Single-phase convection heat transfer characteristics of pebble-bed channels with internal heat generation

Nuclear Engineering and Design 252 (2012) 121–127

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Single-phase convection heat transfer characteristics of pebble-bed channels with internal heat generation Xianke Meng ∗ , Zhongning Sun, Guangzhan Xu National Key Discipline Laboratory of Nuclear Safety and Simulation Technology, Harbin Engineering University, Harbin 150001, China

h i g h l i g h t s

g r a p h i c a l

 We adopt electromagnetic induction heating method to overall heat the pebble bed to be the internal heat source.  The ball diameter is smaller, the effect of the heat transfer is better.  With Re number increasing, heat transfer coefficient is also increasing and eventually tends to stabilize.  The changing of heat power makes little effect on the heat transfer coefficient of pebble bed channels.

The core of the water-cooled pebble bed reactor is the porous channels which stacked with spherical fuel elements. The gaps between the adjacent fuel elements are complex because they are stochastic and often shift. We adopt electromagnetic induction heating method to overall heat the pebble bed. By comparing and analyzing the experimental data, we get the rule of power distribution and the rule of heat transfer coefficient with particle diameter, heat flux density, inlet temperature and working fluid’s Re number.

a r t i c l e

a b s t r a c t

i n f o

Article history: Received 7 September 2011 Received in revised form 29 May 2012 Accepted 30 May 2012

a b s t r a c t

The reactor core of a water-cooled pebble bed reactor includes porous channels that are formed by spherical fuel elements. This structure has notably improved heat transfer. Due to the variability and randomness of the interstices in pebble bed channels, heat transfer is complex, and there are few studies regarding this topic. To study the heat transfer characters of pebble bed channels with internal heat sources, oxidized stainless steel spheres with diameters of 3 and 8 mm and carbon steel spheres with 8 mm diameters are used in a stacked pebble bed. Distilled water is used as a refrigerant for the experiments, and the electromagnetic induction heating method is used to heat the pebble bed. By comparing and analyzing the experimental results, we obtain the governing rules for the power distribution and the heat transfer coefficient with respect to particle diameter, heat flux density, inlet temperature and working fluid Re number. From fitting of the experimental data, we obtain the dimensionless average heat transfer coefficient correlation criteria and find that the deviation between the fitted results and the experimental results is 12% or less. © 2012 Elsevier B.V. All rights reserved.

1. Introduction A water cooled pebble-bed reactor (WCPB) combines the most used and most mature water-cooled reactor technology with the excellent performance of spherical fuel elements. The WCPB is a

∗ Corresponding author. Tel.: +86 451 82569655; fax: +86 451 82569655. E-mail address: [email protected] (X. Meng). 0029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2012.05.041

new, small, modular, long-life reactor with a high inherent security that can prevent nuclear proliferation (Sümer and Farhang, 2008; Tsiklauri and Garner, 2005). There is increasing concern for the worsening global energy crisis. A reactor core is stacked with spherical fuel elements, and the gaps between the adjacent fuel elements are stochastic and often shift. Because of these characters, heat transfer is complicated. Currently, studies regarding the heat transfer characteristics of pebble bed channels are still in their infancy and are more

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X. Meng et al. / Nuclear Engineering and Design 252 (2012) 121–127

Nomenclature Qv ms ml cps , cpl ts , tl  V r H N h Q A tw , tf G iin , iout twi , tfj Qk Ao twk , tfk ik , ik+1 l L Nu Nu∗ Re Gm D d ε V

volumetric heat generation rates in the pebble bed (kW/m3 ) solid mass of unit body (kg) fluid mass of unit body (kg) specific heat at constant pressure of solid and liquid, kJ/(kg K); particle and water temperature of unit body at heating process (K) time (s) volume of unit body (m3 ) diameter of test section (m) metal particles filled length (m) metal particles number in the test section average heat transfer coefficient of pebble bed channels (kW/(m2 K)) heating power (kW) heat transfer area (m2 ) average particle and water temperature within the whole pebble bed (K) mass flow rate of fluid (kg/s) fluid enthalpy of test section at inlet and outlet point (J/kg) particle and water temperature at measuring point (K) heating power of the k-th part pebble bed (J) heat area of every part (m2 ) average particle and water temperature of the k-th part pebble bed (◦ C) fluid enthalpy of the k-th and k + 1 part pebble bed (J/kg) length of every part (m) length of the whole pebble bed (m) Nusselt number Dimensionless Nusselt number Reynolds number area mass flow rate of inlet fluid (kg/(m2 s)) equivalent diameter (m) particle diameter (m) porosity volume of one metal particle in the test

