OF RESSURE DRO O interest or the low through packed beds is the relationship between low velocity and the drop in pressure across the bed. Many theoretical correlations are available in literature to calculate this. However, the Sadri (1952) equation is used to calculate the pressure drop through a packed bed given by µ V0 LB ( 1 ε) 1.75ρV0 LB ( 1 ε) Th = + (11) 2 3 D 3 D ε ε where the bed void raction can be determined rom the relation and Vol = 1 Vol B ε where Vol p Vol are the volume o particles and bed respectively, B V 0 is supericial velocity, 6V D equivalent particle diameter given by D = and S is surace area. S The experimental pressure drop is calculated with the help o dierential height in mercury manometer given by the equation, = R ( ρ ρ ) g / g (12) Exp m A The pressure drops obtained rom the Eq. (11) or dierent low rates are compared with the experimental values and presented. The riction actors are calculated using the equation o Sadri (1952) applying pressure drop relations and presented as Ex b 3 th D ε = 2 L ρ B V S 1 ε c (13) 2 C with data Logger Rotometer ACKED BED TEST SECTION GV1 GV2 1 Supply tank ump Heating tank Manometer Figure 3. Schematic diagram o packed bed column Experimental 6

7 Srinivasa Rao et al. / Journal o Mechanical Engineering and Sciences 1(2011) 1-15 CALCULATION OF HEAT TRANSFER COEFFICIENT The Energy balance equation or the packed bed can be estimated rom the relation Q = mc ( T TO) (14) Exp where m is the mass low rate. The Heat Transer coeicient is estimated using Q and the dierence between surace temperature o the bed and bulk mean Exp temperature o the luid is given by h Exp L I QExp = (15) A (T T ) i= 8 where T = T /8 s and T Si b i= 1 = (TI + TO ) / 2. The experimental Nusselt number is estimated with the relation h D Nu Exp Exp k (16) Alazmi and and Vaai (2000) a correlation by conducting experiments with air, hydrogen, carbon dioxide and water. Experiments are undertaken in a narrow range o randtl numbers or packed bed Reynolds number with the characteristic dimension in Re taken as the bed particle diameter D. The validation o the correlation has been undertaken by Gnielinski (1980) who presented the relation as hd p 0.5 1/3 Nu lam = = 0.664Re p r k (17) 0. 8 hdp Re r Nu tub = k. Re ( r / 1) (18) Gunn et al. (1987) presented an equation which is similar to Eq. (17) o Gnielinski (1980) in the absence o Nu tub as hdp / 3 Nu = = Re r k (19) Figure 4 represents the pressure drop in the packed bed with water and nano luids at various volumetric concentrations. The pressure drop decreases with increase in bed particle diameter and Reynolds number. The pressure drop increases with increase in volume concentration o the nano luid. The values o riction actor rom theory are compared with those rom experiment in Figure 5. The values are compared or water and nano luid at various concentrations or 6mm and mm particles. A regression equation is developed or the estimation o riction actor with an average deviation o ±0.08% and standard deviation o 1.68% as ( 1 φ) 0. =. Re p (20) Figures 6 to 9 represent the variation o heat transer coeicient or various concentrations o nano luid. Figure 6 shows the variation o heat transer coeicient with particle Reynolds. Nanoluids predict higher heat transer coeicients compared to base luid water. A regression equation is developed or the estimation o Nusselt number as a unction o Reynolds number, randtl and volume concentration o nanoluid. It is obtained with a standard deviation o 1.56% and an average deviation o 3.92% given by Nu= Re p 1+ φ r (21) S S b ( )

8 Experimental study on heat transer coeicient and riction actor o Al 2 O 3 nanoluid in a packed bed column Figure 4. Comparison o experimental and theoretical pressure drop or water and nanoluids or mm and 6 mm particles in packed bed Figure 5. Comparison o experimental and theoretical riction actor or water and nanoluids or mm and 6 mm particles in packed bed 8

9 Srinivasa Rao et al. / Journal o Mechanical Engineering and Sciences 1(2011) 1-15 Figure 6. Comparison o heat transer coeicient in packed beds with particle Reynolds number with 6mm and mm glass particles beds with water and nanoluids Figure 7 represents the variation o heat transer coeicient with non dimensional axial distance along the bed length at 40 0 C or minimum and maximum low rates or water and nanoluid at two dierent concentrations or the two particles. The heat transer coeicient increase with increasing low rate and concentration o the nanoluid. Figure 8 represents the variation o heat transer coeicient or 6mm, mm particles or dierent operating conditions. The low rate is 150 LH at 40 0 C or water and nano luids at dierent concentration, the heat transer coeicient increased with decreasing particle diameter. Figure 7. Eect o Al 2 O 3 concentration on heat transer coeicient comparison with non dimensional axial distance with14.56mm particles beds with water and nano luids 9

