Tag Archives: Conduction

Temperature change may not represent heat transfer; heat flux does.

Figure 1 (go to simulation)
There has been some confusion lately about the heat transfer representations in Energy2D simulations. By default, Energy2D shows the temperature distribution and uses the change of the distribution to visualize heat flow. This is all good if we have only one type of medium or material. But in reality, different materials have different thermal conductivities and different volumetric heat capacities (i.e., the ability of a given volume of a substance to store thermal energy when the temperature increases by one degree; the volumetric heat capacity is in fact the specific heat multiplied by the density).

Figure 2 (go to simulation)
According to the Heat Equation, the change of temperature is affected by the thermal diffusivity, which is the thermal conductivity divided by the volumetric heat capacity (now that I have written the terminology down, I can see why these terms are so confusing). In general, a higher thermal conductivity and a lower volumetric heat capacity will both result in faster temperature change.

To illustrate my points, Figure 1 shows a comparison of temperature changes in two materials. The pieces that have the same texture are made of the same material. The upper ones have a lower thermal conductivity but a higher thermal diffusivity. The lower ones have a higher thermal conductivity but a lower thermal diffusivity. In both upper and lower setups, the piece on the left side maintains a higher temperature to provide the heat source. Everything else starts with a low temperature initially. The entire container is completely insulated -- no heat in, no heat out. Two thermometers are placed just at the right ends of the middle rods. Their results show that the temperature rises more quickly in the upper setup (Figure 1) -- because it has a higher diffusivity.

The fact that something diffuses faster doesn't mean it diffuses more. In order to see that, we can place two heat flux sensors somewhere in the rods to capture the heat flows. Figure 2 shows the results from the heat flux sensors. Obviously, there is a lot more heat flow in the lower setup in the same time period.

Figure 3 (go to simulation)
The conclusion is that it is the heat flux, not the temperature change, that ultimately measures heat transfer. If you want to know how fast heat transfer occurs, the thermal conductivity is a good measure. However, if you want to know how fast temperature changes, the thermal diffusivity is a good measure. This may be also important to remember for those who use infrared cameras: Infrared cameras only measure temperature distribution, so what we really see from infrared images is actually thermal diffusion and thermal diffusion alone could be deceiving.

Figure 4 (go to simulation)
To make this even more fun (or confusing), let's replace the pieces on the right of the container with two pieces that are made of the same material that has a volumetric heat capacity between those of the other upper and lower ones. You wouldn't think this change would affect the results, at least not qualitatively. But the truth is that, the temperature in the lower setup in this case rises more quickly than the temperature in the upper setup -- exactly opposite to the case shown in Figure 1! The surprising result indicates how unreliable temperature change may be as an indicator of heat transfer. In this case, the temperature field of the middle rod is affected by what it is connected with. If we look at the results from the heat flux sensors (Figure 4), the heat flux that goes through the rod is much higher in the lower setup. This once again shows that heat flux is a more reliable measure of heat transfer.

In Energy2D, we have implemented an Energy Field view to supplement the Temperature Field view to remedy this problem.

Comparing convection and conduction using Energy2D

The following are two Energy2D simulations that compare convection and conduction, which should run within this page if you have installed Java and Java applets are enabled with your browser. The first one shows the case of natural convection. The second one shows the case of forced convection.

Instruction: Click inside a simulation window. Press 'R' to  start or stop, 'T' to reset, 'L' to reload the initial configurations, and 'G' to open or close a graph. The virtual temperature sensors can be moved around, though most other pieces are locked to their positions. Right-click on the windows for more actions.

Natural convection (driven by thermal buoyancy):

Forced convection (driven by airflow):

A Von Kármán vortex street.
The following screenshot shows a typical Von Kármán vortex street produced from the second simulation. Energy2D is also capable of producing other interesting fluid patterns such as mushroom cloudsBernard's Cell, and the Kelvin–Helmholtz instability.

More generally, Energy2D is a Java application that allows users to create interactive, real-time simulations of heat and mass flow. A simulation you create can be easily placed on the Internet just like what you saw above.

On a separate note, below are two results for conduction simulations using Energy2D that illustrate the circuit analogy: Ohm's Law is the electrical analogy of Fourier's Law of Heat Conduction. It is interesting to note that Ohm actually drew considerable inspiration from Fourier's work on heat conduction in the theoretical explanation of his work (see Ohm's Law in Wikipedia). Ironically, today's students seem to be more familiar with Ohm's Law than Fourier's Law. So the circuit analogy is used in textbooks to help students understand heat conduction.

The analogy to a parallel circuit.
The analogy to a series circuit.

Why do metals feel colder? An infrared view

Metals feel colder because they conduct heat faster, not because they are really "colder." This is often a misconception from students. A very simple IR experiment may dispel this misconception by visualizing what is going on when you touch a piece of metal and a piece of paper.

Lay a piece of aluminum on a foamcore board. Then cover it up with a piece of paper. Put one hand on top of the part of paper above the metal and the other on top of a part of paper that is not above the metal. Have your partner look at the hands on the plate through an IR camera. The reason that we want to cover the metal up with a piece of paper is because we want to make sure that the difference of temperature we observe has nothing to do with the difference of emissivity--the ability of a substance to emit infrared light--between metal and the base material.

The first IR image shows the initial temperature distribution when the hands were on. The second one shows the temperature distribution after two minutes. It clearly shows that the hand above the metal strip is losing more thermal energy than the hand above paper.

This simple experiment, once again, demonstrates the transformative power of IR imaging. IR imaging experiments such as this are much easier to do than conventional experiments. They provide more intuitive, richer results in a snap. Imagine how many other experiments out there that can be transformed by this new instrument!