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Question about NDSolve for combined PDE and ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg14551] Question about NDSolve for combined PDE and ODE
• From: Don Paddleford <don-paddleford at worldnet.att.net>
• Date: Thu, 29 Oct 1998 04:33:43 -0500
• Organization: AT&T WorldNet Services
• Sender: owner-wri-mathgroup at wolfram.com

Would/should Mathematica's NDSolve function be able to solve a PDE
coupled with  an ODE at the boundary? For example, a PDE (the time
dependent diffusion  equation) for heat transfer within a thick wall,
and an ODE for the  adjacent room air temperature (which would include
some time dependent  heat sources/sinks) when they are coupled at their
common boundary by a  convection heat transfer coefficient.

I have seen the examples where NDSolve has been used to solve PDE with a
time dependent boundary condition, and even two coupled PDE's in
special  cases---but haven't seen the above type problem. I have tried
without  any success, and would like to know whether I am not setting
problem up  right, or whether it is beyond NDSolve's capability. In
fact, would be  interested in finding any guidance as to NDSolve's 
capabilities/limitations for solving PDE's.

Thanks
Don