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Título : | Time Varying Heat Conduction in Solids |

Palabras clave : | HEAT TRANSFER PHOTOTHERMAL |

Fecha de publicación : | 16-ene-2013 |

Editorial : | INTECH |

Descripción : | People experiences heat propagation since ancient times. The mathematical foundations of
this phenomenon were established nearly two centuries ago with the early works of Fourier
[Fourier, 1952]. During this time the equations describing the conduction of heat in solids
have proved to be powerful tools for analyzing not only the transfer of heat, but also an
enormous array of diffusion-like problems appearing in physical, chemical, biological, earth
and even economic and social sciences [Ahmed & Hassan, 2000]. This is because the
conceptual mathematical structure of the non-stationary heat conduction equation, also
known as the heat diffusion equation, has inspired the mathematical formulation of several
other physical processes in terms of diffusion, such as electricity flow, mass diffusion, fluid
flow, photons diffusion, etc [Mandelis, 2000; Marín, 2009a]. A review on the history of the
Fourier´s heat conduction equations and how Fourier´s work influenced and inspired others
can be found elsewhere [Narasimhan, 1999].
But although Fourier´s heat conduction equations have served people well over the last two
centuries there are still several phenomena appearing often in daily life and scientific
research that require special attention and carefully interpretation. For example, when very
fast phenomena and small structure dimensions are involved, the classical law of Fourier
becomes inaccurate and more sophisticated models are then needed to describe the thermal
conduction mechanism in a physically acceptable way [Joseph & Preziosi, 1989, 1990].
Moreover, the temperature, the basic parameter of Thermodynamics, may not be defined at
very short length scales but only over a length larger than the phonons mean free paths,
since its concept is related to the average energy of a system of particles [Cahill, et al., 2003;
Wautelet & Duvivier, 2007]. Thus, as the mean free path is in the nanometer range for many
materials at room temperature, systems with characteristic dimensions below about 10 nm
are in a nonthermodynamical regime, although the concepts of thermodynamics are often
used for the description of heat transport in them. To the author´s knowledge there is no yet
a comprehensible and well established way to solve this very important problem about the
definition of temperature in such systems and the measurement of their thermal properties
remains a challenging task. On the other hand there are some aspects of the heat conduction
through solids heated by time varying sources that contradict common intuition of many
people, being the subject of possible misinterpretations. The same occurs with the
understanding of the role of thermal parameters governing these phenomena.
178 Heat Conduction – Basic Research
Thus, this chapter will be devoted to discuss some questions related to the above mentioned
problems starting with the presentation of the equations governing heat transfer for
different cases of interest and discussing their solutions, with emphasis in the role of the
thermal parameters involved and in applications in the field of materials thermal
characterization.
The chapter will be distributed as follows. In the next section a brief discussion of the
principal mechanisms of heat transfer will be given, namely those of convection, radiation
and conduction. Emphasis will be made in the definition of the heat transfer coefficients for
each mechanism and in the concept of the overall heat transfer coefficient that will be used
in later sections. Section 2 will be devoted to present the general equation governing nonstationary
heat propagation, namely the well known (parabolic) Fourier’s heat diffusion
equation, in which further discussions will be mainly based. The conditions will be
discussed under which this equation can be applied. The modified Fourier’s law, also
known as Cattaneo’s Equation [Cattaneo, 1948], will be presented as a useful alternative
when the experimental conditions are such that it becomes necessary to consider a
relaxation time or build-up time for the onset of the thermal flux after a temperature
gradient is suddenly imposed on the sample. Cattaneo’s equation leads them to the
hyperbolic heat diffusion equation. Due to its intrinsic importance it will be discussed with
some detail. In Section 3 three important situations involving time varying heat sources will
be analyzed, namely: (i) a sample periodically and uniformly heated at one of its surfaces,
(ii) a finite sample exposed to a finite duration heat pulse, and (iii) a finite slab with
superficial continuous uniform thermal excitation. In each case characteristic time and
length scales will be defined and discussed. Some apparently paradoxical behaviors of the
thermal signals and the role playing by the characteristic thermal properties will be
explained and physical implications in practical fields of applications will be presented too.
In Section 4 our conclusions will be drawn. INSTITUTO POLITECNICO NACIONAL, CONACYT |

URI : | http://www.repositoriodigital.ipn.mx/handle/123456789/11607 |

Otros identificadores : | 978-953-307-404-7 http://hdl.handle.net/123456789/1138 |

Aparece en las colecciones: | Doctorado |

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