concentrated on heat transfer enhancement. For example, Izadpanah et al. (1998) and Jamialahmadi et al. (2005) found that filling a channel with metallic or non-metallic particles (with water as a working fluid) increased the heat transfer coefficient by a factor of 5–10 compared with an empty channel. Meng et al. (2003) and Jiang et al. (2004) found that, when air is the working fluid, the heat transfer coefficient can be increased by a factor of 3–30. However, the only studies of the complex heat transfer characteristics for pebble bed channels with an internal heat source were performed by Xiao et al. (2007) and Yuan feng et al. (2008). These heat transfer law studies were limited because a resistive wire heating method was used to heat the individual metal elements. Studies performed in other countries mainly involved a packed bed that was formed after a reactor core was severely damaged. Patrick and Günter (2006) and Patrick et al. (2006) simulated the internal boiling and dry-out phenomenon. Andreas et al. (1999), Andreas and Franz (2005) and Andreas and Franz (2006) experimentally simulated the effects of the inclination angle and crack effect on the heat transfer of a molten packed bed. Thus, studies regarding a holistic internal-heat-source pebble bed model based on the heat transfer law are lacking.

Fig. 1. Schematic of the experimental apparatus.

To obtain a holistic internal-heat-source pebble bed model and study the heat transfer characteristics, we used a pebble bed with metal spheres of different materials and diameters. We used electromagnetic induction because it provides complete bed heating, and we considered the entire packed bed to be an internal heat source. Then, the heating power, inlet temperature, mass flow and other factors were used to study the heat transfer characteristics of the pebble bed channels for a single-phase forced flow.

2. Experimental Set-up From Fig. 1, the test section consisted of a crystal glass tube with packed spheres. The glass tube had an inner diameter of 75 mm and length of 980 mm, and the middle section was filled to a height of 670 mm with oxidized stainless steel spheres with a diameter of 3 mm or 8 mm or carbon steel spheres with a diameter of 8 mm. The upper and lower sections were filled with glass spheres of the same diameter to reduce the entrance and exit effects. The spheres were heated with a two-winding induction coil connected to an IF-generator. The test section had 32 thermocouples (0.3 mm, Type K): two were separately installed at the inlet and outlet of the test section, and the others were installed in the pebble bed. The thermocouples inside the pebble bed were in sets of two, of which one was buried in a metal sphere to detect the spheres’ temperature and the other was near the sphere (at distance of one-tenth of the sphere diameter from the sphere) to detect the temperature of the fluid. The surface and center temperatures of the sphere differed minimally, so we considered the center temperature to be approximately equal to the surface temperature. The experimental system is shown in Fig. 2. This system consisted of a water tank, cooler, circulating pump, filter, pressure regulator, flow-meter, pre-heater, test section and the related tubes and valves. Distilled water was used as a coolant, and the atmospheric pressure was used as the operating pressure. In the loop, the pumped water first flowed through the cooler and pre-heater to reach the preset inlet temperature and then flowed into the test section at the bottom of the bed. After absorbing the heat generated by the pebble bed, the water flowed from the top of the test section to the water tank.

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the liquid flux was then increased to achieve a new operating point, and data were recorded. The heating power was increased, and the above steps were performed to determine the temperature inside the pebble bed with different liquid flow rates and amounts of heating power. Based on the walls of the bed, there is a porosity distribution across the bed radius. The near-wall positions have greater porosity. This distribution influences both the heat transfer and flow distribution. When the pebble diameter is small and the bed diameter is constant, the side-wall effect is eliminated (Yassin et al., 2008). Because the pebbles in this experiment are small, we do not consider the side-wall effect. This study experimentally and theoretically determined the average heat transfer coefficient of whole pebble bed, as well as the adjacent temperature measurement sections. Thus, a heat transfer coefficient law curve based on various factors was obtained. Eq. (3) provides the average heat transfer coefficients of the pebble bed channels, which were derived from the Newton cooling formula:

Fig. 2. Schematic of the experimental pebble-bed set-up.

