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Introduction to Thermal Engineering

This is an engineering introduction to thermal systems. It covers the basic principles of thermal transfer and explains the terminology and performance graphs used on this site.

What is heat?

At the atomic level, heat is nothing more than the vibration of the atoms that make up the matter around us. Molecules that are vibrating excite other molecules through the emission of photons. This transfer of energy has the effect of increasing the vibration of the receiving molecule, and decreasing the vibration of the emitting molecule. These interactions are very complex at the atomic level, but at the bulk level, which averages the effects of many molecules working simultaneously, the heat transfer situation becomes much simpler. At the bulk level, there are just three primary forms of heat transfer: conduction, convection, and radiation. Lytron’s products are simpler still, relying primarily on just conduction and convection.

When considering the bulk heat transfer properties of materials, it is important to understand an interesting feature of heat transfer: Heat always moves from the higher temperature body to the lower temperature body. The following diagram compares the similarity between the electrical world and the thermal world in this regard:

Electrical Thermal Diagram

Just as electrical current flows from a higher voltage source to a lower voltage sink, heat flows from a higher temperature source to a lower temperature sink. The ability of this heat, “Q”, to flow is directly proportional to the temperature difference between the source and the sink, and inversely proportional to the thermal resistance, “θ”, between them. This is analogous to the electrical world where current flow, “I”, is impeded by electrical resistance, “R”.

Every object in the universe is subject to these effects. Higher temperature bodies are constantly sending heat to lower temperature bodies, to raise their temperature. Consequently it is very difficult to make accurate heat transfer measurements, because unwanted thermal effects are attempting to participate in every experiment. While these effects can be mitigated through careful planning, they can never be eliminated. Heat transfer measurement is an exacting science.

What is conduction?

If the two ends of a solid bar are maintained at different temperatures, heat will flow from the higher temperature end of the bar to the lower temperature end. The rate at which the heat flows is directly proportional to the temperature difference between the ends of the bar, the cross-sectional area of the bar, and a property of the bar called the “thermal conductivity”. If the temperature difference is increased, or the cross-sectional area of the bar is increased, or if a material with greater thermal conductivity is selected, the heat flow rate will increase. On the other hand, heat flow is inversely proportional to the length of the rod. If the rod is twice as long, the heat flow will be cut in half. Sometimes engineers speak of the ‘temperature gradient’ in a conducting material. This is the temperature difference divided by the length. For example, if the temperature difference is doubled, but the length is doubled as well, the temperature gradient would stay the same, and the heat flow will remain unchanged. Heat flow is directly proportional to the temperature gradient.

Below is the thermal conductivity equation, where Q is the rate of heat flow, “k” is the thermal conductivity of the material, “l ” is the length of the rod, “A” is the cross-sectional area, and “ΔT” is the temperature difference between the hot and the cold ends of the rod.

Rod Diagram

This equation makes clear several principles that are used in Lytron’s cold plates and heat exchangers. If we define the thermal resistance “θ” as (l /kA), this equation looks like the thermal resistance equation defined earlier:

Equation

In this example, anything we can do to increase “k” or “A”, while decreasing the length “l/kA” that the heat has to travel will reduce the thermal resistance. The common thread in Lytron’s product offerings is that they have been designed for reduced thermal resistance.

What is convection?

A typical cold plate or heat exchanger application is more complicated than the solid bar example described previously. In addition to the transfer of heat by thermal conductivity through the solid materials of a cold plate or heat exchanger, there may be one or more fluids that bring the heat to the hot side, and/or which take the heat away from the cold side through the process of convection.

Convection is a very efficient means of heat transfer. Unlike conduction, where the molecules are stationary, in convection, the molecules are moving. Because the molecules are moving, the rate of heat transfer can be considerably higher than in conduction. The equation for heat transfer by convection is:

Equation1

where “A” is the area where the solid surface and the fluid interact, Tsolid and Tfluid are the temperatures of the solid surface and the fluid respectively, and “h” is the film coefficient. The film coefficient varies widely depending on the properties of the fluid and how fast it is moving. The table below shows typical values of the film coefficient¹:

Table showing the typical values of the film coefficient

Like the conduction equation, the convection equation can be rewritten in terms of thermal resistance:

Equation2

Heat exchanger performance

The heat transfer performance of a heat exchanger can now be characterized by including the convective thermal resistance terms in addition to the conductive thermal resistance term described earlier. In summary there are three components to the overall thermal resistance of a heat exchanger:

Electrical Thermal Diagram2

  1. A convection component, “θ1”, which describes the transfer of heat from a heated fluid into the surface of the heat exchanger;
  2. A conduction component,“θ2”, which describes the transfer of heat through the solid materials of the heat exchanger;
  3. And, a second convection component, “θ3”, which describes the flow of heat out of the heat exchanger into a cooling fluid.

Each of these separate thermal resistance components can be summed together to generate a global thermal resistance for the heat exchanger and the two fluids, as shown:

Equation3

By comparison, a cold plate typically has a single fluid (for cooling). Therefore a cold plate would have just two components: a thermal conductivity component and a single convective component.

