Measuring Heat Transfer Coefficient for Solar Heating (Cooling) Systems Using Water Container Heat Storage

 Some solar air heating system use water containers for heat storage. The hot airstream from the solar collectors is directed over the water containers and heat is transferred from the hot air to the water. At night or during cloudy periods room air is passed over the water containers to pick up heat from the containers to heat the house. Water containers can also be used in cooling systems in which the containers are cooled through some means (typically at night), and then during the following hot day, the "coolth" stored in the water container is used for space cooling. This page covers a small test to determine one of the key parameters in estimating how many water containers they need, what size they should be, and how much heat or coolth can be stored how fast.

Background

In sizing the containers for such a system, it is important to be able to know how many containers of what size are needed to store a given amount of heat or to match the output of the planned solar collector.

The heat transfer from air stream to container can be estimated by this equation:

Heat Transferred = h A (Twater - Tair) t

where:

h is the heat transfer coefficient (BTU/sf-F-hr)

A is the heat transfer area (sf) (the outside surface area of the containers)

Twater is the temperature of the water in the containers (F)

Tair is the temperature of the air stream flowing over the containers (F)

t is the time period for the heat transfer (hr)

For example, if you 200 two liter plastic pop bottles with a 120F airstream passing over them, and h is 2.0 BTU/sf-F-hr and the starting water temp is 80F, and the heat transfer takes place for 0.5 hour, what is the energy stored and the final water temperature?

Each 2 liter bottle has an area of 0.89 sf and holds 4.56 lbs of water, so for 200 bottles, the area (A) is 178 sf and the total weight is 912 lbs.

Heat Transferred aprox = (2.0 BTU/sf-F-hr)(178sf)(120F - 80F)(0.5 hr) = 7120 BTU transferred from the air stream to the water.

Water Temperature Gain = Q / w Cp = (7120 BTU) / (912 lbs)(1.0 BTU/lb-F) = 7.8F or, 80F+7.8F = 87.8F final temperature.

It is important to have a good estimate of the heat transfer coefficient (h), but I find that values given for it in several references vary and its not clear how well the values given for it apply to the case of solar heated air flowing over plastic bottles or buckets. So, this page documents a small test I did to try to get an idea what a good value to use for h for a a typical home solar heating or cooling system that uses water containers like 2 liter bottles or small drums. I did this for sitll air (natural convection only) and for air moving at 2.8 mph.

Experimental Determination of Heat Transfer Coefficient

Bottom line testing for values of heat transfer coefficient (h):

Measured value for h of 1.4 to 1.8 BTU/sf-F-hr for still air
Measured value for h of 2.7 to 3.6 BTU/sf-F-hr for air moving at 250 fpm.

This shows the experimental setup. There is a 2 liter polycarbonate pop bottle and a 2.7 gallon ice cream container.

Both containers have temperature sensors placed near the middle of the container. A third sensor between the two containers senses the air temperature. Both containers were supported on an insulation board, and the area of the bottom of the containers was not counted in the heat transfer area.

The test starts with hot water (about 130F) in the containers, and the temperatures are logged over several hours as the water in the containers cools.

For the still air test, the only circulation around the containers is due to natural convection.

For the fan test, a fan is used to produce an airflow velocity of about 250 ft/min (2.8 mph) over the containers. This might be typical of the kind of air velocity you might get is the output of a solar air heating collector was directed into an enclosure filled with water containers.

Still Air Test

This plot shows the cooldown for the two containers.

This shows the cool down for the still air case for a period of about 6 hours.

The 2 liter bottle is the red line and the purple line is the 2.7 gallon ice cream bucket.

The 2 liter bottle has a heat transfer area of 0.89 sf and a water weight of 4.56 lb, giving an area to weight ratio of 0.195 sf/lb.

The 2.7 gallon container has a heat transfer area of 2.7 sf and a weight o 22.9 lbs, giving an area to weight ration of 0.12 sf/lb.

So, the 2 liter bottle has 1.6 times more heat transfer area per pound of water than the 2.7 gallon container, and this is why it cools faster. The lesson here being that if you want more heat transfer to your heat store as the collector air passes through it, smaller containers have more surface area per pound of water and will result in more heat transfer.

The green line is room temperature -- the dipsy doodle in the room temperature at about 5:30 was a door open to the outside for a while.

The value of h is estimated for 14 minute periods and plotted above. For the 2 liter bottle, it is about 1.8 BTU/sf-F-hr when the bottle is hottest and drops to about 1.6 as the bottle cools. This makes some sense to me in that the hotter bottle results in faster convection currents around the container.

The 2.7 gallon container shows a somewhat lower h. This may be in part due to the fact that the top of the container was included in the heat transfer area even though ran at a temperature somewhat lower than the sides of the container, which are in full contact with the hot water. But, in any case the two h's are close.

How h is estimated:

The heat transferred from bottle to air by convection over time period t is:

Qcon = h A (Tbot - Trm) t

whre h is the heat transfer coef, A is heat transfer area, Tbot and Trm are the average temperatures of the bottle water and room air over the period.

This heat loss from the water in the bottle causes it to cool by:

Qwater = w (Tbot0 - Tbot1) Cp

where w is weight of water, Tbot0 is water temp at start of period, Tbot1 is water temp at end of period, and Cp is the specific heat of water.

If you set these two equal to each other, and solve for h:

h = w (Tbot0 - Tbot1) Cp / (A (Tbot - Trm) t) ---- in BTU/sf-F-hr

The plot above of h values is done by using a large number of 14 minute periods over the course of the test to estimate values of h.

Fan Forced Air Test

This shows the setup for the fan forced air test. The air velocity was fairly uniform over the containers -- about 260 to 270 fpm in the center and about 240 fpm to the outside of each container. Measured with a Kestrel anemometer.

This is the cool down plot for the test in which air was blown over the containers at about 250 fpm.

As expected, the containers cool more quickly with the fan forced air: the 2 liter cools from 130F to 90F in 1.05 hrs with fan forced air, while the same drop takes 2.4 hours in still air. This is due to the higher heat transfer coefficient that the moving air brings.

The heat transfer coefficient is nearly constant throughout the test and does not decrease as the bottle temperatures go down as it did in the still air test. This seems reasonable as fan velocity does not change over the test in the way that the convection current velocity changes for the still air case.

h for the 2 liter container is about 3.6 BTU/sf-F-hr -- about twice what it was for the still air test.

h for the 2.7 gal container is about 2.7 BTU/sf-F-hr.

The lower value for the 2.7 gal container might be due in part to counting the lid area in the heat transfer area -- h would increase to about 3.3 BTU/sf-F-hr if the lid area was not included. There may also be some differences in the flow around these two container shapes.

Thermal Images

Some thermal images during the test.

This shows the two containers most of the way into one of the tests. The 2 liter has cooled significantly more than the 2.7 gallon container. Not a lot of thermal stratification has occurred in the containers.

I wondered if the fact that the air flow likely separates as it flows around the back of the container would result in higher temperatures on the back of the bottle, since there would be lower velocity airflow, but IR images don't seem to show any significant difference in back and front temps.

Click for full size.

Looking straight down on the bottle.