Implement constant heat flux boundary condition

new_at_this · April 6, 2012, 12:09

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?

ztdep · April 6, 2012, 22:46

"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)=?

new_at_this · April 7, 2012, 00:35

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.

April 6, 2012, 12:09	Implement constant heat flux boundary condition	#1
new_at_this Member Peter Join Date: Oct 2011 Posts: 52 Rep Power: 16	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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April 6, 2012, 22:46		#2
ztdep Senior Member p ding Join Date: Mar 2009 Posts: 436 Rep Power: 20	"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)=?

April 7, 2012, 00:35		#3
new_at_this Member Peter Join Date: Oct 2011 Posts: 52 Rep Power: 16	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 yH = 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.