Dear Mr. Israel,

Thanks for your comment. I have attached the worksheet. I am solving the simple heat conduction equation (below) for three domains.

diff(T(x,t),t)=r*diff(T(x,t),x,x)

and r is defined as a piecewise function.

I do agree with you the heat flux should be continuous. I am not sure if the use of piecewise function in PDEs is the right strategy. 

I used a very small spacestep=0.0005, bot no answer after one hour of waiting. 

Thanks in advance for your help,

Mo

multilayer-conductio.mw