A customer recently emailed in a Thermal simulation study to our Technical Support help line with a question about radiation.
Prompted by this I delved into a simple test study to do some trials and found a number of important facts that I had not previously realised - which I will pass on to you!
Firstly radiation becomes increasingly important to heat transfer problems when the temperature difference between hot and cold bodies is large. At small differentials, radiation can often be ignored as heat transfer will be dominated by conduction and convection. This is because of the Stefan-Boltzmann constant being tiny and dominating the radiation equation until the temp differential is substantial.
Secondly, and this was one of my two main discoveries, a steady state Thermal study assumes all bodies are at absolute zero as a starting point. In many studies this is not self-evident as the bodies will receive heat to warm it up from one of the following ...
- A heat source or temperature on the body itself
- An ambient condition specified in a convection load
- An ambient condition specified in an open system radiation load
- Conduction of heat from another body that is being warmed by one of the above
However, if a body is not in contact with any means of heating and does not have one of the above associated with it, SOLIDWORKS assumes that it is at absolute zero - -273 deg C or 0 Kelvin. I proved this with a simple test as shown below. I have modelled a bulb (a sphere) with a surrounding (but not contacting) hollow hemisphere similar to a reflector. The boundary conditions are ...
- 25W of heat applied to the sphere.
- 15W/m2.K convection applied to the bulb. I did this as, in the absence of any other cooling, the 25W would cause an infinite temperature on the bulb.
The result below shows that the bulb is in thermal equilibrium at about 900 deg C but that the reflector is at absolute zero.
To overcome this I need to apply some heat or some ambient condition to the reflector in a steady state study. (NB I could also use an 'Initial Temperature' if I set up a Transient study).
I then applied radiation to the bulb using the 'Surface to Surface' option and the 'Open system' selected with ambient set to 25 deg C. This means that heat can radiate to other surfaces and out of the study from the bulb. I used an emissivity of 0.9 - which is quite high so I expected to see a large drop in the bulb temperature. The results shows that this was achieved with the bulb temperature dropping to a relatively cool 380 deg C. However, the reflector is still at absolute zero. It has not received any of the radiation coming from the bulb!!! Why is this?
To get the radiation to transfer from one body to another requires a second radiation condition to be defined - this time on the reflector. This was the second important fact I deduced - and critically important too!
Therefore I applied a radiation condition to the reflector with 'Surface to Surface' selected and an ambient of 25 deg C. I used an emissivity of 0.25 which is indicative of a shiny reflecting surface. This allows the reflector to receive the radiated heat coming from the bulb as well as radiate itself. The temperature of the reflector is now at 41 deg C. This is achieved by warming the reflector to the ambient of 25 deg C plus an extra 16 deg C received from the bulb via radiation.
I am glad I checked this out as I had not previously recognised the absolute zero starting condition and the need to specify radiation on both emitting and receiving bodies.
By Andy Fulcher
Solid Solutions Management Ltd