If we generically reduce any cold plate or heat exchanger application to a black box that transmits heat from a hot side to a cold side, then anything we can do to decrease the global thermal resistance² will allow one of two things to happen:

  1. If the temperature difference is fixed, more heat will flow, or,
  2. If the heat flow is fixed, the temperature difference will reduce.

For example, if active heat-producing components are mounted onto a cold plate with a low thermal resistance, the temperature of the components will be much closer to the temperature of the cooling fluid, than had they been mounted onto a cold plate with a large thermal resistance. The lower the global thermal resistance, the better the performance.

Air-side versus liquid-side limits

The graph below depicts the thermal capacity performance of our 6340 copper heat exchanger. The 4 gpm trace depicts a steep rise in performance as the air flow increases from zero, and then a plateau at larger air velocities. This behavior is typical of heat exchangers.

To understand what is causing this behavior, it is useful to revisit the global thermal resistance equation which we derived earlier:

Equation3

We can rewrite this as:

Equation4

where the first term is the thermal resistance from the heated liquid, the second term is the thermal resistance due to thermal conductivity through the heat exchanger, and the third term is the thermal resistance to move the heat out of the heat exchanger into the air.

Air flow graphIn practice, the second term tends to be much smaller than the other two terms, so we can simplify this equation as:

Equation5

At very low air flow rates, the slope of the trace is very steep. In this regime, the second term is much larger than the first term. When this happens we say that the heat exchanger is “air-side limited”. In this regime, different levels of liquid flow make little difference to performance. When this happens, the only way to improve the performance of the heat exchanger is to increase the air flow.

At very high air flow rates, the second term approaches zero. When this happens, we say that the performance of the heat exchanger is “liquid-side limited”. In other words, further increases in the air flow make no significant improvement because the second term is already so small. When a heat exchanger is liquid-side limited, the only way to increase the performance is to increase the liquid flow.

The trade off between these two terms is what causes the characteristic shape of our heat exchanger curves. When the two terms are roughly equal in magnitude, this is when the heat exchanger is balanced. A balanced heat exchanger makes optimum use of its materials.

Boundary layers

As a fluid moves past a stationary surface, there will be a velocity gradient of fluid molecules in the fluid stream. The slowest moving molecules will be the ones that are in direct contact with the surface, and which are being slowed down by friction with the surface, while the fastest moving molecules will be the ones that are farther away.

A useful engineering approximation is to assume that there is a thin layer of fluid which is completely stationery along the surface. This thin layer is called a boundary layer. Because the boundary layer is stationary, the heat transfer through this layer is determined using thermal conductivity equations instead of convection equations.

Thermal performance is affected by the thickness of the boundary layers in a heat exchanger. When the fluid velocity increases, the boundary layers become smaller. This has the effect of increasing the film coefficient and thereby reducing the thermal resistance.

The graphs in this catalog

The performance graphs that describe our cold plates in this catalog are based on thermal resistance. The lower the trace on the graph, the better the performance. In contrast, the performance graphs for the heat exchangers in this catalog are based on thermal conductance. In these graphs, the higher the trace, the better the performance. Thermal conductance is the reciprocal of thermal resistance:

Equation6

The reason for this difference in approach in our cold plates and heat exchangers is due to industry conventions. To avoid confusion, look at the units of the Y-axis. If the units are °C/W, then this is thermal resistance and a small number is the better result. If the units are W/°C, then this is thermal capacity and a large number is the better result.

Another thing to know about the graphs in this catalog

The performance data for heat exchangers provided in this catalog are based on the temperature of the fluid when it enters the product. Our Selecting a Heat Exchanger application note, which describes how to size a heat exchanger, is based on the assumption that we already know the desired entrance temperatures of the heated fluid and the cooled fluid. To convert between the entrance and exit temperatures, we can use the heat capacity equation shown below:

Equation7

This equation describes the change in temperature of a fluid that occurs based on the heat being transferred “Q”, the density “ρ” of the fluid, the volumetric flow rate of the fluid “γ”, and the specific heat of the fluid “Cp”. These calculations can be cumbersome to do manually. The four graphs on our Temperature Change Graph page provide a quick way of calculating the results of this equation for four common heat transfer fluids: air, water, oil, and 50% ethylene glycol/water.

Working with Lytron

Fortunately, you do not have to be a heat transfer expert to work with Lytron. Our web site provides convenient sizing programs that will select the correct Lytron product based upon your thermal requirements. We also have applications engineers who are available to work with you if you have special requirements. In addition to our standard products, we also routinely build custom products for qualified original equipment manufacturers. Contact your Lytron sales representative and we will put you in touch with the appropriate Lytron resource.

¹Chapman, Alan J., Fundamentals of Heat Transfer, Macmillan Publishing Company, 1987, p. 14. ²A heat exchanger or cold plate with zero thermal resistance, while physically impossible, would be the ideal heat transfer product. Such a product would provide a thermal short-circuit: heat would flow without the requirement of a temperature gradient.