Introduction

Heat transfer is a simple process yet it is very dynamic. You probably learned in physics at some time that the net energy flow is from a body with more energy to another body with lower energy. This transfer can take with several mechanisms: radiative, direct contact, and other variations. This process is dynamic, because as one body looses heat the other gains heat, their relative temperatures are changing and the heat flux is changes with that.

We're going to start exploring a very simple experimental set up; a beaker of warm water immersed in a larger volume of colder (room temperature) water. The net heat flux will be from the warm beaker to the larger bath. The rate of heat transfer will depend on the relative temperature, the area of the beaker, and the efficiency of transfer per area. The transfer of the heat can be accelerated by mixing the water near the surface of the beaker on both sides, so at first we will leave the both solutions un-mixed. The directions for each lab are described below.

Heat loss is governed by the flux of heat from the beaker to the bath. The flux is the rate of energy transfer per cm^2 of beaker surface in contact with the bath. This describes the rate of energy that is going through that surface. The flux_ constant is the rate of energy transfer per cm^2 per degree temperature difference. The equation for heat flux in calories is

heat_flux (calories min^-1) =

heat_flux_constant (calories*cm^-2^*min^-1*temp^-1) * temp_difference * beaker_area

You have to know the temperature in both containers to calculate this flux.

Temperature is a measure of the amount of thermal energy contained in a substance. You're probably well aware that the heat capacity of water is 1 calorie per deg per gram. (Remember that on mL of water = 1 gram.) This means it takes the addition of one calorie of thermal energy to increase the temperature of a mL of water 1 degree C. Some materials hold less energy per change in temperature and some hold more than water. For example, aluminum changes temperature about 4 times faster than water for the same input of energy.

In this lab you will work with a very simple set up to record temperature differences, calculate energy flow and get an estimate of the flux_constant for your system. This set up is overly simple and has opportunities for improvement. Your second lab session will be to construct your own heat flux experiment that you think will be an improvement. During the third session you will construct a STELLA model that describes your experimental design. Since all designs are unique, your model will have unique to represent your particular system.

Heat flux an example of diffusion, the movement of material or energy from a higher, more concentrated state to a lower, less concentrated state. We see examples of diffusive flux in many environmental science studies, such as:

spread of a benzene from oil that has been leaked into ground water

oxygen movement from air back into streams that have been impacted by organic effluent

The details of the movement of a pollutant or oxygen would be very different than heat, but the general approach to addressing the problem would be to study how fast the material moves from a high concentration to a low concentration and estimate some sort of diffusion constant in the medium of interest.

Description of Exercise

This exercise has three parts:

part 1: first week in lab - measure the rate of temperature change in a beaker and water bath

part 2: second week before lab - modify the beaker/bath system or create your own experimental contraption to estimate energy flux

part 2: second week in the lab: measure the rate of temperature change in a beaker and water bath

part 3: third week on computers - create a STELLA model that matches your experimental design and simulates the temperature change

 

Part 1: first week in lab - measure the change of temperature in a beaker immersed in a bath

You will need:

• beaker with hot water
• immersed in a water bath of much larger volume and at near room temperature
• stop watch or other timer
• thermometers

Measure the change in temperature over a time period of significant temperature change in the beaker.

Measure the volume of water in each container and calculate the area of shared contact between the beaker and bath. (It helps if these are at the same level.)

Enter the temperature of each container with time into a spreadsheet. Calculate the gain or loss of energy in that container for each time interval.

For example: if you had a 200 mL beaker of water and it lost 5 degrees in 10 minutes, your calculation would be

(200g * 5 deg)/10 min = 10 calories per min

You can then relate that to the average temperature difference of the water over that time interval. Your spreadsheet might look something like this table:

	beaker_volume	bath_volume
	200	1000
time	beaker_temp	bath_temp	beaker_heat_loss	bath_heat_gain	ave_temp_diff
0	60	22
5	55	23	(60-55)*200	(23-22)*1000	57.5 - 22.5
10	and on	23.8
15	and on

These are totally made up values. You might notice that the larger you allow the temperature change to be in the beaker, the broader range of temperatures you have to deal with as the average temperature.

Plot the heat flux in the beaker (adjusting for the area) as a function of the average temperature difference. The slope of this line will give you the heat_flux_constant in units of calories cm^-2 deg^-1 min^-1.

An example EXCEL speadsheet is provided here.

Part 2: second week before lab -

The beaker and bath set up has many design faults. You have to assume that the major source of heat transfer is between the water in the beaker and the bath. You can check the exchange by accounting for the heat lost and gained by each. Still, there are significant potential errors, such as:

heat lost to the air

heat lost to the table

the impact of slight turbulence in the beaker and bath

where the temperature is taken

You need to design and assemble an apparatus for testing heat transfer and determining the heat flux constant.

Part 2: second week during the lab -

Set up and use your apparatus to determine the heat flux constant. Measure all the characteristics of the system and make measurements that you will be able to use in your simulation model.

Part 3: third week on computers - create a STELLA model for your experimental set up and data

Design a STELLA systems diagram that describes the processes in your system. You might want to include possible pathways for heat to leak out. Use the heat flux constant you derived to set up a simulation. Run the simulation over the same temperature and time interval that you ran your experiment to see how closely they compare.

It'd be good for you to try to set up a model from a blank page. Sometimes the most difficult step is that first act of the first design of the system. After that you can modify and delete portions.

If you get stuck, you could look at this set of instructions for setting up a STELLA model for the "beaker in a bath" system. LINK

Part 4: written assignment - compare measured to modeled

Each student in a group that has worked together will submit a separate report. The report will contain four parts:

1. a description of the overall assignment
2. the data and graphs (in a neat and presentable manner) from the measurements in both the heat-transfer systems you used
3. a description of the STELLA model and example output
4. A comparison and evaluation of how closely the model described your direct observations and reasons why they might be different. Suggestions how what might have lead to errors and what you might do differently if you were to do this again.

The total report should only be about four pages.

last modified Feb 15, 2008