The aim of this investigation is to determine the effect of free and forced convection on the distribution of heat in a fluid.

The first experiment was repeated however on this occasion a follower and magnetic stirrer were used, the magnetic stirrer was adjusted so that the follower would rotate at its maximum potential. The length of time measured would be the same as the first experiment as well as the same initial temperature and volume of water.

The second experiment was repeated as described above, but without the follower but leaving the magnetic stirrer functioning as it was before at the same speed.

Diagram

Figure 1. Illustrates lay out of apparatus to determine the effect of free and forced    

               Convection on the distribution of heat in a fluid.

Results

Heat balances

Qw = Theoretical amount of heat required to raise the temperature of water in a beaker

           to its final temperature.

 M = Mass

Cp = Specific heat capacity

ΔT = Changes in temperature

Calculate Cp of water :   Mr of water = 18

                                        Therefore 18g = 1 mol

                                        Therefore 18Kg = 1 Kmol

                                        So Cp of water = 75.36/18 = 4.19 KJ Kg-1K-1

First experiment

Qw = m Cp ΔT = m1CpΔT1 + m2CpΔT2 + m3CpΔT3

                          = 1 x 4.2 x (51-19)   + 0.25 x 4.2 x (30.5 – 19)   + 2.25 x 4.2 x (19.5-19)

                          = 150 KJ

Electrical energy input = 288 KJ

Heat loss = 288 –150.72 = 137.28 KJ

Second experiment

Qw = m Cp ΔT = m1CpΔT1 + m2CpΔT2 + m3CpΔT3

                          = 1 x 4.2 x (36-19)   + 0.25 x 4.2 x (36 – 19)   + 2.25 x 4.2 x (36-19)

                          = 249.9KJ

Electrical energy input = 288 KJ

Heat loss = 288-249.9 = 38.1 KJ

Third experiment

Qw = m Cp ΔT = m1CpΔT1 + m2CpΔT2 + m3CpΔT3

                          = 1 x 4.2 x (51-18)   + 0.25 x 4.2 x (33 – 18)   + 2.25 x 4.2 x (18 - 18)

                          = 153.86 KJ

Electrical energy input = 288 KJ

Heat loss = 288 –153.86 = 134.14 KJ

Results & Discussion

Heat balances suggest that second experiment was much more efficient in not loosing much energy since it contained the magnetic stirrer. The first and third experiments had similar heat losses, which were much higher than that of the second, however the third experiment had slightly less heat loss than the first, since it had generated heat from the motor to compensate some energy loss.

Refer to (Graph 1), it can be seen that thermometer 1 begins as uniform heating but as time increases above 10 minutes then the line starts to develop into a curve indicating heat loss.

The first and third experiments were similar (refer to tables 1 & 3), thermometer 3 remained approximately constant. This suggests that a very small amount or no heat reached the lower region of the beaker. Regions containing thermometers 1 and 2 had general increases in temperature. Thermometer 2 took slightly longer to heat even though it was much nearer to the heated coil, this may be due to density of the water becoming low when water is warmed, so as the warm water rises, the cold water from below which has a higher density, replaces the region of empty space.

In the second experiment (refer to graph 2), there was a regular distribution of temperature, this was because the magnetic follower rotated and increased the velocity within the water, evenly spreading the heat.

Increasing the scale of the beaker would have decreased the boundary of error for measuring the weight of water in each of the regions.

Weight          +/-    0.25 (Kg)

Temperature  +/-   0.1 ( °C )

Conclusions

Forced convection increases the velocity within the water, evenly distributing the heat through out the volume of water, however it takes a lot longer to warm water at specific regions using forced convection compared to free convection.

In free convection the area further below the heated coil gets very little or no heat contributed by the coil, that is why there is a greater loss of heat in comparison to forced convection.