Heat transfer from water to oil

[tup]

ok, this is more of a question of theory than actual calculation. Me and my friends did a physics lab on heat transfer vs. surface area of contact. We used water and oil (since oil will float above the water and creating a surface of contact). We heated the water to ~50 degrees C and oil was left at room temperature. We used different sizes of beakers (with ghetto style insulation) to create different areas of contact, and we measured the temperature with a temperature probe that's plugged into the laptop. so basically we have graphs with the temperature of water decreasing while the temperature of the oil increasing.

the problem: the usual equation for heat transfer through conduction has Q (heat transfer), t (time), k (conductivity of barrier), A (area of contact), T (temperature final and initial), and d (thickness of barrier). The problem is with d. since there wasn't an actual barrier in our experiment (it's just water and oil), there wouldn't be a d (d would equal to zero). and if that's true, then the equation won't work.

so my question: what should I do now? is there another equation that fits my purpose?

 

[AlephZero]

It would be hard to make a mathematical model of your experiment. By "hard", I mean the relevant equations are known, but many people are currently doing PhD-level research looking for good ways to solve them!

You are right there is no "barrier" to heat flow between the two liquids. The heat flow is partly by conduction through the liquids, but mostly by convection - i.e. the liquid moves because its density changes with temperature, and it carries the heat with it. The flow patterns in convection can be very complicated. The equations modelling the fluid behaviour are called the Navier-Stokes equations, if you want to look them up on the web.

I think one option would be to change the experiment so you eliminate convection. Then you could use the heat conduction equation to model what happens.

One way to do that would be to have the hottest part of the system at the top and the coldest at the bottom. If you had a movable temperature probe (or several probes) you could measure the temperature gradient through the depths of the liquids and compare it with the conduction equation solution.

 

[tup]

thx so much for the reply

basically, we obtain the rate of temp changes from the data, so according to our hypothesis, the larger the surface area the higher of the rate, right?
but the thing is, one of our trial, the one with the largest beaker, is really screwed up. the rate of that one is actually lower than the 2nd largest beaker, while still larger than the 2 smallst ones; if we ignore that data, the graph of rate vs surface area would be almost a straight line or in other words, in a directly proportional relationship.

my group wants to try the lab with a improved procedure but our phys teacher says we got enough data to finish it up and won't let us do a new one. so any suggestion what we should do?
thx man, pls reply

 

[AlephZero]

If you are not allowed to do any more experients, then you can't do anything very much! (That also happens in real life, when the money runs out).

The obvious possibilities would be

(1) You made a mistake, e.g. wrong "hot" temperature of the water, wrong quantity of liquids, wrong temperature probe calibration, etc.

(2) There is something different about the experimental setup with the largest beaker - e.g. a different amount of heat insulation, the beaker was made from a different material, etc.

Don't get too worried if you can't find the reason. You should get some credit for noticing you had one result that doesn't fit with the others, even if you can't explain it.