 In this segment what we're going to do is we're going to do a physical experiment and we're going to investigate the lumped capacitance method. So if you recall from the last segment what we did is we solved a problem where we took a can of pop and we brought it out of a cool refrigerated environment. So it was initially at 1°C and we put it in an environment that was at 19.5°C and we asked the question how long does it take to get to the temperature for this can of pop up to 15°C and we said that we had this can placed on an insulated pad and what we did is we performed the calculation using the lumped capacitance technique and with that we had the following relationship that enables us to determine the temperature as a function of time within our system under the assumption that the temperature within this can is uniform. So we were assuming that there would be no temperature variability within the can as a function of time and so what we're going to do in this little experiment is we're going to investigate that a little bit further and the other thing we had here was the time constant and that had rho the C sub p divided by h a s and h being the convective heat transfer coefficient for the environment that this can was sitting in and that would be T infinity and h. So that was the problem what we're going to do now is we're going to check and see if the assumptions we made were valid and at the conclusion we did say that the bio number should be less than 0.1 but for this experiment bio number was approximately 0.159 so we we do know that we were that violating that restriction on the bio number and consequently we may expect that our experiment may show something along those lines so let's begin and what we have here is a can that has just come out of the refrigerator and it was opened and there was a thermocouple stuck inside of the can on the left hand side we have the temperature distribution as a function of time and then superimposed on that we have the results from an infrared camera viewing the same can sitting on the table and and so there you can see on the left we're at 40 minutes 50 minutes and the IR camera showing us the temperature is going up as well as the thermocouple is showing that which is the plot on the left hand side and there's something interesting going on there there's a bit of a pattern or a wave that comes through and that is indicating that actually the temperature is not uniform throughout the can as we had originally assumed and enabling us to do the lump capacitance techniques so the fact that we get that wave going through the can of of different temperatures suggests that there there is strong spatial variability within the can we can continue running the experiment we go on and on the reason why I was running is we let it go until we got to approximately 15 degrees C and there you can see on the IR it's measuring around 13.5 and that's what the thermocouple was measuring as well so that's 110 minutes actually that's 160 170 180 and the experiment stopped at about 195 minutes and finally there you can see at the end of the experiment the can wasn't quite at 15 degrees C but it was pretty close to that so with that the the next thing that we're going to do we're going to take a look at the data that we collected so this is the raw data that we got from the thermocouple and superimposed on that now that is a lump capacitance model with a convective heat transfer coefficient of 6.4 and there you can see two lines that are indicating where that temperature wave started to come across the pop can and it began at a time of it was approximately 30 minutes and it went all the way up to 110 minutes and and in there that is strong indication that the lump capacitance technique does not apply in that region and consequently that's probably also why it's kind of hard to be able to fit the curve as shown by the difference between the raw data and the red curve which shows the results of the lump capacitance assuming that the convective heat transfer coefficient was 6.4 watts per square meter kelvin what is the cause of that it it's difficult to speculate I think we need further experiments one thing that was interesting I didn't show you in the results here I did do the experiment without opening the can first and in doing that experiment the wave that that we saw going from top to bottom began immediately and and then eventually the can came to a new thermal equilibrium and so that wave started very quickly which makes me wonder if the first 30 minutes of the open can that wave was not prevented by the fact that we had gas coming out of the pop and and so there would be CO2 bubbles rising and causing mixing but again it would require further experimentation to be able to investigate that so what that tells us is the the number that we had with the bio number being a little bit greater than 0.1 is kind of validated by this experiment it shows that the lump capacitance technique is not perfect for this particular application mainly because the object we're looking at is a fluid and we know fluids can have all kinds of convective processes inside of them I usually you'll want to have that inside of a solid so anyways that is an example of the lump capacitance technique being investigated experimentally