3. Experimental measurements and data processing 3.1. Power distribution For this study of the heat transfer characteristics of an internal heat generation pebble bed model, we assumed that the generated heat within the pebble bed was uniform. We obtained the power distribution law within the channels based on the calculated volumetric heat generation rates of the measurement points. During the experiments, we first filled the experimental section with water and then opened the electromagnetic induction heater to heat the test section until the internal temperature of the working fluid was close to the fluid’s boiling point. All of the temperatures at the measurement points were recorded in this process. This method is similar the method used by Catton and Jakobsson (1987). A uniform temperature distribution was assumed for the metal sphere, as well as for the surrounding water. The volumetric heat generation rates were then determined for the metal sphere and water at specific measuring points with Eq. (1). Qv =

(ms cps (dts /d)) + (ml cpl (dtl /d)) V r 2 H N

h=

Q A(tw − tf )

(3)

where Q = G(iout − iin )

(4)

A = d2 N

(5)

1  twi 15 15

tw =

(6)

i=1

1  tfj 15 15

tf =

(7)

j=1

3.3. Local heat transfer coefficient (1)

where V =

123

(2)

3.2. Average heat transfer coefficient of the pebble bed channels The calorific value of the induction heating method is mainly affected by the frequency of the alternating current, alternating current strength and load permeability. Patrick and Günter (2006) and Patrick et al. (2006) conducted experiments with pre-oxidized stainless steel spheres with low permeability to achieve high levels of heating power with the 200 kHz RF induction heating method. In comparison, the previously mentioned experiment used a 3 kHz IF induction heating method to reduce the magnetic field interference from the equipment and signals. This study also reduced the uniformity of heating from the skin effect. First, oxidized stainless steel spheres were used to form a pebble bed; then, high permeability carbon steel spheres were used as a filler to study the heat transfer characteristics of pebble bed channels under low- and high-power conditions, respectively. The initial experimental flow was 0.6 m3 /h. First, the pump was opened to regulate the control valve and stabilize the inlet flow at 0.6 m3 /h. Then, the electromagnetic induction heater was turned on to achieve the power for heating the test section. The cooler and pre-heater were regulated to maintain the inlet temperature. Data were recorded when the test section reached heat transfer equilibrium (the temperature changed by less than 0.2 ◦ C for one minute),

For the test section, the thermocouples were located in five sections along the axial direction, which divided the test section into four sections from the top to the bottom. We calculated the average heat transfer coefficient of each section and provided a more detailed analysis of the test section based on heat transfer. The following assumptions were used to calculate the local heat transfer coefficients: the average water temperature of the upper and lower ends at the surface of each section were equal to the outlet and inlet temperature, respectively; the average sphere temperature of both end surfaces was equal to the sphere temperature of this test section; the average water temperature of both end surfaces was equal to the total average water temperature. The axial k-th segment heat transfer coefficient hk (k = 1, 2, 3, 4) is expressed as: hk =

Qk Ao (twk − tfk )

(8)

where Qk = G(ik − ik+1 ) 1 (twki + tw(k+1)i ) 6

(9)

3

twk =

(10)

i=1

1 (tfkj + tf(k+1)j ) 6 3

tfk =

j=1

(11)

X. Meng et al. / Nuclear Engineering and Design 252 (2012) 121–127

1.0

1.0

0.8

Dimensionless axial position (z/H)

Dimensionless axial position (z/H)

124

radial positions 0mm

0.6

13mm 26mm

0.4

literature 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

0.8 0.6 0.4

radial positions 0mm 13mm 26mm literature

0.2 0.0

Normalied power (P/Pmax )

(a) Axial power distribution

0.0

0.2

0.4

0.6

0.8

1.0

Fig. 4. Power calibration of the pebble-bed at 50 kW.

1.0

axial positions 635mm 485mm 335mm 185mm 35mm

0.8 0.6 0.4

establish an internal heat source model, which was required for the experiment. Fig. 4 shows the axial dimensionless power distribution of the pebble bed at the high-power level. Based on this figure, increasing power decreases the stability of the axial power due to the increased edge effect. Therefore, to reduce the impact of the power non-uniformity, this study uses the data from the middle uniform sections. From Figs. 3a and 4, there is a consistent depression in the axial profile at the axial center line because this position corresponds to a gap between the two windings.

literature 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

4.2. Heat transfer coefficient of pebble-bed channels

Normalied power (P/Pmax)

(b) Radial power distribution Fig. 3. Power calibration of the pebble-bed at 10 kW.

