Heat transfer principles in engineering

Introduction

“… It’s very cold today!!” “And windy too !!” or “… I like cold beer, put it in the freezer for a while so that it cools down three or four degrees …” or “… Our production process needs the mixture to warm up to X°C in 45 minutes and to be kept at that temperature for 1 hour… “

We have all heard and said expressions like these many times. They are part of our daily and professional lives. All of them have concepts such as heat, temperature and degrees in common, which we consider to be well known but about which we can occasionally be confused.

Let’s try to clear them up! And, what is more important, check how their application can answer and resolve the previous expressions.

Heat and temperature

Heat and temperature are different concepts, although related. Heat is the total energy of molecular motion in a substance, while temperature is a measure of its average molecular energy.

Heat depends on the speed of the particles, their number, size and type. Temperature does not depend on the size, number or type.

For example, the temperature of a small glass of hot water will be higher than the temperature of an ocean, but the ocean has more heat because it has more water – more particles – and therefore more total thermal energy.

There are also differences in the types of study of the processes that need to be developed. Beginning with the sciences involved:

The transfer of energy – heat – always goes from the higher temperature medium (with a higher measurement) to the lower temperature, and stops when the two media have the same temperature and reach therefore a state of thermal equilibrium.

Thermodynamics is the science that deals with the amount of heat transfer from one initial equilibrium state to another, and makes no reference or indication to the duration of the process.

A thermodynamic analysis simply tells us how much heat must be transferred to make a change from a specific state of equilibrium to another, to satisfy the principle of conservation of energy.

Although it establishes the necessary basic parameters and a framework for action, in practice it is not enough.

It tells us how much heat to dissipate to cool our beer to get the temperature we want, but does not give us any guidance on the time to do so and, of course, in our production process problem, we cannot establish any solution.

Heat transfer

What we are really interested in is the rate of heat transfer. The determination of the heat transfer rates to or from a system and, therefore, the heating or cooling times and temperature variation is the subject of the science of heat transfer.

Heat transfer helps us resolve the issues raised at the beginning of this text and plays a decisive role in the design of virtually all the equipment and devices that surround us: our computers and televisions must consider heat transfer rates so they cool and do not overheat, affecting their operation; appliances such as cookers, dryers and fridges have to ensure the heating and cooling properties for which they will be sold.

When building our homes, a heat transfer study is carried out, based on which the thickness of the thermal insulation or the heating system is determined.

In the industrial sector, equipment such as heat exchangers, boilers, furnaces, condensers, batteries, heaters, fridges and solar panels are mainly designed on the basis of heat transfer analysis.

More sophisticated equipment such as cars and planes require these studies to prevent engines or cabins from overheating.

Heat transfer processes not only increase, decrease or maintain the temperatures of the affected bodies, they can also produce phase changes, such as melting ice or boiling water.

In engineering, heat transfer processes are often designed to take advantage of these phenomena. Space capsules that return to the Earth’s atmosphere at very high speeds are equipped with a thermal shield which is melted in a controlled manner in a process called ablation to prevent overheating inside the capsule.

Most of the heat produced by friction with the atmosphere is used to melt the heat shield and not to increase the temperature of the capsule.

The transfer of heat is therefore the process by which energy is exchanged in the form of heat between different bodies, or between different parts of the same body at different temperatures. This heat can be transferred in three ways: by conduction, convection or radiation. Although these three transfer methods take place many times simultaneously, usually one of the mechanisms predominates over the other two.

Conduction

Conduction is the transfer of heat by direct contact between bodies or through the same body. In conduction, there is no transfer of matter, only energy.

Molecules vibrate or move with greater speed in a region at a higher temperature. When interacting with neighbouring molecules of a lower temperature, they transfer part of their energy, whether within the same body or from another body in contact with the first.

In 1822, the French mathematician Joseph Fourier formulated a precise mathematical expression known today as Fourier’s law of heat conduction.

This law states that the conduction rate or heat transfer through a body per unit cross section is proportional to the temperature gradient that exists in the body:

The proportionality factor, k, is the thermal conductivity of the material and indicates the amount of heat transferred per unit time, temperature and length. A is an area that can change if it depends on the distance (dx), so an appropriate average (Am) should be used.

For a constant normal section, e.g. the walls of a building, Am = A.

Materials such as gold, silver or copper have high thermal conductivities and conduct heat well, while materials such as glass or wood have smaller conductivities and conduct heat very badly.

Therefore, to answer the questions posed at the start of this text, the materials involved, their thermal conductivity and dimensions in the temperatures of the process need to be known well, as the conduction heat transfer takes place through them.

