I'm working on an experiment where I'm trying to simulate the natural cycle of temperature changes in a River. I have the data and know how I'm going to implement it in a theoretical sense. The experiment is set up so that a tank will have water pumped in, (keeping volume constant), between 4-10 degrees C*, and a heater that will shut off when it reaches a certain maximum. (* we have two pipes one of 4 degrees C and one of 10 degrees C and through experiment, since we don't have an analytical way of determining how much is flowing from each one, we can mix the two to keep the water flow from the pump at a constant temperature.) The goal is to have the water go through one cycle, which can be thought of as going through one sinusoidal cycle, per day. The main problem I'm facing is that it seems like the temperature would cool down too quickly when the heater shuts off. We also don't want to more than one cycle per day, (in attempt to mimic nature), but some noise is fine. In looking up examples on the web I've found them to be oversimplified. And even if I took the simple equation by using Newton's law of cooling I anticipate that the water will cool too quickly as there is very little difference between the two temperatures, e.g. max of 12.8 C and min of 11.1 C. I'm also not certain if the constant flow of constant temperature water will be enough to offset any ambient temperature. (the tanks are made of a thick plastic and will be covered, maybe no more volume then appx 0.25 cubic meters.) I'm hoping for a little physics help to determine how to best use my instruments in the design process and what type of equation to use for my model, to know when to turn my heaters on and when I need to monkey with the valves that control the 4 and 10 degree C pipes. If nothing else at least a more appropriate differential equation to use. Thanks!