# Calculating the heat loss of an open water tank (aquarium)

• A
• Apgomes3
In summary, when it is winter and the water in the aquarium is higher in temperature than the surrounding air, the heat transfer goes from the inside of the tank towards the surroundings - so the aquarium loses heat. When it is summer and the water in the aquarium is lower in temperature than the surrounding air, the heat transfer goes from the surroundings to the water inside - so the aquarium gains heat.f

#### Apgomes3

Hi,

I have been calculating a series of hypothesis for some aquariums/tanks situations, using heat transfer equations (conduction, convection, radiation, evaporation)

Typically we have aquariums that run at higher temperatures than the surroundings in winter and lower temperature than the surroundings at summer ... I stumble into a silly question in trying to establish the scenario

Question 1 is about Conductive heat transfer

When the conduction is in a horizontal plane between two different fluids ( in this case air and water) instead of using Fourier's law

Q= K.A (ΔT/L)

should I do it

Q = = U A dT where U , overall heat transfer coefficient (W/(m2K), captures the individual fluid (air and water) convection heat transfer coefficient

1 / U = 1 / hci + Σ (sn / kn) + 1 / hco

Is this a correct way of thinking ? Because the following 2 scenarios then will be more accurate ?

A. When in winter - water is higher in temperature than surrounding air, the heat transfer goes from the inside of the tank towards the surroundings - so I consider a loss of heat.

B. When in summer - water is lower in temperature than surrounding air, the heat transfer goes from the surroundings to the water inside - so I consider a gain in heat.

Question 2 is about Convection heat transfer

Does the same principle above applies to the rationale ? So using Newton's Law of Cooling

Q = = Hc A dT, where dT is temperature difference between the surface and the bulk fluid

I won't go into the details of calculating Hc_water (which is a all new thread...!) but my silly questions remains the same:

A. When in winter - water is higher in temperature than surrounding air:

so I consider the hot plane to be the superficial water film layer and the heat transfer is done from this layer to the surrounding air. I use here Hc_water ( convective heat coefficient of water). I consider a loss of heat ( regarding the aquarium)

B. When in summer - water is lower in temperature than surrounding air:

so I consider the hot plane to be the superficial air film layer and the heat transfer is done from this layer to water. I use here Hc_air ( convective heat coefficient of air). I consider a heat gain ( regarding the aquarium)

This is not looking as correct to me ... but I couldn't get my head around to be more accurate would greatly appreciate inputs and ideas

For now I am only considering the convective heat transfer in the open top of the aquarium.

The main reason why the water cools is evaporation from the surface.
Evaporation is endothermic.
I think you should look into that.
Obviously the rate of evaporation depends on several things such as air humidity, whether there's a draft or not, size of the surface, temperature of water etc.

• vanhees71
Hi @Philip Koeck yes that is true; i am looking or trying to look past it as well so to compute in the losses or gain by conduction, convection and radiation and their role. I have all of that computed now. Evaporation is not linear to calculate in indoor situations when the surface is not calm but also found a good article detailing this known equations and their deviations so its at least a starting point. Typical evaporation is derived from an empirical equation that is accurate enough but for wind speeds above 2 m/s outdoor; indoor hvac is more around 0.15 m/s per some notes.

I do think it is an interesting exercise and sometimes i do need to challenge my logic so to say if i am following a coerent one!

Thank you for your input! Greatly appreciated

• Lnewqban and Philip Koeck