10 Experimental study on heat transer coeicient and riction actor o Al 2 O 3 nanoluid in a packed bed column Figure 8. Heat transer coeicient Vs article Reynolds number at luid rate 150 LH or 6 mm, particles Figure 9 shows the variation o heat transer coeicient o water and nanoluid at high low rates or two temperatures and particle concentrations. At higher low rates and temperatures, the heat transer coeicient is greater, or 6mm compared to mm particle size. Figure 9. Heat transer coeicient Vs article Reynolds number at luid rate 300 LH or6mm, mm particles Figures 10 to 11 represent the temperature distribution o the bed or two particle sizes. The experimental values are in agreement with Schumann-NTU method and other authors rom literature. There is a reasonable agreement o experimental data 10

11 Srinivasa Rao et al. / Journal o Mechanical Engineering and Sciences 1(2011) 1-15 with other theoretical investigations. The pressure drop with nanoluids is higher by 10%, and it increases with concentration o the nanoluid. Figure 11 shows a comparison o temperature proiles at minimum and maximum low rate or bed o mm particles. At the low low rate, the temperature is greater than at high low rate. There is no signiicant temperature variation with low rate. The temperature variation is signiicant at higher concentrations o the nanoluid. Figure 12 represents the non dimensional luid exit temperature distribution or 6mm particles at dierent low rates in comparison with NTU method. The temperatures obtained with nanoluid are higher than or water. The theoretical results indicate reasonable agreement with the experimental values with a deviation o 10%. Figure 10. Comparison o non dimensional temperature distributation with non dimensional axial distance with NTU-ε method at 150 LH and 300 LH Figure 11. Comparison o non dimensional temperature distribution with non-dimensional axial distance with NTU-ε method at 150 LH and 300 LH or 6 mm particles 11

12 Experimental study on heat transer coeicient and riction actor o Al 2 O 3 nanoluid in a packed bed column CONCLUSIONS Heat transer in a packed bed column illed with glass beads o 6.0 and mm size is employed to determine heat transer coeicient and pressure drop. The riction actor increased with decreasing particle diameter and increasing volume concentration o nanoluids compared to base luid. The pressure drop is higher with nanoluids than with water by 10 to 15%. The pressure drop increased with nanoluid concentration. At lower concentration, the deviation o riction actor with nanoluid and water is signiicant than at higher concentration. The heat transer coeicient is higher with 6mm particles due to larger surace area and the number o particles. Similarly, the heat transer coeicient is greater at higher concentrations o the nanoluid. With an increase in volume concentration, the heat transer is more and increases with the low rate and inlet luid temperature. The enhancement in heat transer coeicient with nanoluids than base luid lies between 10 to 15% due to higher values o thermal conductivity. The values rom Schumann model agree with the experimental data or the two bead sizes o 6.0 and 14.56mm. The deviation between the two is less than 10%. REFERENCES Alazmi, B. and Vaai, K Analysis o variants within the porous media transport models. Journal o Heat Transer, 122(2): Adeyanju, A.A Eect o luid low on pressure drop in a porous medium o a packed bed. Journal o Engineering and Applied Sciences, 4(1): Araiza, C.C.O. and Isunzay, F.L Hydrodynamic models or packed beds with low tube-to-particle diameter ratio. International Journal o Chemical Reactor Engineering, 6: article A1. Carlos, O. Araiza, C. and Lopez-Isunzay, F Hydrodynamic models or packed bedswith low tube to particle diameter ratio. International Journal o Chemical Rector Engineering, 6(A1): Choi, S.U.S Enhancing thermal conductivity o luid with nanoparticles. Developments and applications o non-newtonian low. ASME, FED 231/MD, 66: Das, S.K., utra, N., Thiesen,. and Roetzel, W Temperature dependence o thermal conductivity enhancement or nanoluids. ASME Journal o Heat Transer, 125: Duie, J.A. and Beckman, W.A Solar engineering o thermal processes. 2 nd ed. New York: John Wiley& Sons Inc. Gnielinski, V Warme- und Sto ubertragung in Festbetten, Chem. Eng. Tech., 52: Gunn, D.J., Ahmad, M. and M and Sabri, M.N A distributed model or liquid phase heat transer in ixed beds. International Journal o Heat and Mass Transer, 30: Jeigarnik, U.A., Ivanov, F..and Ikranikov, N Experimental data on heat transer and hydraulic resistance in unregulated porous structures. Teploenergetika, 12: Lamine, A.S. Colli Serrano, M.T. and Wild, G. 1992a. Hydrodynamics and heat transer in packed beds with liquid up low. Chemical Engineering roc., 31:

