Aquarium Thermodynamics
Temperature control and stabilization in any aquarium is a constant battle. Fluctuation in temperature is caused by many different factors. Heat flow rate or heat transfer is the amount of heat transferred to and dissipated from the water in BTU/hr. The four basic heat transfer mechanisms to consider are conduction, convection, radiation, and evaporation.
Conductive Heat Transfer
Heat is conducted through the tank walls. Different materials and tank shape cause this to happen at different rates. Fourier’s Law can be used to determine conductive heat transfer.
qcond = hcond ∙ A ∙ ∆T (BTU/hr)
where
A = heat transfer area (sq. ft.)
∆T = temperature difference across the material (F)
hcond = effective conduction heat transfer coefficient (BTU/hr/F/sq.ft.)
Where the effective conduction heat transfer coefficient is given by:
hcond =
where
k = thermal conductivity of the material (BTU/hr/F/sq.ft.)
s = thickness of the material (sq. ft.)
Thermal conductivity of common types of aquarium materials
| Material | Thermal Conductivity (BTU/hr/F/sq.ft.) |
|---|---|
| Aluminum | 144 |
| Glass | 0.61 |
| Water | 0.34 |
| Acrylic | 0.12 |
| Hardwoods | 0.09 |
| Styrofoam | 0.02 |
| Air | 0.014 |
Convective Heat Transfer
Heat is transferred from a surface to a circulating fluid. There are two primary sources of this transfer. The first being water flowing next to the inner walls of the aquarium, through pumps, heaters, and chillers. The second being air circulating past the outer walls of the aquarium and between the lights above the aquarium surface. Newton’s Law of Cooling is used to determine heat transfer by convection.
qconv = hconv ∙ A ∙ ∆T (BTU/hr)
where
A = heat transfer area (sq.ft.)
∆T = temperature difference between the surface and fluid (F)
hconv = convective heat transfer coefficient (BTU/hr/F/sq.ft.)
Convection Heat Transfer Coefficients
| Material | Convection Coefficient (BTU/hr/F/sq.ft.) |
|---|---|
| Air | 20-Feb |
| Water | 100-2,000 |
Radiation Heat Transfer
Radiation heat transfer is how the sun heats the earth and a fireplace heats a room. Heat waves are ejected in the form of electromagnetic waves. Every object emits electromagnetic radiation anywhere from 0.1 to 100 microns depending on its temperature. There are two major sources of this type of heat transfer in aquarium applications. Aquarium lighting emits heat radiation in the form of infrared waves into the water surface. Infrared waves are also emitted from the outer tank walls to the air in the room.
The Stefan-Boltzmann Law is used to determine this type of heat transfer.
qrad = A1 ∙ F1-2 ∙ ∙ (T14– T24) (BTU/hr)
where
= 0.1714 x 10-8 (BTU/hr/sq.ft./R) (Stefan-Boltzmann constant)
F1-2 = transfer factor
A1 = area of emitting body (sq.ft.)
T1 and T2 in degrees Rankin (R)
*Note that temperature in degree R = degree F + 460*
Radiation heat transfer coefficient determination with hrad
Evaporative Heat Loss
Evaporation as a means of chilling aquariums can be effective to remove hundreds of BTU’s an hour. However, a chiller can remove thousands of BTU’s an hour. Evaporative cooling works by transforming water to water vapor through latent heat vaporization (he). This is a natural process of all tanks and easily determined by multiplying the number of gallons of water replaced each week by 8050 (he) and dividing by 168 (hours in a week). Air humidity is the most important determining factor in regard to evaporative heat loss.
qevap = he ∙ A ∙ (5.1 + 1.2 ∙ v)(x5 – x) (BTU/hr)
where
A = heat transfer area (sq.ft.)
v = air velocity (ft/s)
he = latent heat of vaporization
= 970 BTU/lb
X5 = humidity ratio in saturated air at same temp. as water surface (lb/lb)
X = humidity ratio in air over tank (lb/lb)