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Implement constant heat flux boundary condition

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Old   April 6, 2012, 11:09
Default Implement constant heat flux boundary condition
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Peter
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I have written a matlab code that will solve for the developing temperature field given a velocity field. At the moment I have already implemented the constant wall temperature boundary condition and the results look correct.

Now I am trying to implement the constant heat flux boundary condition. I have the equation below
q'' = -k \frac{\partial T}{\partial n} = -k \frac{T_1-T_w}{\Delta y}

where T_1 is the first interior point and T_w is the wall temperature.

I convert to non dimensional temp
\theta = \frac{T - T_e}{q''\frac{H}{K}} and calculate the appropriate \theta_w so that it satisfies the flux and implement it as a dirichlet condition.

When I calculate Nu, defined as
Nu = \frac{1}{\theta_w-\theta_b}

it doesn't ever reach steady state. When it is supposed to reach steady state, the wall temperature increases more slowly than the bulk temperature and I get a decreasing Nu. Anyone seen this type of behavior before or know whats going on? Am I implementing the constant flux boundary condition properly?
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Old   April 6, 2012, 21:46
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"and calculate the appropriate so that it satisfies the flux and implement it as a dirichlet condition"
Could you pleaase explain" implement the second kind bc as a first kind".

at the heat flux bc, the boundary condition should like
partial(theta)/partial(n)=?
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Old   April 6, 2012, 23:35
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so by subbing in \theta the equatioin becomes

q'' = -k\frac{\theta_1-\theta_w}{H\Delta y^*}q''\frac{H}{k}

In my case I have also non dimensionalized y as y*H = y.

I know everything in the above equation except for \theta_w so I can solve for it and then I implement it as a dirichlet condition.
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