Page 151 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 123

Define all of the involved terms, their unit measures and their physical
meaning. Write the equation for the cases where there is no internal heat gen-
eration, temperature is independent of time, or both conditions occur. Specify
the meaning of an internal heat generation and when temperature can be
assumed to be independent of time.
bb. Generically, to solve the Fourier heat conduction equation uniquely there is
the need to specify initial and boundary conditions for the specific problem.
Can you detail the role of both initial and boundary conditions in the heat
transfer problem? Are initial conditions always necessary for the resolution?
cc. Boundary conditions must be given at the boundaries of any medium to solve
the energy conservation equation, obtaining the temperature distribution in the
medium. Summarise the boundary conditions commonly encountered in heat
transfer problems.
dd. How is the contact thermal resistance defined for an interface of a unit area and
what are its units?
ee. Discuss how the contact thermal contact resistance is affected by the roughness
of two adjacent surfaces.
ff. Write the formulation of the energy conservation equation for an isotropic slab
considering conduction, convection with a fluid and radiation from a surround-
ing environment with no heat generation.
gg. How is the thermal diffusivity defined and what are its units?
hh. Soils of large thermal diffusivity respond:
i. Quickly to variations in their thermal environment
ii. Slowly to variations in their thermal environment
iii. Irrespectively of the variations of their thermal environment
iv. Depending on the thermal conductivity
ii. The thermal diffusivity α d is the controlling transport property for transient
conduction. Using appropriate values of λ, ρ and c p , calculate α d for the follow-

ing materials at the temperature level of 15 C and complete the table presented
below.
Material Thermal conductivity, λ Volumetric heat capacity, Thermal diffusivity,
2
[W/(m C)] ρc p [MJ/(m 3 C)] α d [m /s]

Dry Saturated Dry Saturated Dry Saturated
Clay 0.2 0.3 1.1 1.6 0.3 0.6 2.1 3.2
Silt 0.2 0.3 1.2 2.5 0.6 1.0 2.1 2.4
Sand 0.3 0.4 1.7 3.2 1.0 1.3 2.2 2.4
Gravel 0.3 0.4 1.8 3.3 1.2 1.6 2.2 2.4
Concrete 0.9 2.0 1.8 2.0
Water 0.57 4.186
Air 0.025 0.0012