find the convection heat transfer coefficient in a heat exchanger

Forced and free convection Laboratory
Introduction
Convection, along with conduction and radiation is one of the three ways in which heat is transferred. In convection, heat can be exchanged from one fluid to another. In this experiment, a heated plate is in contact with air inside a rectangular cross section duct. The air is heated by conduction from the heated plate. The density of the air decreases as it is heated and this makes the warm air rise. Colder air, which in turn is less dense, then replaces the warmer air, which has risen. The plate then heats this colder air, which will eventually rise to be replaced by colder less dense air. This is known as free convection. However in forced convection, the flow of air is not due to small currents set up by natural convection. Forced convection is due to a large interfering flow of air such as a fan.
Aims and objectives
The aim of this laboratory experiment it to find the convection heat transfer coefficient of a flow of air that is flowing over a heated plate at a known speed. The convection heat transfer coefficient can be determined using the values of temperatures recorded, the area of the heated plate and finally the energy converted into heat.
The main objective of this laboratory is to prove the theory of forced convection is true. This can be completed, by using the boundary conditions at each value of Airflow, i.e. if the system is in laminar or turbulent flow. Also needed to prove the theory of forced convections is the theoretical equation to determine the Reynolds number. From the Reynolds number we can work out the relevant Prandtl number or look up the relevant Prandtl number from properties tables. Also we can determine, from the Reynolds number, if the system is in Laminar or turbulent flow. For our system any figure above 500000 would dictate a turbulent flow, while a figure below this would mean a laminar flow. Once both the Reynolds number and Prandtl numbers have been determined we can work out the Nusselt number using the relevant laminar or turbulent flow equations. From these numbers we can determine a value for the convective heat transfer coefficient. If the theoretical figures that we obtain match the experimental heat transfer coefficients then the theory of forced convection is accurate and true.
Method
In the experiment, we are testing heat transfer by forced convection using a flat heat exchange plate. The system contains a fan with variable speed this fan can be controlled by digital controller. The speed of the fan can be measured using the anemometer fitted to the system. When fan is on, forced convection is taking place and thus forced convection can be tested and measured. The power being supplied to the heater block is measured and controlled by a potentiometer and a wattmeter. There are two temperature sensors within the apparatus. One temperature sensor is used to measure the heater block and the other temperature sensor is used to measure the temperature of the hot plate of the temperature of the air in various areas of the duct. The temperature sensor is simply put into various cut out holes in the side of the duct, each of these hols allows a temperature reading at that are to be measured. The experiment method is below:
1. Secure the heat exchanger (flat) into the duct
2. Set the air flow to 1 m/s and allow system to settle
3. Using the temperature sensor measure the ambient temperature
4. Record the Ambient temperature
5. Record the Wattage used by the Heater
6. Allow the system to settle for 15 minutes and record the heated block temperature.
7. Repeat steps 1-6 using the new flow rates of 0.8m/s, 0.6m/s
Results
Here are the recorded results from the experiment.
Time (Mins)
Power (watts)
Block Temperature (Celsius) Ts
Ambient temperature (Celsius) T
Air Velocity (M/S)

0
7.8
47.0
22.1
1

15
7.8
48.2
22.0
0.8

30
7.7
49.4
22.0
0.6

Using Newton’s law of cooling we can determine the convection heat transfer coefficient (h) for the experiment. This can be calculated for all three Air Velocities (1m/s, 0.8m/s and 0.6m/s).
This law is; Q=hAs (Ts- T
Where Q=Power in Watts
As= Area of heated block= 110mm by 100mm=0.011m2
T= Ambient temperature (Celsius)
Ts= Block temperature (Celsius) h=Convection heat transfer coefficient

Theoretical Values
Now that the experimental values for the convection heat transfer coefficient (h) have been determined, the theoretical value for the convection heat transfer coefficient must be calculated. The Reynolds number was calculated using Re=(da and was used it to see if the flow is laminar/ turbulent. If the Reynolds number was greater than 500000 then the flow was turbulent, if the flow was below 500000 then it was laminar. The Prandtl number for each airflow has been calculated from properties tables to be . The Reynolds number and Prandtl number were to calculate the Nusselt number for each airflow using the relevant laminar/turbulent equations. The theoretical value for the convection heat transfer
Coefficient (h) was then calculated.