Because each part of the test section has the same length, the heat transfer areas are equal and are expressed as: Ao =

l A L

(12)

4. Analysis of experimental results 4.1. Power distribution Fig. 3 shows the axial and radial power distribution curves for the 20 kW pebble bed channels. For comparison, the diagram also provides the results from Catton and Jakobsson (1987). From Fig. 3a, the three axial power distribution curves at the radial positions exhibit the same trend; less power is observed at the ends than at the middle, which is similar to the results from Catton and Jakobsson (1987) and Naik and Dhir (1982). This distribution of induction coil power is related to the magnetic field strength. This relationship is observed because the induction coil has a finite length and both ends of the coil display the magnetic field line scattering phenomena, which results in an edge effect such that the edge of the magnetic field is weaker than the middle. From Fig. 3b, although the test section in this study is much larger than that in the compared literature, the radial power distributions at the five temperature measurement sections are uniform, and the radial normalized power ranges from 0.9 to 1.1. These results indicate that the test section does not alter the skin effect, and they also verify the use of this electromagnetic induction heating method to

The sphere diameter significantly affects heat transfer. The 3 mm and 8 mm stainless steel spheres were used for low-heat flux heat transfer experiments to verify the effects of sphere diameter on pebble-bed heat transfer. Fig. 5 shows that the pebble bed with 3 mm diameter particles has a better heat transfer intensity than the pebble bed 8 mm diameter particles. This difference increases as the Re number increases. The contact surface area between the particles and the water increases with decreasing particle diameter, which intensifies the convection heat transfer. Therefore, for packed beds with the tested conditions, the heat transfer coefficients increase with decreasing particle diameter. Figs. 6–9 show tests performed with a pebble bed with 8 mm carbon steel spheres. From Fig. 6, as the working fluid Re number increases, the average heat transfer coefficient of the channels

16000

14000

h/ W/(m2.K)

Dimensionless radial position(r/R)

Normalied power (P/Pmax )

12000

10000

Tin=25oC 8000

3mm 8mm

6000 500

1000

1500

2000

2500

3000

Re Fig. 5. Effect of sphere diameter on the average heat transfer coefficient.

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130

110 100

110 100

90

Nu

Nu

120

10.4kW 21.9kW 32.3kW 41.3kW 52.6kW

120

125

80

diameter 8mm Tin=25.3oC

70

90 80

Tin=25.3oC P=21.9kW

70

o Tin=25.3 C P=32.3kW

60

o Tin=49.6 C P=21.5kW

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60 50 0

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Re

Fig. 6. Effect of heat power on the average heat transfer coefficient.

Fig. 7. Effect of the inlet temperature on the average heat transfer coefficient.

increases with a decreasing growth rate. Based on this tendency, we predict that, if the working fluid Re number increases to a certain flux, it will no longer be one of the main factors affecting the heat transfer coefficient. Additionally, from this figure, when increasing the heating power from 10–50 kW, the heat transfer coefficient of the channels at the same Re number is within 5%, which indicates that changes in the channel power do not significantly affect the heat transfer in the channel. Fig. 7 shows the influence of the inlet temperature on the average heat transfer coefficient of the pebble bed channels. From this figure, as the coolant inlet temperature increases, the heat transfer coefficient decreases, similar to previous studies (Xiao et al.,

a

275 250

225

P=10.4kW

225

200

545mm 405mm 265mm 125mm

175 150

b P=21.9kW

545mm 405mm 265mm 125mm

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Nu

2007; Yuan feng et al., 2008). This relationship is due to the increasing inlet temperature, which reduces the viscosity of the working fluid in the pebble bed channels. The water speed is higher at a low temperature than at a high temperature with the same Reynolds number because the momentum and heat transfer of the low temperature water in the channels is greater, eventually resulting in a higher heat transfer capacity. To better understand the heat transfer coefficient within the channels, the average heat transfer coefficient of the middle section (between adjacent temperature measurement sections) was

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Nu

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Re

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545mm 405mm 265mm 125mm

2000

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4000

Re

Fig. 8. Heat transfer coefficient of the pebble bed at different distances from the inlet when Tin is 25 ◦ C.

