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pressure loss in presence of conjugate heat transfer in internal flows

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Old   September 2, 2019, 09:32
Default pressure loss in presence of conjugate heat transfer in internal flows
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Hi Eeryone,

I am trying to calculate presssure loss of a flow in a pipe while the flow is being heated. I would not use the Darcy-Weisbach equation in presence of heat transfer because the quantity of heat being introduced into the system is not negligble.

Can anybody give me an idea where can I begin to make an analytical/numerical model?

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Old   September 5, 2019, 14:03
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There aren't analytical solutions for arbitrary heat transfer quantities unless you can constrain the process in some way to exploit some characteristics.

Consider the Darcy-Weisbach not in the discrete sense, but in differential sense.


Discrete form:
\frac{\Delta P}{L}=f\frac{\rho}{2}\frac{U^2}{D}

Differential form
\frac{dP}{dx}=f\frac{\rho}{2}\frac{U^2}{D}

This is now an ordinary differential equation that you can integrate numerically provided you have addition equations of state to get density and velocity along x and the friction factor f being a known property of the flow (dependent only on Reynolds number). Keep in mind of course that the Darcy-Weisbach relation is an empirical relation and doesn't work for all flow scenarios. At the end of the day, it is a model.

You can also integrate the discrete case as well (it artificially looks like you would treat the pipe as a bunch of successive segments with constant densities). This seems theoretically not sound to people not familiar with discrete calculus, so I like to show people this way via an ode how it would work.
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