Introduction

Whilst conduction is of great importance in the transmission of thermal energy through continuous media, particularly solid media, heat transfer in industrial equipment (heat exchangers, evaporators, etc.) very often involves exchanges between fluids (gas or liquid) and solid walls (Leontiev, 1985). Indeed, in most situations, we heat a liquid or gas by putting it in contact with a hot surface, or cool a fluid through contact with a cold surface. To resolve such problems, conduction equations are no longer applicable, given that there is a large difference: in convection, the fluid concerned is in motion.

In this document we will therefore be focusing on convective heat transfer between solids and fluids in motion.

Generally, the motion of the fluid is one of two types:

• – It is induced by the temperature gradients existing in the system, without the intervention of any external device (pump, compressor or other). In this case we speak of natural or free convection.
• – It is created by an external device that sets the fluid in motion (pump, fan, etc.). In this case we speak of forced convection.

Yet whether the motion is natural or forced, we are often faced with a problem where the equations describing the fluid dynamics are coupled with those reflecting the heat balance. It will therefore be necessary to simultaneously solve the equations reflecting the energy and momentum balances (Navier-Stokes equation: see Bird, Stewart and Lightfoot, 1975; Kays and Crawford, 1993; Giovannini and Bédat, 2012). The problem is therefore far from straightforward and this difficulty has driven various researchers to propose approximation methods leading to practical results.

Since the approximation proposed by Boussinesq (1901) to solve the natural convection equations, several analyses have been developed to provide answers to classic problems of thermal engineering, such as the transfer of heat to a fluid in forced circulation within a tube (the Graetz problem), the heat transfer between a fluid and a flat plate (the Blasius problem), or the heat transfer generated by Archimedes forces in natural convection (the Boussinesq problem).

These different analyses lead to solutions that may be implemented using numerical tools (Landau and Lifshitz 1989; Kays and Crawford 1993; Giovannini and Bédat, 2012). This is done using certain approximations, notably regarding the incompressibility of Newtonian fluids in forced convection. However, the validity of these approximations is sometimes disputed (Boussinesq approximation: see Lagrée, 2015), and their real justification is, above all, related to the simplifications necessary in order to soften the "rebel" equations, as Boussinesq himself calls them:

“Thanks to the simplifications then obtained, the question, still very difficult and almost always rebellious to integration, is no longer unaffordable.” (Boussinesq, 1901)

The results of the analytical developments are available in various works (Knudsen and Katz, 1958; Bird, Stewart and Lightfoot, 1975; Landau and Lifshitz, 1989; Kays and Crawford, 1993; Giovannini and Bédat, 2012). Yet, the complexity of the developments and the tools to be implemented for their application makes them unsuited to our perspective, which is to provide fast orders of magnitude for engineering calculations. Thus, where the analytical demonstration allows, and particularly to give an example of the complexity that might be encountered, the equations used to determine the transfer coefficient are established; this is the case for forced convection inside a pipe in laminar flow (see Chapter 2).

In the opposite case, which represents the majority of situations, dimensional analysis is applied to determine the general expressions of the transfer coefficients in forced and natural convections, then the correlations available for calculating these coefficients are presented.

It is for this reason that in Chapter 1 of this volume, we propose to proceed with a phenomenological analysis of convection, based on a representation of all the complexities by a convection heat transfer coefficient, h, such that the heat flux transferred by convection is given by (see Volume 1, Chapter 2):

where:

A is the transfer area

h is the convection heat transfer coefficient, also known as the convective heat transfer coefficient

Δθ = θ₂ – θ₁ is the heat transfer potential difference. This is the temperature gradient between the fluid and the solid being considered.

In this way, all the analytical complexity of the problem is grouped together in the coefficient h, for which dimensional analysis reveals the expression structure.

Chapters 2 and 3 present the correlations which make it possible to calculate the coefficient h for a fluid circulating in forced convection inside cylindrical pipes or pipes of other shapes. Forced convection on the outside of pipes or around objects is dealt with in Chapter 4.

Yet, while forced convection is the most common case in industrial installations where the fluid is set in motion by means of fans, pumps or compressors, the fact remains that several natural convection situations are also encountered: central-heating radiators, cold rooms, electronic heat sinks, etc. For this reason, Chapter 5 is dedicated to this type of convection.

Moreover, for specific circuits operating at very high temperatures (around 700°C), the usual heat-transfer fluids are no longer suitable. This is the case for concentrated solar power plants or fast neutron nuclear reactors where liquid metals, nanofluids and, sometimes, molten salts are used to ensure the transfer of the energy produced. Of course, the correlations established for “ordinary” fluids are no longer valid. Correlations specific to this type of situation are developed in Chapter 6, whilst the physical data required for the calculations are grouped together in Appendix 1 (database).