5000

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X. Meng et al. / Nuclear Engineering and Design 252 (2012) 121–127

140

120

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60

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40

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545mm 405mm 265mm 125mm

140

Nu

120

P=21.5kW

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180

P=10.8kW

180

Nu

200

a

200

3000

4000

5000

6000

7000

1000

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2000

3000

4000

c 180

545mm 405mm 265mm 125mm

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7000

8000

P=39.7kW

545mm 405mm 265mm 125mm

160 140 120

Nu

Nu

120

6000

d 180

P=31.9kW

160

5000

Re

Re

100

100

80 80

60 60

40 1000

2000

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4000

5000

6000

7000

40

8000

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5000

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7000

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Re

Re

Fig. 9. Heat transfer coefficients of the pebble bed at different distances from the inlet when Tin is 50 ◦ C.

calculated. Figs. 8 and 9 show the average heat transfer coefficient curves for each section with different inlet temperatures and power, respectively. Power has little effect on the heat transfer coefficient (see Fig. 8). The heat transfer coefficient is smaller with an inlet temperature of 50 ◦ C than 25 ◦ C, as shown in Fig. 9. When the inlet temperature is increased from 25 to 50 ◦ C, the heat transfer coefficient decreases by up to 16%, which verifies the results from Figs. 6 and 7. The section closest to the inlet has a low water temperature and high heat transfer coefficient. Along the flow direction, the water temperature increases and the heat transfer tends to stabilize. This law is consistent with the results shown in Fig. 7.

D=

dε 1−ε

(16)

ε=

NV r 2 H

(17)

For comparison with other Heat criteria relationships and to eliminate the effect of the Pr number, we define of the dimensionless Nusselt number as shown in Eq. (14). In Fig. 10, the Nusselt

4.3. Heat criteria relationship of pebble bed channels

Nu = 3.212Re0.335 Pr 0.438 Nu∗ =

Nu Pr 0.438

(13) 10

= 3.212Re0.335

(14) 1000

where Gm D Re = f

Nu

Based on the above analysis, the single-phase convection heat transfer coefficient of the pebble bed channels is mainly affected by factors such as the working fluid temperature and mass flow rate. From the experimental data, we obtain the following new correlation for the Nusselt number as a function of the Reynolds and Prandtl numbers for Re numbers ranging from 720 to 8010 and Pr numbers ranging from 2.6 to 5.7.

*

100

experiment prediction kay and london nie whitaker kuwahara

Re (15)

Fig. 10. Experimental data and correlation of the Nusselt number versus the Reynolds number for pebble beds.

X. Meng et al. / Nuclear Engineering and Design 252 (2012) 121–127

number data are presented along with the well known correlations for packed beds with spheres from Kays and London (1984), Whitaker (1972), Kuwahara et al. (2001) and the very recent correlation from Nie et al. (2011). With the exception of a few data points, the experimental and predicted results are within 12%. Additionally, from Fig. 10, the power loading (Fig. 7) is mainly affected by the Pr number. The correlations in Fig. 10 are from a gas system with varying application conditions, so they do not correlate well with the experiment data. Currently, there is no correlation that perfectly applies to the forced convection heat transfer of pebble beds with internal heat generation and a liquid medium. Thus, Eq. (14) should be extended, verified and improved in future studies. 4.4. Experimental error The experimental uncertainty of the convection heat transfer coefficient was mainly introduced by the experimental errors for measurement and calculation. The errors are a result of the following: From preliminary tests, the maximum error was within ±0.1 ◦ C for temperature measurements (wall and water temperatures). The maximum flow rate error was less than 0.7%. It was assumed that both the radial and axial power profiles were uniform, although the power was slightly different at both ends of the bed (see Figs. 3 and 4). Consequently, the measured bed power was slightly over estimated. The bed porosity ranged from 0.378 to 0.387. For all calculations, 0.38 is used. From Eqs. (13)–(17), when the porosity changes by 2.3%, the heat transfer coefficient changes by 3.2%. The error in measuring the number of steel spheres in the test section is expected to reach 0.5%, which affects the surface temperature and porosity. The composite error from Eqs. (4) and (13) is 1.2%. Assuming random errors, the maximum experimental uncertainty in the convection heat transfer coefficient from Eqs. (3)–(17) is ±18.9%. 5. Conclusion To investigate the heat transfer of a pebble bed in a multidimensional configuration with metal particles, an experimental study of single phase convection heat transfer was conducted. These experiments used water, and the following conclusions were obtained. Within the pebble bed, when the Re number increased, the heat transfer coefficient increased until it eventually stabilized. Smaller sphere diameters greatly improved the heat transfer. The heating power had little effect on the heat transfer coefficient of the pebble bed channels, while it mainly affected the coolant temperature and physical parameters. As the inlet coolant temperature increased, the heat transfer coefficient decreased. When the temperature

