Page 117 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 89

3.5.2 Convection heat transfer coefficient values
In the analysis of internal and external flows, the convection heat transfer coefficient,
h c , is typically used to express with the relevant temperature variation, ΔT, the heat
flux density. In the analysis of seepage flows, the separate terms ρ c pf v rf are used to
f
equivalently express the convection heat transfer coefficient. Accordingly, the convec-
tion heat transfer coefficient depends on (1) the fluid thermophysical properties and
(2) the fluid velocity. These factors should be considered in the analysis and design of
energy geostructures.
The convection heat transfer coefficient may be broken down for convenience
into two components as

ð3:7Þ
h c 5 h c;n 1 h c;f
where h c;n is the portion of convection coefficient accounting for the natural convec-
tion phenomenon, whereas h c;f is the portion accounting for the forced convection
phenomenon.
A large number of expressions are available for estimating the natural convection
coefficient with reference to airflow over surfaces (Khalifa, 2001a; Khalifa, 2001b).
Bourne-Webb et al. (2016) report values of h c;n for heat flow from vertical external
surfaces in the range of 1 3 W/(m 2 C) (Khalifa, 2001a) and values for enclosed
vertical surfaces in the range of 2 4 W/(m 2 C) (Khalifa, 2001b). EN ISO 6946
(2007) suggests a value of 2.5 W/(m 2 C) for horizontal heat from internal surfaces.
Various expressions are also available for estimating the forced convection coefficient
with reference to airflow over surfaces. A power law theoretically relates the forced
convection coefficient h c;f to the airflow velocity v ra . However, Bourne-Webb et al.
(2016) suggest that a simple linear relationship is sufficiently accurate for airflows
characterised by a velocity lower than approximately v ra 5 5 m/s. Fig. 3.9 highlights
the previous fact by reporting correlations for flows over concrete between the
forced convection coefficient h c;f and the airflow velocity v ra . A correlation pro-
posed by Palyvos (2008), additional correlations that describe a comparable relation-
ship between the considered variables (EN ISO 6946, 2007; Lee et al., 2009;
ASHRAE, 2012) and experimental data provided by Lee et al. (2009) as well as by
Guo et al. (2011) are considered.
Different thermophysical properties should be considered for the diverse fluids that
characterise convection heat transfer phenomena associated with energy geostructures.
The fluid that characterises internal flow problems in pipes is water in the simplest
case, but may be a mixture of water and other constituents. The fluid that characterises
internal flow problems over a surface of an energy geostructure or external flow pro-
blems associated with convection at the ground surface is air. The fluid that charac-
terises seepage flow problems occurring underground is water.