Experimental and Numerical Analysis of a PCM-Supported ...

where G=ρU d /ε g is the pore mass flux of the gas phase, Re=4r h G/µ g is Reynolds
number, M g is the molecular weight of gas (g/mol), P a is the dry air pressure (pa), U d
is the Darcian velocity of gas, and r h =ε g /a is the hydraulic radius for gas flow in the
porous medium.
4.2.3.6 Fluid-particle heat transfer coefficient
The interfacial convective heat transfer coefficient for fluid flow in fixed packed beds
(thermal regenerators), which is needed when the local thermal equilibrium between
the fluid and solid phases breaks down, is a very important factor in the heat transfer
performance of the storage medium. It is known that the heat transfer performance
of thermal regenerators is dependent upon many other factors, for example, the heat
exchanger design, the physical properties of the heat transfer fluid, etc. Among
them, the heat transfer coefficient between the packing (solid phase) and the heat
transfer fluid (h sf ) is one of the most important factors, which may strongly influence
the heat transfer performance of the regenerator. Therefore, careful selection of the
heat transfer coefficient correlation from literature is important. Various approaches
and correlations for determining the interfacial convective heat transfer coefficient
between the bed packing and the working fluid are discussed and compared in
Appendix (C).
The correlation of Wakao and Kaguei [15] was used for the fluid/solid heat transfer
coefficient in both the single and two phase flow regenerators, where “fluid” stands
for either liquid or gas phase. Wakao and Kaguei [15] have experimentally
examined the results on h sf for both steady and transient behaviors and reached to a
reliable correlation. They have found the following correlation for h sf for spherical
particles (or the dimensionless form of it; the Nusselt number):
Nu
d
h
1
sf
dp
.6 3
2.0 1.1Re 0 Pr
(4.54)
k
f
Where Re=u p d p / =u D d p /; where u p and u D are the average pore velocity (bulk
mean velocity) and the Darcian velocity of the fluid respectively. However, Wakao
and Kaguei correlation neglects the axial diffusion effects and is valid only for
packed beds with ( ≈ 0.4). The Jefferson degradation factor [14] was introduced in
the fluid-solid heat transfer coefficients to account for the conduction resistance
inside the PCM spheres while using a one-dimensional model for the packed bed as
mentioned earlier and described by equation (4.9).
Figure (4.6) compares the values of effective heat transfer coefficients obtained with
four different Nusselt correlations (described in appendix C) for the flow through a
spherical packing in dependency on the Reynolds Number. The values differ
significantly from each other, which could be due to differences in experimental
boundary conditions under which these correlations were determined. The
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