Fluid going through pipe: what is the influence of speed on exchanging heat?

[rumborak]

I'm doing a fun home project, and it involves water flowing through a metal pipe, where the surrounding is significantly lower temperature than the water in the pipe. The point of the exercise is to cool the water in the pipe as it flows through it.

The question is, what influence does flow speed have in the heat exchange? The extreme case is of course if it's flowing way too slow where the water is in equilibrium with the surrounding, meaning the overall heat transfer is impeded.

However, is there any downside to flowing too fast? My gut feeling is no, I suspect that from a certain speed on you transfer less heat per water volume, but it's offset by the increased transfer volume.

 

[dRic2]

if you fix the geometry of the pipe and you increase the speed you may go from laminar flow to turbulent flow. Turbulent flow is more effective in exchanging heat

 

[Chestermiller]

If you go very slow, then, if the objective is to lower the temperature of the water as much as possible as it goes through the pipe, this will give the minimum exit temperature. On the other hand, at very high water flow rate, even though the heat transfer coefficient is high, the amount of time available for heat transfer is very short so that, in the end, the water temperature won't change (that is, the shorter heat transfer time wins out over the higher heat transfer coefficient). The equation for quantifying all this is as follows:
$$T-T_0=(T_{in}-T_0)\exp{\left(-\frac{h\pi DL}{\dot{m}C_p}\right)}$$where $\dot{m}$ is the mass flow rate, Cp is the fluid heat capacity, and h is the heat transfer coefficient. h increases with mass flow rate, but the rate of change with $\dot{m}$ is less than the first power of $\dot{m}$ at all values of mass flow rate. So $h/\dot{m}$ always decreases with increasing $\dot{m}$. This means that, as $\dot{m}$ increases, the amount that the water cools in passing through the pipe decreases, and, in the limit of very high mass flow rates, the temperature doesn't change from the inlet temperature at all (even with turbulent flow).

 

[dRic2]

Oh I'm sorry I didn't pay much attention to the question... I though you where asking about heat transfer in general. My comment is pretty useless and pointless. @Chestermiller is of course right

 

[James Demers]

Chester is correct to the extent that the flow is consistently laminar, or consistently turbulent. In those situations, the amount of heat transferred is a simple function of the time required to transit the pipe.
But dRic2 does make an important observation: when the flow transitions from laminar to turbulent, the rate of heat transfer will jump considerably. Heat exchangers have been designed which deliberately itnroduce turbulence into the flow: https://www.sciencedirect.com/science/article/pii/S1290072915301794