Discussion
From the graph for T-Too vs. Velocity we see that as the Velocity decreased the T-Too increased. If no airflow was present (no forced convection) there would be a much bigger T-Too value, this makes sense as if there is no convection the difference between the heating plate and ambient temperature of the duct will increase. The graph produced from our experimental values is in general following the form of a typical forced convection graph. This shows that the experimental values follow the relationship expected and as such the experimental data is correct and accurate.
Looking at the Graph for h (both experimental and theoretical) vs. velocity there are some similarities to the first graph drawn. However, both these graph lines for the experiment and the theoretical values should increase in a linear fashion between the 0.6M’S and the 1M/S points. This appears to be the case for the experimental values; however there seems to be a sharp increase in the gradient of the graph line (for theoretical h) between the 0.8m/s and 1m/S. This may be due to the theoretical value at this point was determined to be turbulent flow while the other two points where determined to be under laminar flow. The values for h in both the experiment and calculations show the correct relationships to prove the initial aim of this laboratory. However the theoretical values are slightly higher than the actual recorded experimental data. The experimental values being lower than the calculated values is down to several possible errors. There errors are listed below.
The and wattmeter only measures values to 1 decimal place this will reduce accuracy of calculations
The airflow is only measures values to 1 decimal place this will reduce accuracy of calculations
The system has not fully stabilised the 15-minute period allocated to it. This may have resulted in a higher value for h if more time had of been given,
The experiment does not take into account heat lost or transferred to the experimental structure or air. As such the value for Q may be slightly different in reality
Conclusion
There is a difference in the values recoded in the experiment and those calculated theoretically, however as both follow the trend expected, the results can be accepted to prove the original aims and objectives. The experiment did contain errors which have gave us a much lower actual value for h than was theoretically calculated, however these where mainly due to accuracy errors and overly optimistic assumptions. There were no errors that would have changed the results to an extent to make them incorrect or unusable. Both the graphs drawn show that as the airflow increases over the plate then the rate of convection will increase. This proves Newtown’s law of convection.

Convection lab calculation appendix

Counter Flow Heat exchange Laboratory

Introduction

This laboratory experiment consists a counter flow heat exchanger with a simple concentric tube. The aim of this experiment was to analyse the performance of the heat exchange system and determine the over all heat transfer coefficient for the heat exchanger. This was carried out using the Log mean temperature difference method.

Aims and objectives of experiment

A. The aim of this experiment is to determine the overall heat transfer of the heat exchange system. Using experimental results it its possible to determine the rate of heat exchange between hot water and cold water flowing through a counter-flow concentric-tube heat exchanger. It is then possible to determine the overall heat transfer coefficient of this system using the equation. We will meet this aim by;
1. To determine the rate of heat loss by the hot water.
2. To determine the rate of heat gain by the cold water.
3. To determine the overall heat transfer coefficient using the Log Mean Temperature Difference method
4. Discuss any factors, which might affect the accuracy of the results.
Method

The heat exchanger was turned on; the flow for hot water was set at 2000cm3/min and the flow of cold water at 950cm3/min. The system was left for a few minuets, these few minuets allowed the system to settle. The volumetric hot water flow rate was then observed and measured. The volumetric cold water flow rate was also observed and measured. The system was further allowed to settle and the temperature was measured at various points throughout the system. These points where at the hot water inlet, the hot water outlet and the hot water mid point along the hot water pipe. Similarly the cold water points of temperature measurement where cold water inlet, the cold water outlet and the cold water mid point along the cold water pipe. From these results I was able to work out the heat exchange that took place in the hot water pipe using the following equation: Heat exchange in warm fluid pipe= MH*Cp*(Temperature In-Temperature Out)
I was also able to calculate the heat exchange taking place in the cold water pipe using: Heat exchange in cold fluid pipe= Mc*Cp*(Temperature Out-Temperature In).
I then followed the Log Mean Temperature Difference method to calculate the over all heat transfer. (For calculations see end of report

