Boundary Conditions Question

anonymousbach · April 3, 2015, 09:37

I'm trying to solve an unsteady thermal diffusion problem, where a flat plate at 0 C has one end immersed in 25 C water. The boundary condition at the immersed end (x=0) is given by

-λ(∂T/∂x)=h(Tinf-T(0,t))

where h and λ are known (Presumably T(0,t=0) can be assumed to be 0 C)

Here is where I am lost, I am not sure how to implement this boundary condition in my TDMA matlab code. Would it be reasonable to make the assumption that the temperature at x=0 immediately goes to steady state? Or is there a way to solve the PDE directly?

Any help would be greatly appreciated

shahrooz.omd · April 3, 2015, 11:01

you don't need to specify the temperature at immersed end. you need to discretize your boundary equation using one-way differencing for (∂T/∂x) then you have aW, aP, aE, Sc, Sp. (either aW or aE will be zero depending on the boundary location)

April 3, 2015, 09:37	Boundary Conditions Question	#1
anonymousbach New Member anonymous Join Date: Apr 2015 Posts: 7 Rep Power: 11	I'm trying to solve an unsteady thermal diffusion problem, where a flat plate at 0 C has one end immersed in 25 C water. The boundary condition at the immersed end (x=0) is given by -λ(∂T/∂x)=h(Tinf-T(0,t)) where h and λ are known (Presumably T(0,t=0) can be assumed to be 0 C) Here is where I am lost, I am not sure how to implement this boundary condition in my TDMA matlab code. Would it be reasonable to make the assumption that the temperature at x=0 immediately goes to steady state? Or is there a way to solve the PDE directly? Any help would be greatly appreciated Last edited by anonymousbach; April 3, 2015 at 09:40. Reason: Clarified type of solver being written

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April 3, 2015, 11:01		#2
shahrooz.omd Member shahrooz Join Date: Aug 2011 Posts: 41 Rep Power: 14	you don't need to specify the temperature at immersed end. you need to discretize your boundary equation using one-way differencing for (∂T/∂x) then you have aW, aP, aE, Sc, Sp. (either aW or aE will be zero depending on the boundary location)