# Notes on thermal phenomena

## Introduction

This section provides some general information about thermal phenomena (a reminder of physical principles) and some useful definitions.

## Thermal equilibrium

When two bodies that do not exchange heat with their environment but have different temperatures are brought into contact, they exchange heat until an equilibrium state is reached. This state is characterized by the uniform and time independent temperature field of the two bodies.

More generally, a system is in thermal equilibrium when the heat flux is null at any point of the system. The temperature gradient is zero at any point and the temperature field is time and space independent.

## Thermal non-equilibrium

In a system that contains internal heat sources or which is in contact with external heat sources, there is thermal heat transfer; such a system is in a state of non-equilibrium.

## Heat transfer

Heat transfer, also called thermal exchange, can be achieved by:

• Thermal conduction :

In this type of thermal exchange, without transport of matter, the heat transfer is determined by the existence of a temperature gradient. The heat flux is oriented along this gradient. Only this type of heat transfer is possible in solid bodies.

• Thermal convection :

The thermal convection phenomenon presupposes heat transfer on the surface that separates a solid body from a fluid, or inside a mixture of two fluids. A macroscopic transport of matter is associated with heat transfer by thermal convection.

• Thermal radiation :

A heated body emits energy through electromagnetic radiation. One of the particularities of this phenomenoncalled “thermal radiation” is the possibility of heat propagation in a vacuum.

## Different thermal states

The non-equilibrium states can be classified as follows:

• Steady thermal state :

When the temperature at different points of the system is time independent, the thermal state is “steady” (or stationary). The non-equilibrium state in this case, in the sense of temperature non-uniformity in the volume of the system, is due to internal heat sources. In a thermal steady state, the power generated by the internal sources is equal to the heat flux through the external surface of the system.

• Transient thermal state :

The transient thermal state corresponds to the evolution of a system from an initial steady or equilibrium state towards another steady or equilibrium state, caused, for example, by a change at the initial moment in the power of the heat sources. The temperature field is time dependent; it depends on the initial temperature field and on the new value of the power of the sources. The time variation of the temperature decreases during the transient state.

• Variable thermal state :

In a variable thermal state, the value of the power of the heat sources is time dependent; as a result, the temperature field is time and space dependent.

Transient states must not be confused with variable states; in variable states the value of the power of the heat sources varies with time.