13 Srinivasa Rao et al. / Journal o Mechanical Engineering and Sciences 1(2011) 1-15 Lamine, A.S., Colli Serrano, M.T. and Wild, G. 1992b. Hydrodynamic and heat transer packed beds with concurrent up low. Chemical Engineering Sci., 47: Lee, S., Choi, S.U.S., Li, S. and Eastman, J.A Measuring thermal conductivity o luids containing oxide nanoparticles Journal o Heat Transer, 121: Mahalingam, M Thermal management in semiconductor device packing. roc, IETE73, pp Maiga, S.B.,alm, S.J., Nguyen, C.T., Roy, G. and Galanis, N Heat transer enhancement by using nanoluids in orced convection lows. International Journal o Heat and Fluid Flow, 26: Mansour, R., Galanis, N. and Nguyen, C Eect o uncertainties on orced convection heat transer with nanoluids. Applied Thermal Engineering, 27(1): Maxwell, J.C A treatise on Electricity and magnetism. Cambridge: Oxord University ress. Sadri, E Fluid low through packed bed vertical column. Chemical Engineering rogress, 48: Sagana, K. and Nakahara, N Thermal perormance and pressure drop o rock beds with larger storage materials. Journal o Solar Energy, 47(3): Sarma..K., Subramanyam. T, Kishore,.S., Dharma Rao, V. and Kakac, S Laminar convective heat transer with twisted tape inserts in a tube. International Journal o Thermal Sciences, 42(9): Schumann, T.E.W Heat transer :a liquid lowing through a porous prism. Journal o the Franklin Institute, 208(3): Sivleira, A.M Heat transer in porous media one phase model in ixed beds. h.d. Diss., EQ-COE/UFRJ. Syam Sundar, L., Sharma, K.V. and Ramanathan, S Experimental investigation o heat transer enhancements with Al2O3 nanoluid and twisted tape insert in a circular tube. International Journal o Nanotechnology and Applications, 1(2): Tuckerma, D.B. and ease, R.F Ultra high thermal conductance microstructures or cooling integrated circuits. IETE, 781-4: Weekman, V.W. and Myers, J.E Heat transer characteristics o concurrent gasliquid low in packed beds. American Institute o Chemical Engineers Journal, 11: Wen, D. and Ding, Y Experimental investigation into convective heat transer o nanoluid at the entrance region under laminar low conditions. International Journal o Heat and Mass Transer, 47(24): Xuan, Y.M. and Roetzel, W Conceptions or heat transer correlation o nanoluids, International Journal o Heat and Mass Transer, 43(19): Xuan, Y.M., Li, Q. and Hu W Aggregation structure and thermal conducting o nanoluids. American Institute o Chemical Engineers Journal, 49(4): Xue, Q.Z Model or eective thermal conductivity o nanoluids. hysics Letter- A, 307(5-6): Yagi, S., Kunii, D. and Endo, K Heat transer in packed beds through which water is lowing. International Journal o Heat and Mass Transer, 7: You, W.J. Moon, H.J., Jang S.., Kim, J.K., Koo,J Eects o porosity, pumping power, and L/D ratio on the thermal characteristics o an N 2 O catalytic igniter 13

14 Experimental study on heat transer coeicient and riction actor o Al 2 O 3 nanoluid in a packed bed column with packed bed geometry. International Journal o Heat and Mass Transer, 53: Nomenclature 2 A area o the bed, m C constant in Equation (9) C speciic heat, J kgk D diameter, m riction actor 2 g local acceleration o gravity, m s 2 g gravitational constant, kg m N s c h heat transer coeicient, W m 2 K h average heat transer coeicient, W m 2 K h Volumetric heat transer coeicient, W/m -3 K -1 V k thermal conductivity, W mk L length, m m& mass low rate, kg s N number grids in axial direction, x / L NTU Number o transer units Nu Nusselt number, h D k pressure, a pressure drop, a r randtl number, µ C L k rate o heat transer, W Q R e Reynolds number, ρv µ Re p acked bed Reynolds number, ρ s µ ( 1 ε ) R m dierential height in manometer luid T Temperature, K T mean temperature, K Vol 3 volume, m V velocity, m s X x Subscripts LB sd A B b Ex I mercury bed bulk luid experimental inlet 14

15 Srinivasa Rao et al. / Journal o Mechanical Engineering and Sciences 1(2011) 1-15 lam laminar low O outlet luid L liquid particle 0 supericial S surace Th theoretical tub turbulent low x local values Nano nano luid Greek Symbols θ non-dimensional luid temperature ρ density o the luid, kg 3 m µ dynamic viscosity, N s m ε void raction φ volume concentration 15