| Author | Message | ||
     Wilson Chen (emptyempty) Member Username: emptyempty Post Number: 4 Registered: 09-2003 |
Hi, Mr. Nelson, I am trying to convert a line source into an equivilent surface source in a heat conduction problem (The discription of the problem is at the beginning of the script). According to Divergence Theorem, I think both sources should give the same temperature field. But in the simulation, all results seems have a 2 times relationship. In particular, the result of intergrating flux along the perimeter for line source is even not the same as 2*Pi*R*LineSource. Is there anything wrong about my understanding? If it is, could you please show me how to convert between two kind of sources? Thank you very much! Best regards, Wilson ######################################################## { This is to test if the surface heat source has the same effect as line heat source. In surface heat source case, heat is produced inside the circle with a constant heat production rate, and is conducted outward the square, whose edges are specified to be T=0. In the line heat source case, heat is only generated in the erimeter of the circle, other conditions are the same According the Divergence Theorem, temperature field and heat flux flowing out of the circle should be the same for both cases. But in this simulation, there is a 2 times relationship between all results. Is there anything wrong? } title 'Surface Source = line source?' select errlim=1e-3 variables T definitions L=600 W=500 R1=25 C1_x=L/2 C1_y=W/2 k=1 source=0 !Surface source =5 Ssource=5 !Line source: Line source * 2 * Pi * R = Surface source * Pi * R^2 Lsource=Ssource*R1/2 { Heat flux flowing out of the perimeter of the circle } Tflux = LINE_INTEGRAL(NORMAL(-grad(T)), "ring 1") equations div(k*grad(T))+source=0 boundaries region 1 source=0 start(0,0) value(T)=0 line to (L,0) value(T)=0 line to (L,W) value(T)=0 line to (0,W) value(T)=0 line to finish region 2 !source=Ssource { Inactive this line if use Line Source condition} START "ring 1" (C1_x-R1, C1_y) natural(T)=Lsource {! inactive this line if using surface source condition.} ARC (CENTER=C1_x,C1_y) ANGLE=360 TO FINISH monitors contour(T) plots contour(T) surface(T) vector(-grad(T)) elevation(T) from (0,W/2) to (L, W/2) elevation(dx(T)) from (0,W/2) to (L, W/2) !history summary report(Tflux) {!Note that in the line surface source case, this flux does not make sense, why?} end | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 284 Registered: 06-2003 |
It appears that in version 4.2 we introduced an error in handling interior surface sources (imbedded Natural BCs) that causes double application. I will correct this and post a revised version in a few days. | ||
| Wilson Chen (emptyempty) Member Username: emptyempty Post Number: 5 Registered: 09-2003 |
Hi Mr. Nelson, Thanks a lot! I am looking forward to seeing the new version. Best regards, Wilson |