Page 149 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 121

Questions and problems
Statements
a. What is an isotropic material?
b. List the three fundamental modes of heat transfer.
c. Discuss the physical mechanisms associated with heat transfer by conduction, con-
vection and radiation.
d. The driving cause of heat transfer by conduction is generally considered to be:
i. The motion of a fluid
ii. An invisible motion of the particles that constitute a medium
iii. Waves of the electromagnetic field propagating at the speed of light
e. Define Fourier’s law.
f. Write the general mathematical formulation of Fourier’s law in steady-state condi-
tions. What are the vector and scalar quantities? Why is there a minus sign on the
right-hand side of the equation?
g. Define the temperature gradient. What are its units?
h. Write the different forms that Fourier’s law takes for each of the orthogonal direc-
tions of Cartesian, cylindrical and spherical coordinate systems.
i. Write Fourier’s law from memory with respect to the case of a plane energy wall
in a steady state represented in the following picture.

j. Define thermal conductivity. What are its units? What role does it play in heat
transfer?
k. The thermal conductivity of a solid is generally larger than that of a liquid. Why?
Then, why is the thermal conductivity of a liquid larger than that of a gas?
l. Is the thermal conductivity of a saturated soil greater or smaller than that of the
same dry soil? Justify your answer.
m. Calculate the effective thermal conductivity, λ, of a dry sand at the temperature

level of 15 C characterised by a porosity n 5 0:42 and a value of thermal conduc-

tivity of solid particles λ s 5 0:41 W/(m C). Repeat the calculation for the same