Thus, analysing how to cool our beer from a totally scientific point, we need to know the properties of the aluminium alloy of the can and its thickness, as the beer transfers heat to the can via conduction.

Convection

Convection transfers heat via the interchange of hot and cold molecules. It occurs when a surface at a certain temperature is in contact with a fluid moving at a different temperature.

It was Newton’s Law of Cooling which indicated the form of the transfer via the equation; thus defining the heat transmitted from the surface of a solid to a fluid in motion:

where

• Ts is the body (solid) surface temperature.
• T is the fluid temperature.
• h is the coefficient of heat transfer by convection.
• A surface in contact with the fluid

Two main types can be considered depending on the source of the fluid motion:

• Natural convection, in which the fluid motion is entirely because of differences in the density of the fluid temperature due to the variation between two points.

• Forced convection where the fluid movement is due to some external factor. The transfer of heat is better with forced convection, since the movement – the speed – is much higher, as there is support for that external factor (e.g. pump, fan, wind or stirrer) in addition to the density difference.

The temperature of our body is 36.5°C and the surrounding air is generally lower, so that a certain amount of heat is constantly being transferred from our body to the ambient air.

When the transfer occurs quickly, because the two temperatures are quite different, we feel cold. This energy transmitted from our body to the ambient air is by natural convection.

And obviously, if it is very windy, there is more transfer and a greater feeling of cold, since the convection is forced.

The coefficient of heat transfer by convection, h in formula (2), depends mainly on the physical and thermodynamic properties of the fluid (e.g. density, specific heat capacity and viscosity) at its temperature when the heat transfer is evaluated as well as its speed at that time.

To resolve our questions, whether routine or professional, both the fluid properties in our processes as well as their state or speed in that process need to be known.

Radiation

Radiation is heat transfer via electromagnetic waves. It could be termed as molecular transport, as energy is produced by changes in the electronic configurations of constituent molecules or atoms and transported by electromagnetic waves or photons.

There is no direct contact between the two media and the intermediary or interface does not participate in the exchange functions; in most cases this is air, although there is also heat transfer in a vacuum.

The heat received by the Earth from the Sun is transmitted by radiation through empty space. The heat felt in front of a campfire is also from radiation.

In 1900, the German physicist Max Planck used the quantum theory and the mathematical formalism of statistical mechanics to formulate the fundamental law of radiation.

The mathematical expression of this law relates the intensity of the radiant energy emitted by a body at a certain wavelength with the temperature of the body.

For each temperature and each wavelength there is a maximum radiant energy. Only an ideal body – a black body – emits radiation exactly according to Planck’s law. Real bodies emit at a slightly lower intensity.

The contribution of all wavelengths to the radiant energy emitted is called the body’s emitting power, and corresponds to the amount of energy emitted per unit area of the body and unit time.

From Planck’s law, two Austrian physicists, Joseph Stefan and Ludwig Boltzmann, discovered in 1879 and 1884, respectively, that the emitting power of a surface is proportional to the fourth power of its absolute temperature.

This proportionality factor is called the Stefan-Boltzmann constant in their honour:

where

• Ts, is the temperature of the body surface
• ε, is the coefficient of emissivity, which is property of the material related to its thermal radiation capacity with that of the ideal black body.
• σ, is the Stefan-Boltzmann constant, = 5.67 x 10-8 W/m2 K4
• A, is the emission surface

If we consider that all substances emit radiant energy only by having a temperature above absolute zero, the formula (3) becomes

Where F_1-2 is a module that weights the geometric relationship of the two bodies and their emissivity coefficients.

In the production process referred to at the beginning of this text, we have described all the heat transfer processes involved.

The heat is mainly transmitted by convection in the exchangers, reactors and batteries of the facilities between the heat transfer fluids (thermal fluid, steam and hot water) and the fluids contained in the equipment.

The heat is produced from the fuel in a boiler with the transfer mainly by radiation in its combustion chamber and by convection in the coils or smoke pipes.

Finally, in the calculation to avoid losses through the pipes or equipment, the properties and thickness of the thermal insulation must be considered, as the heat transfer between the metal wall of the tubes or exchangers and our insulation is via conduction.

So far a quick overview of heat transfer processes. The large number of applications and their complexity and diversity mean that the four formulas mentioned in this document are derived in their hundreds, to be able to consider each particularity and allow for each specific application to have specific and appropriate design criteria.

The document Heat Transfer Form includes the most important.