# Can one use incompressible flow approximation for fluid flow in heated pipes?

I was wondering if the use of incompressible flow approximation for fluid flow in heated pipes is reasonable. A previous question (Definition of incompressible flow) seemed to focus on Natural Convection heat transfer. It does not seem to apply to Forced Convection problems where the fluid is heated as it moves in a pipe with a heated wall? In this situation the temperature is increasing overtime (non steady state) and hence the density of the fluid is changing, In my case of a solar thermal system this heating time can be in order of hours and the temperature can vary between 80 and 250 °C.

The model I'm creating is a run-time numerical model, and it has to be fast enough for that purpose, so what I'm doing now is using incompressible flow differential equations for each time step (assuming density is constant) and then modify the density after the solution is obtained. I'm not sure if this is really ok to do.

It depends on the temperature range and the thermal expansion coefficient of the fluid. You can't treat a gas as incompressible if you heat it from 300K to 1000K, but if you heat water from 20C to 80C the density variations are so small that you can treat the fluid as incompressible (even though the density variations of course drive the convection -- this then leads to the Boussinesq approximation).

• Apart from the validity of the Boussinesq approximation, it also depends on the physics characterized the Grashof number: If Gr is small, we can completely neglect density changes. – akid Nov 27 '13 at 16:18
• But in my equation, natural convection is really negligible compared to forced convection (flow velocity is around 0.5 m/s). So what am worried mostly about is the contribution of the change in density in the energy equation as shown below: $u\frac{\partial \rho}{\partial t} + \rho\frac{\partial u}{\partial t}= \frac{1}{A}\bigg[\dot{q_f} - \dot{m}\frac{\partial h}{\partial x}+h\rho\frac{\partial v}{\partial x}+hv\frac{\partial \rho}{\partial x}\bigg]$ Yeah,as suggested, there is no direct answer, maybe i have to calculate the relative terms – Marwan Nov 28 '13 at 14:12