Sure no problem. It might take me a little while to derive a reasonable solution but now I finally got something to go on. I'll post as soon as I get a somewhat closed solution. Again thanks a lot for your help.
I think I finally understand what you were going for. You are linearizing with respect to the steady-state solution using the steady-state equations as "critical points". So now using your solution
\begin{equation}
\frac{\partial T^1}{\partial t}+w^0\frac{\partial T^1}{\partial...
Sorry about this late reply, I was lately a bit short on time.
I am a bit confused, to be honest...
Pls, correct me if I am wrong but if I understand everything correctly you expanded my equation (27) with your argument, neglected the term with transient temperature, and used the...
Okay so here is the equation written with thermal diffusivity:
\begin{equation}
\frac{\partial T}{\partial t} + w \cdot \frac{\partial T}{\partial x} = \alpha \cdot \frac{1}{r}\frac{\partial}{\partial r} ( r \frac{\partial}{\partial r} T )
\end{equation}
Inserting into the equation above and...
Firstoff a little correction to my previous post:
I skipped several steps here: using the no slip boundary condition( Velocity has to be zero) we find an expression for c1. We set c2 = 0 because of a singularity at r = 0. And then we combine the homogenous and particular solution together to...
Yes you are right, I am assuming viscosity and density to be temperature independent.
The deriviation of the velocity profile can be done like this:
Looking at the axial component of the Navier Stokes equation:
\begin{equation}
\rho \frac{\partial}{\partial t}w = -\frac{\partial}{\partial...
I am sorry for being inaccurate. I really appreciate you for taking your time with my problem.
I am only solving for the steady oscillatory state without transient behavior.
I attached a velocity profile for my stationary oscillatory flow velocity profile at my initial question. The plot...
Well my inital thought comes from my understanding of the steady poiseulle flow temperature profile with constant heat flux on the walls (and as you mentionend assumed infinitly long pipe). In that case we should have a constant heat gradient in axial direction. I understood this to be the fluid...
The plot I attached in my previous post is done by examining the oscillatory behavior with no mean velocity on the flow. But I am intending to superimpose a constant pressure gradient on the flow.
Just to give you some context, the endgoal would be to analyse heat flow in a blood vessel with a...
Good evening everybody.
I am new here I hope it is okay to ask this question here.
As part of a project I am trying to examine the effect of a pulsating laminar duct flow on the heat transfer behavior for constant heat flux at the wall for a Newtonian incompressible fluid.
As such I am...