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increased from 25 to 50 ◦ C, the heat transfer coefficient decreased by up to 16% because the water in the channels had increased momentum and heat transfer at low temperatures, resulting in a higher heat transfer capacity. Acknowledgments The authors would like to thank the National Natural Science Foundation of China for financial support for this work. References Andreas, Z., Franz, M., 2005. Void fraction and heat transport in two-dimensional mixed size particle beds with internal heat sources. Nucl. Eng. Des. 235, 2209–2218. Andreas, Z., Franz, M., 2006. Heat transport and void fraction in granulated debris. Nucl. Eng. Des. 236, 2117–2123. Andreas, Z., Peter, H., Franz, M., 1999. Boiling in particle beds with internal heat sources. In: NURETH-9. Catton, I., Jakobsson, J.O., 1987. The effect of pressure on dryout of a saturated bed of heat generating particles. J. Heat Transfer 109, 185–195. Izadpanah, M.R., Steinhagen, H.M., Jamialahmadi, M., 1998. Experimental and theoretical studies of convective heat transfer in a cylindrical porous medium. Int. J. Heat Fluid Flow 19, 629–635. Jamialahmadi, M., Steinhagen, H.M., Izadpanah, M.R., 2005. Pressure drop, gas holdup and heat transfer during single and two-phase flow through porous media. Int. J. Heat Fluid Flow 26, 156–172. Jiang, P.X., Si, G.S., Li, M., 2004. Experimental and numerical investigation of forced convection heat transfer of air in non-sintered porous media. Exp. Therm. Fluid Sci. 28, 545–555. Kays, W.M., London, A.L., 1984. Compact heat exchangers. McGraw-Hill, New York. Kuwahara, F., Shirota, M., Nakayama, A., 2001. A numerical study of interfacial convective heat transfer coefficient in two-energy equation model for convection in porous media. Int. J. Heat Mass Transfer 44, 1153–1159. Meng, L.I., Peixue, J., Lei, Y.U., 2003. Experimental research of forced convection heat transfer in sintered porous plate channels. J. Eng. Thermophys. 24 (June), 1016–1018. Naik, A.S., Dhir, V.K., 1982. Forced flow evaporative cooling of a volumetrically heated porous layer. Int. J. Heat Mass Transfer 25 (April), 541–552. Nie, X., Besant, R.W., Evitts, R.W., Bolster, J., 2011. A new technique to determine convection coefficients with flow through particle beds. Trans. ASME J. Heat Transfer 133 (4), 041601. Patrick, S., Günter, L., 2006. Boiling experiments for the validation of dryout models used in reactor safety. Nucl. Eng. Des. 236, 1511–1519. Patrick, S., Manfred, G., Rudi, K., 2006. Basic investigation on debris cooling. Nucl. Eng. Des. 236, 2104–2116. Sümer, S., Farhang, S., 2008. The fixed bed nuclear reactor concept. Energy Convers. Manage. 49, 1902–1909. Tsiklauri, G.V., Garner, F.A., 2005. Long Life Small Nuclear Reactor Without Openvessel Re-fueling. PNNL, 15134. Whitaker, S., 1972. Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE Journal 18 (2), 361–371. Xiao, Y., Yuan feng, Z., Jun, M., 2007. Experimental investigation on flow and heat transfer in porous media with internal heat source. In: Tenth National Conference Proceedings of Reactor Thermal Fluid, Beijing. Yassin, A., Hassan, E.E., Dominguez-Ontiveros, 2008. Flow visualization in a pebble bed reactor experiment using PIV and refractive index matching techniques. Nucl. Eng. Des. 238, 3080–3085. Yuan feng, Z., Tao tao, W., Ze jun, X., 2008. Experimental study on local heat transfer characteristics of porous media with internal heat source. Nucl. Power Eng. 29, 57–65, January.