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Research Papers: Heat and Mass Transfer

Modeling the Heat Transfer Coefficient Between a Surface and Fixed and Fluidized Beds With Phase Change Material

[+] Author and Article Information
María A. Izquierdo-Barrientos

ISE Research Group,
Thermal and Fluid Engineering Department,
Universidad Carlos III de Madrid,
Leganés 28911, Spain
e-mail: maizquie@ing.uc3m.es

C. Sobrino

ISE Research Group,
Thermal and Fluid Engineering Department,
Universidad Carlos III de Madrid,
Leganés 28911, Spain
e-mail: csobrino@ing.uc3m.es

José A. Almendros-Ibáñez

Escuela de Ingenieros Industriales,
Dpto. de Mecánica Aplicada e Ingeniería de
Proyectos,
Castilla-La Mancha University,
Albacete 02071, Spain;
Renewable Energy Research Institute,
Section of Solar and Energy Efficiency,
C/de la Investigación s/n,
Albacete 02071, Spain
e-mail: jose.almendros@uclm.es

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 2, 2015; final manuscript received February 27, 2016; published online April 5, 2016. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 138(7), 072001 (Apr 05, 2016) (11 pages) Paper No: HT-15-1086; doi: 10.1115/1.4032981 History: Received February 02, 2015; Revised February 27, 2016

The objective of this work is to model the heat transfer coefficient between an immersed surface and fixed and bubbling fluidized beds of granular phase change material (PCM). The model consists of a two-region model with two different voidages in which steady and transient conduction problems are solved for the fixed and fluidized bed cases, respectively. The model is validated with experimental data obtained under fixed and fluidized conditions for sand, a common material used in fixed and fluidized beds for sensible heat storage, and for a granular PCM with a phase change temperature of approximately 50 °C. The superficial gas velocity is varied to quantify its influence on the convective heat transfer coefficient for both the materials. The model proposed for the PCM properly predicts the experimental results, except for high flow rates, which cause the contact times between the surface and particles to be very small and lead the model to overpredict the results.

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Figures

Grahic Jump Location
Fig. 1

Temperature profile in a packed bed in the region near the wall, where Tw is the wall/surface temperature, Tb is the bed temperature at a distance dp/2 from the surface, T is the bed temperature far from the wall, and Tap is the extrapolation of the temperature profile within the bed to x = 0 (apparent temperature)

Grahic Jump Location
Fig. 2

Equivalent thermal circuit of the heat transfer model through a bed of particles

Grahic Jump Location
Fig. 3

Scheme of two neighboring particles for determining Q˙s

Grahic Jump Location
Fig. 4

Graphical representation of ϕb and ϕw for two models and different values of κ. The data for ϕb are calculated for εb = 0.4. (a) Kunii and Smith [52] and (b) proposed model.

Grahic Jump Location
Fig. 5

Scheme for determining Q˙s at the wall surface

Grahic Jump Location
Fig. 6

(a) Evolution of the mean h¯s and instantaneous hs heat transfer coefficient for the sand as a function of the flow rate. (b) Corresponding contact times for the flow rate.

Grahic Jump Location
Fig. 7

(a) Evolution of the mean h¯s and instantaneous hs heat transfer coefficient for the PCM as a function of the flow rate. (b) Corresponding contact times for the flow rate.

Grahic Jump Location
Fig. 8

Enthalpy variation with temperature for the PCM GR50

Grahic Jump Location
Fig. 9

Evolution of the Nusselt number for (a) the sand and (b) the PCM in the fixed bed as a function of the product between the Reynolds and Prandtl numbers. Continuous lines are the results for the theoretical model with aw = 0.29 for the sand and aw = 0.25 for the PCM. εw = 0.9.

Grahic Jump Location
Fig. 10

Total heat transfer coefficient hw calculated through the model (continuous line) and the experiments (isolated triangles) as a function of the flow for (a) the sand and (b) the PCM GR50. The dashed line (a) represents the results of the model assuming a reduction of 20% in the equivalent thermal conductivity at the wall.

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