NFC: How to determine heat transfer

["Andrew S Dalton" <ASDALTON at prodigy_net>]

1.  The easy way.

Most native fish tanks don't have a heater, but you probably have a
powerhead or submersible filter that will inevitably add heat to the water.
Determine the power consumption in watts.  Then measure the temperature of
the water and the ambient air.

Q = power consumption in watts
T = water temperature
Ta = ambient air temperature

Since Q = UA*(T - Ta), UA = Q/(T - Ta)

The units of UA will be watts/deg C if you measured the temperatures in deg
C, and watts/deg F if you measured the temperatures in deg F.  If you want
the power units in Btu/hr, multiply by 3.41.

Some precautions:

Since this method assumes that the powerhead is the only source of heat in
the aquarium, it won't work if the tank lights have been on for more than a
few minutes.  It also won't work if the tank is not covered to prevent
evaporation.  In other words, the aquarium must be in a steady state where
the only significant source of heat gain is the powerhead, and the only
significant source of heat loss is directly through the walls of the tank.

Also, if you use the same thermometer for the water and air, make sure that
the thermometer is completely dry when you take the air temperature.


2.  The hard (but probably more accurate) way.

This method measures the temperature change over time when an aquarium
starts out significantly warmer or cooler than the ambient air.  It requires
all of the precautions that I mentioned for the "easy" method.  It also
requires that you have _no_ internal heat sources, so you can't use a
powerhead to circulate the water.  Use an airstone, and adjust the air flow
in order to match the intensity of water circulation that you will use
during the tank's normal operation.

For this experiment, you will need a clock or stopwatch and two accurate
thermometers--one for the water and one for the ambient air.  Make a table
arranged in the following way:

Time (t)         Ambient temp. (Ta)        Water temp. (T)


You can record either the clock time or elapsed time (with the first
measurement being taken at t = 0), but the elapsed time is what will
actually be used in the calculations.

The equation to use is V*d*Cp*ln((T0 - Ta)/(T - Ta)) = UA*t.

V = volume of aquarium
d = density of water = 8.35 lb/gal or 1000 g/L
Cp = heat capacity of water = 1 Btu/lb/deg F or 1 cal/g/deg C = 4.134
J/g/deg C
T0 = water temperature at first measurement (t = 0)
t = elapsed time since first measurement

Strictly speaking, Ta needs to be constant, but you can just use an average
as long as Ta doesn't vary too much over time.

Make a graph with the quantity V*d*Cp*ln((T0 - Ta)/(T - Ta)) on the y-axis
and t on the x-axis.  The result will be a line passing through the origin
with a slope of UA.

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[\   Andrew Dalton
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