Cooling Pond Design (POME medium)

Hi All,

Good day to you.

Currently, i'm looking for the calculation of surface temperature of cooling pond with medium of palm oil mill effluent (POME).
This cooling pond is operated in plug flow system with retention time of 2 days for cooling.
On the upper layer of the POME, a layer of oil was found due to poor filtration after the palm oil extraction from the factory.

Generally the process is as below:
Factory --> POME --> Cooling Pond

Since there is a layer of oil on the top of the medium, evaporation is excluded from the heat transfer calculation. Conduction, convection and radiation are the main heat transfer involved.

Heat inputs:
1. qs = short-wave solar radiation,
2. qa = long-wave solar radiation,
Outputs:
1. qsr = reflected portion of qs,
2. qar = reflected portion of qa,
3. qbr = long-wave black radiation from water surface,
4. qc = conductive heat loss.

therefore,

qt = (qs + qa)-(qsr + qar + qbr) + qc

where,
qt = net heat flux across the air-water interface (pond surface).

Question:
May i know, is there any simplified equation for the above equation? As i found the following equation, but the equation included the evaporation, which is not fit to my current condition.
[The following equation aim to calculate the exit temperature of the medium]

dqt/dt = -K (Ts - E)

where,
dqt/dt : net rate of surface heat exchange,
K : heat transfer coefficient,
Ts : pond surface temperature,
E : equilibrium temperature.

where it simplified from the equation below:
qt = (qs + qa)-(qsr + qar + qbr + qe) + qc

where,
qe : evaporation heat loss.

Appreciate if anyone can share some idea or information at here.

Advance Thanks,
Charles CL

Hello charles welcome to the forum! I saw your discussion over on chemicalforums But could not get the link you poasted to your pond design to come up. I agree with enthalpy that if your book covers a model with humidity, you could set yours to 100 percent to calculate. Although i would be skeptical of an equation that was simpler than the one you describe, unless you had taken a lot of data that could be developed into a heat transfer coefficient. Like for example i think you could get accurate predictions with a simple equation like the Dq/dt=-k(Ts-e) but you would have to develop the k constant for your particular pond/oil scenario. Otherwise it is kind of grasping at straws. Looking at the literature, things get pretty hairy with variables pretty quickly. It takes a lot of data to develop a meaningful model that can be applied in various situations. With most differential equations students are always told " but this wont be completely accurate because it assumes **** and neglects ****. "
I found a book online here called Mathmatical Predictive Models for cooling ponds, made in the late 70s by the MIT energy laboratory. A lot of info.
I am currently working on developing a mathmatical model for brewing microbes, and i got to a point where i just needed to collect a lot of data to continue with the work, which takes a lot of time and attention. There is a reason sewage treatment plants pay a pretty penny to have activated sludge modeling software, it took a ton of research and experience to get where they are!
Anyway, goodluck on your search.