internal natural boundary conditions

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Author Message   Greg Stortz (g_to_the_reg) Member Username: g_to_the_reg Post Number: 4 Registered: 06-2008 Posted on Thursday, July 10, 2008 - 02:45 pm:    Hi Mr. Nelson, I have a script where I specify a natural boundary condition on an internal boundary. When I specify natural(u) = 10 for example, the flux coming from one side of the boundary plus the flux coming from the other side of the boundary will SUM to 10, not necessarily being split evenly (8 and 2). Take a look at this script to see what I mean. FlexPDE script internal natural bc test.pde (1.2 k) What I really want to specify is that the flux moving into the circle is 10. I could care less what outgoing flux is. Thanks, Greg   Greg Stortz (g_to_the_reg) Member Username: g_to_the_reg Post Number: 5 Registered: 06-2008 Posted on Thursday, July 10, 2008 - 04:40 pm:    I've now realized that the an internal natual boundary condition just increases the flux by what ever is specified. Is there a way to actually specify the value of the flux along the boundary of a region, not the change in flux?   Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1149 Registered: 06-2003 Posted on Thursday, July 10, 2008 - 05:14 pm:    A NATURAL boundary condition on an internal interface specifies the difference between the flux as seen on one side of the boundary from the flux as seen on the other side of the boundary. It is a surface source or sink, not a control on the absolute flux. Natural(0) on an interior interface means that flux is conserved. A Natural() on an interior interface is not strictly a "boundary" condition, because the interface is not a system boundary. If you want to specify a flux of 10 into the inner shell, then throw away the outer shell and program a Natural BC of 10 on the outer surface of the inner shell. If you want to suck a flux of 10 out of the outer shell, throw away the inner shell and program a flux of 10 on the inner boundary of the outer shell. In the general case, the flux at an interior interface is dictated by the equations, material properties, sources and boundary conditions. There is no way in a physical system whereby you can insist that an internal flux be a given number regardless of the properties of the materials and the driving boundary conditions. In your problem, the flux across the interior interface is dictated by the conductivity and the boundary values of 5 on interior and exterior boundaries. In the absence of interior sources, the flux at the interior interface is of necessity zero. If you want a flux of 10 entering the inner shell, you will have to control the outer boundary temperature to be greater than the interior boundary temperature. You can do this in FlexPDE in a manner similar to the example problem "Samples | Misc | HeaterSSI.pde". In that problem, a source rate is varied to produce a desired temperature. In your problem, you can define Tout to be the outer driving temperature, declare it a GLOBAL VARIABLE, and give it the equation for the desired boundary flux. We have done this in the attached script, and the result is that the outer boundary temperature must be 118. bc1.pde (0.6 k)   Greg Stortz (g_to_the_reg) Member Username: g_to_the_reg Post Number: 6 Registered: 06-2008 Posted on Friday, July 11, 2008 - 11:43 am:    Thanks. The file that I sent you isn't my actual project. Though you say that it is un-physical, I have a situation where I really do need to specify an absolute value of a flux at an internal surface. My problem is a heat transfer one where heat is transfered by both conduction and radiation. Please see the attached schematic. schematic schematic.bmp (262.7 k) The flux of conducted heat is -grad(T) and the flux of radiative heat is -grad(e). I am assuming that the flux of radiative heat is a conservative field. At the interface between the hot fuel (molten uranium to be exact) some of the conducted heat is tranfered to radiative heat due to black body radiation. The appropriate bc for T at that boundary is natural(T) = - sig*T^4 - because that's how much conducted heat is lost. The amount of radiative heat that is gained is sig*T^4. But when I specify the BC along that line, I get a flux of about half the flux going up into the air gap, the the other half going through the molten metal. What I want is for all of the flux of radiative heat to move upwards towards the upper wall. I have a natural BC on the upper wall that adds heat according to the normal value of -grad(e). I can't remove all regions except the air gap b/c I still need to model heat transfer by conduction in the rest of the regions. Is it possible to have the variable e only defined within the airgap region?   Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1150 Registered: 06-2003 Posted on Saturday, July 12, 2008 - 07:24 pm:    The PDE system is the controlling description of the model. Any process you want to include in the model must be represented by terms in the PDE system. You can't just jam an inconsistent boundary condition onto an inadequate PDE system and expect to model a new phenomenon. In your case, you will have at the very least three regions with differing diffusivities. In order to incorporate the T^4 loss at the liquid boundary, you will have to pose a system that knows about radiative transfer. There are many ways of simulating radiative transfer, depending on the level of detail needed and on the presence or absence of direct shine and shadowing. One rudimentary approach is that described in our example "Samples | Steady_State | Heatflow | Radflow.pde". That problem models only the radiation energy density (a*T^4) in the system, and provides for some amount of "gap jumping". In some applications, separate variables are declared for the material temperature and radiation temperature. You should consult a text on radiative transfer.