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# Boundary Element Method for 2 Layer Heat conduction

Hi there,

I'm trying to solve this heat conduction problem using boundary element methods. The problem involves a circle that is cut into half, with each having its own thermal conductivity (k). I'm required to determine the temperature field for both these halfs so that i can find the temperatures at any given point within the region.

I managed to do the one for a homogeneous material but faced problems with this case. There was this eqn i saw from an article that involved the combination of regions :

HU = GQ

I understand the approach would be to solve one half of the circle at a time. But i don't understand how to include the boundary conditions at the interface btwn both the halves. And to solve the matrices. Help anyone?
csanthosh1989 • Jan 12, 2009
Don't worry refer the correct formulas in heat & mass transfer data book
bemsoc • May 8, 2009
Depends on the interface. If the solids are perfectly bonded on the interface, that is, "an ideal (perfect) interface" the two conditions to impose on the interface are:

(a) "T in R1"="T in R2" at points on interface
(b) "heat flux of T in R1 across interface"
="heat flux of T in R2 across interface"

Notes: "T in R1" means "temperature in solid 1"
In (b), the fluxes on RHS and LHS are calculated
using unit normal vector pointing in the same direction.

You can also have imperfect interfaces in which case (a) and (b) have to be modified appropriately.