## I have seen the other side.

Well, I haven’t written in a long while. I’ve been quite busy recently. Work has been consuming most of my time. Don’t take that as a bad thing, though; I’m actually liking it immensely. I’ve been working especially hard these last couple of days with a grad student helping to fix and write code in an FEM package he’s been working on in C++. It’s hard work but I really enjoy it. Unfortunately it does take time away from thinking about totally useless but interesting things. Sometime this week we’re going to come up with a finite element formulation for two or three different models of fluid flow (at the very least we’re going to try the continuity equation and a linearized flow model). So when that’s done I might post it up here.

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Is this a *generalized* model of fluid flow (whatever that means)… or is this for a particular flow problem?

Like air flow around an aircraft part? Or maybe coolant flow through an engine or something?

It’s flow through micro channels. We’re mostly interested in solving for the flow field in junctions between these different channels, as we’ll model the velocity field within the channels as simple Poiseuille flow.

So far the model I’ve really been looking at is potential flow. This is where we assume the flow is incompressible and irrotational and is the gradient of some scalar field. Then, this scalar field would satisfy Laplace’s equation:

“flow through micro channels”…

For cooling? I’ve read things on the web about micro-channel flow for cooling. So where do the heat-exchange effects come in? There’s no temperature term in Poiseuille’s equations. Is temperature embedded in the viscosity term?

Also, is the liquid hot? Do you have to worry about bubbles forming and stuff like nucleation?

We’re not quite up to modeling the heat part yet. First we just want to look at the flow by itself (particularly in the junctions between channels) so we can pick a good model for it (as well as make sure the code we have works).

“…so we can pick a good model for it…”

So how will you know whether it’s a good model or not? I mean, almost any model will predict fluid goes in and fluid goes out, right? So how will you tell whether your particular model is accurate?

I assume you’re going to make measurements on the micro-channel flow. What exactly are you going to measure?

Basically we’re just looking for something that looks good in the junctions where several channels meet. We know the velocities entering and leaving the different edges of these junctions. We want the flow pattern within the junction so that we can use that to solve for the temperature in the whole material.

Additionally, assuming that the flow is incompressible, its temperature won’t affect its flow properties (solving these problems in tandems is tricky), so we only need the flow solution to get the temperature solution.