Heat Transfer 2

Radiative Transfer

Michel Ledoux, Abdelkhalak El Hami

• Publisher: Wiley-ISTE
• Year: 2021
• ISBN:
  9781119821298
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

Heat is a branch of thermodynamics that occupies a unique position due to its involvement in the field of practice. Being linked to the management, transport and exchange of energy in thermal form, it impacts all aspects of human life and activity.

Heat transfers are, by nature, classified as conduction, convection (which inserts conduction into fluid mechanics) and radiation. The importance of these three transfer methods has resulted – justifiably – in a separate volume being afforded to each of them. This second volume is dedicated to radiation. After recalling photometry, the calculation of luminance is addressed using the theory of the black body and associated laws: Stefan, Wien. The reciprocal radiation of two surfaces in total influence is discussed extensively, and the case of finished surfaces is also considered.

Heat Transfer 2 combines a basic approach with a deeper understanding of the discipline and will therefore appeal to a wide audience, from technician to engineer, from doctoral student to teacher-researcher.

1
General Remarks

1.1. Introduction

Any matter that is not at absolute zero emits radiation. This radiation is electromagnetic by nature. Electromagnetic radiation is characterized by its frequency or its wavelength as well as by the sizes of the electric and magnetic fields that it transports, or better, by the energy it transports. The entire wavelength or frequency spectrum can be used by radiation. Electromagnetic radiation has been modeled by Maxwell and thermal emission by Planck. We note that what we normally call light, more precisely visible light forms, is only a small part of a wavelength spectrum ranging from zero to infinity. Our concern here will be to decipher the radiative energy transmitted or received by material bodies, by linking it with radiations that can be identified by their wavelengths (or their frequencies). We will go over the definition of these terms. Moreover, the propagation of radiative energy involves a particular metrology called photometry. We should therefore introduce some common definitions from this domain.

1.2. Propagation of a sinusoidal electromagnetic wave

1.2.1. Frequencies and wavelengths

We will refer to some specialist work for a general study of wave propagations, as well as for the modeling of electromagnetic waves.

We will simply recall here the definitions of two importance parameters, the frequency ν and wavelength λ of a ray.

An electromagnetic radiation is manifested by the evolution in space of an electric field E (x, t) and a magnetic field B (x, t) paired, and so variable in time and space.

In the simplest case of a plane wave propagating along a rectilineal axis 0x (which results in the “light ray”), the space state is identical on any plane of abscissa x normal to this axis. The fields E (x, t) and B (x, t) are therefore expressed in the form of a function such that

[1.1]

This formula, which can be notably obtained by solving the laws of electromagnetism (Maxwell’s theory), is thus interpreted:

At a given point, f is a wave function, of amplitude A. ν is the frequency of the perturbation observed, and T is the time for a movement or period.

We can “follow” the propagation in space. We seek the evolution in time of the abscissa of a given st...