.
Temp Hot Water In (Celsius)
Temp Hot Water Mid (Celsius)
Temp Hot Water out (Celsius)
Temp Cold Water In (Celsius)
Temp Cold Water Mid (Celsius)
Temp Cold Water Out (Celsius)
47.17
44.12
40.64
15.18
22.7
28.5

Hot water Flow Rate
Cold Water Flow rate
2400cm3/min
0.0000408m3/sec

1000cm3/min
0.000017 m3/sec

Equations used in calculations

Discussion

In this experiment we expected to see that as the temperature in the hot water pipe decreased, that there would be an increase in the cold water pipes temperature. This is due to heat transferring from an area of higher temperature to an area of lower temperature. We also expected to see a higher calculated heat exchange value in the hot water pipe than that of the cold water pipe. Again this is due to the fact that heat generally transfers from an area higher temperature to an area of lower temperature, thus the heat exchange value for an area with a higher temperature must be greater. Both these trends where seen in our results. The hot water dropped from 47.17 to 40.64 degrees Celsius, while the cold-water temperature increased from 15.18 to 28.5 degrees Celsius. We also expected the hot water to have a high heat exchange value than the cold water. This was also observed when the relevant heat exchange values where calculated (see below). For these reasons I believe there to be little, if any, errors made within this experiment, with any errors made resulting to minor variances in predicted the results rather than affecting the overall outcome of the experiment. The graph produced from the table of results follows that of a typical Temperature vs. Length graph for a counter flow heat exchanger. The hot water flow enters the heat exchanger at zero meters and exits the system 1.5m. Subsequently due to this experiment being a counter flow heat exchanger, the cold water flow enters at length 1.5m and travels through the exchanger and exits at length 0m. This graph shows that the heat exchanger performed as expected. The experiment is very useful but however does not give us exact values for several reasons, such as;
.
The experiment also assumed that the water flow rate of both pipes is constant, when in reality it is constantly changing to small degrees.
Current experiment does not allow us to accurately work out the heat transfer at a specific point within either pipe.
The heat exchange system is assumed to be fully insulated. In reality however this is unlikely to be a correct assumption. Therefore heat will be exchanged to other unmeasured mediums such as heat lost to air or indeed lost to the pipe. Due to this there will be more heat lost to other mediums than is calculated to be happening due to the heat exchanger alone.
Also as the system is assumed to be fully insulated, the recorded heat transfer for the cold flow will be inaccurate. The cold flow will be absorbing heat from the air and the heat exchanger structure. This will provide a greater heat gain than you get from the heat exchange system alone. This will affect the rate of heat transfer calculated.
The temperature sensors recorded to 2 decimal places, this may cause calculation inaccuracies. Also it may effect any figures looked up from properties tables.
The pipes are assumed to have no furring. This is an inaccurate assumption, as there will always be furring to a small extent. Furring will affect the rates of heat transfer calculated to a small degree. Even though the system was allowed to settle, the system may not have fully settled when the temperatures were recorded. This will give an incorrect measurement of the rate of heat transferred.
Conclusion

In this experiment we where able to successfully determine the rate of heat lost by the hot water and the rate of heat gained by the cold water. Both these valued followed the trends we expected to see with the hot water losing heat while the cold water subsequently gained heat. The heat lost and gained by the hot and cold water can be see below on the calculations page. Using the log mean temperature difference method I was able to calculate the over all heat transfer coefficient. This heat transfer coefficient again shows the trends, which we expected from the experiment. A graph was drawn to show the hot and cold water temperature changes between the points measured (In-Mid-Out). The accuracy of these results are not as accurate as they could be however. Human error in both measurement recording and calculation rounding is always an area of inaccuracy however this experiment also does not take into account heat transferred to other mediums such as air or the pipes metals. It assumes a constant flow rate in each of the pipes, which in reality, the flow rate in each pipe is constantly varying to small degrees. The experiment also does use pure water, the water in one or both of the pipes, may contain contaminates, residue and impurities which may affect both the flow rate and heat transfer rate of the water. In conclusion this experiment followed the trends expected and I was able to satisfy each of the aims and objectives. The results obtained I believe are accurate and a true representation of heat exchange rates between hot and cold water in pipes. However adjustments could be made to improve further on the accuracy of the results.

Heat transfer lab calculations appendix