Page 88 - Analysis and Design of Energy Geostructures

58 Analysis and Design of Energy Geostructures

transfer occurs, for example, in the subsurface between the heat carrier fluid circulating
in the pipes, the pipes, the energy geostructure and the ground. Mass transfer charac-
terises the flow of the heat carrier fluid circulating in the pipes embedded in the
energy geostructures, the flow of air in underground built environments potentially
adjacent to the considered structures (e.g. metro tunnels adjacent to energy tunnels
and walls), and the possible flow of groundwater in the subsurface. Deformation affects
energy geostructures because of the influence of loadings applied to these structures.
The understanding, modelling and prediction of the aforementioned phenomena
rely on the determination of laws that govern such physical evidence as well as to rela-
tions between variables involved in these evidences. These (balance) laws and relations
are typically termed governing equations and constitutive equations, respectively. Only
when these laws and relations are used to define determined problems can these and
all general phenomena be addressed.

2.7.2 Governing and constitutive equations

Governing equations explicate general physical principles that are valid for all materials
(solid, fluid and gaseous) and characterise physical phenomena. Constitutive equations
are mathematical expressions that relate two physical quantities for describing the
behaviour of materials (solid, fluid and gaseous) and characterising physical phenom-
ena. These latter equations are included in the governing equations to complete the
description of phenomena of interest with reference to the materials involved, while
leaving the governing equations valid a priori.
The relevant physical principles for addressing heat transfer, mass transfer and

deformation phenomena through relevant governing equations are the conservation of
energy, the conservation of mass and the conservation of linear and angular momentum,
respectively.
• The principle of conservation of energy states that the time rate of change of the
kinetic energy and internal energy for a fixed part of material is equal to the sum
of the rate of work done by the surface and body forces and the heat energy enter-
ing the boundary surface.
• The global principle of conservation of mass states that the total mass of a fixed
part of material should remain constant at all times.
• The global principle of linear momentum states that the total force acting on any
fixed part of material is equal to the rate of change of the linear momentum of the
part.
• The global principle of moment of momentum states that the total moment about
a fixed point of surface and body forces on a fixed part of material is equal to the
time rate of change of total moment of momentum of the part about the same
point.