Rigorous definition of convective heat transfer

Question

Through all textbooks I've come across, convective heat transfer is traditionally defined along the line of "[...] a process by which heat is transferred by movement of a heated fluid such as air or water". It is my intuition that this is incomplete, or is not rigorous since heat can be transported by bulk movement of mass in any physical state.

Consider the following thought experiment. A hot block, denoted A, and a cold block, denoted B, are separated in space such that there is no traditionally defined conductive heat transfer. A small cold block, perhaps containing fluid and made of metal, is placed atop of block A and heats up. This small block, now hot, is then placed atop of the cold block, which heats up.

This to me appears as some form of convective heat transfer per the traditional definition, no different than the phenomena with liquids or gases, where matter first absorbs heat through conduction then is moved across space, displacing the heat along with itself. But I fail to find such discussion in any textbook I come across.

Is the heat transfer process described in the presented thought experiment an example of convection?

Answer 1

As usual with definitions, their value is not in their truth but in their usefulness. It would be possible to define convection as any heat exchange by bulk movement of mass in any physical state. However, such definition is less valuable than the one you may find in the Convection Wikipedia page:

Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow.

The critical part of this definition is the word spontaneously. Its greater usefulness is that it limits the phenomenon of convective transport to cases where it only pertains to the physical system of interest without introducing external mechanisms. Such a limitation allows, for example, the investigation of the conditions triggering convective transport as a consequence of a temperature gradient.

Nevertheless, it is also possible to use a broader definition. In particular, in the cases where the system contains a mechanism to force or increase internal fluid fluxes, like in the case of the presence of a fan.

A final word of caution about the possible confusion between different mechanisms. In the example of the two blocks at different temperatures, A and B, and a small block used to transfer energy, the way it is stated does not correspond to convection in any possible definition. It looks like a double conduction-transfer mechanism. Once from the hot block to the cold small block and a second from the heated small block to block B. A consistent example of convection by material transport would be the case of blocks A and B at the same temperature, and a small block separated from block A and transferred to become part of block B. This would be a transfer of energy only due to a material displacement.

Answer 2

Your thought experiment is a useful illustration on what happens at the micro-level in convection during heat transfer at an interface from a solid to a fluid. The immediate transfer mechanism is conduction through lattice vibrations (solid) to molecular collisions (fluid). After this heat transfer, the subsequently hotter or colder fluid packet moves away from its previous contact point with the solid surface either of its own accord due to a density change relative to the remaining bulk fluid (free or natural convection) or due to motion of the entire bulk fluid surrounding it (forced convection).

Answer 3

Below I give a definition of conduction to make it clear why it is not convection that just by itself is a macroscopic matter transport conserves entropy.

Heat conduction can be defined unambiguously as follows: heat conduction is a form of irreversible entropy transport of the amount of $S$ in which the infinitesimal increase of entropy $\delta S$ is $$\delta S =-S\frac{\delta T}{T},$$ where $T$ is the absolute temperature around which the transport process takes place over an infinitesimal temperature drop $\delta T$. In other words the transport of entropy $S$ starts at temperature $T$ and at temperature $T+\delta T$ the entropy is now $S+\delta S$.

The conceptually significant consequence of this constitutive definition, constitutive because it defines a material's answer to a specific form excitation, is that $T\delta S= - S\delta T$ and therefore $\delta (TS)=0$ or $TS=const$ across the length of the conductor, which is a form of energy conservation. This particular form of thermal energy conservation is the unfortunate historical reason for introducing "heat" instead of "entropy" as a primary concept in almost all undergraduate courses.