Hi, As part of an experiment I am doing I have a small uniform circular disc that is submerged in 20ml of a liquid and is spinning at 2000rpm for 60 seconds. The disc is 1mm thick and 40mm in diameter. I am trying to see what effect the spinning disc has on the growth of cells that are in the liquid but I am worried that the rotation of the disc at this speed for this length of time might be causing the liquid to heat up a couple of degrees, compromising the accuracy of my results. Is there any way that I can calculate the amount of heat energy dissipated into the liquid due to the rotation of the disc? To make it simpler, it can be assumed that the liquid has the same properties as water (density, viscosity, specific heat capacity etc.). Any help would be hugely appreciated, I have made a stab at it but am unsure about the method. Thanks very much! Michael
There's no substitute for experimenting with this. The temperature rise will depend upon a lot of factors - like the thermal capacity of the container and disc. Best to measure it (perhaps without the cells) for various periods of time and with different external conditions. It would be a couple of hours well spent, I reckon and would test you equipment at the same time.
You can always bound the answer by assuming that all the heat generated stays in the fluid. To analyze this properly, you need to more precise and specific about the geometry of the cell and the disc. Chet
To be honest I only really need a very rough estimate, a ballpark figure, of how much the liquid would heat up. If it is assumed as Chet says that all of the heat stays in the fluid does anybody know of any equation or correlation I could use to get an idea? I was thinking there might be a way to convert the power of the motor (J/s) into energy dissipated or something. Thanks.
OK. Ball park figure. It takes 4.2J or raise the temperature of 1gm of water by 1 degreeC. 1J is 1 Watt for 1 second. Energy in = mass X temperature rise X 4.2 When Mass is in grammes (same as cc when it's water), energy is in Joules and temperature rise is in C Putting it the way round you want it: Temp rise = Energy in/ (4.2 times mass) That should be enough and will be the most pessimistic answer. Some heat will go elsewhere. Edit: I just thought - you don't know the Energy directly. Take the power of the motor (or the Volts times rated current) times the time in seconds. If you don't know the power of the motor then there is a big hole in the required knowledge, I think. You need to do some investigating (look on the side of the motor / measure the current when it's running / etc etc)
Yes. What you are asking for can be done by means of an analysis of the fluid mechanics and the viscous heating. But to do it, as I said earlier, we need to have a better picture of the details of the geometry: Chamber geometry and disk geometry. I assume that the geometry is axisymmetric. What does the cross section look like. We need to know the clearances. Once we see the geometry, we may be able to make some decent simplifying approximations to the kinematics of the flow and get the rate of viscous heat generation. If you're unable to reveal the geometry, I understand. Chet