time step!!!

vijeshjoshi23 · February 2, 2010, 11:09

Hello friends,

I am solving 1-d transient heat conduction equation by FVM. I am trying to analyze "heat flow through a very thin sheet of steel". Sheet thickness is 0.5mm. q on one side is given AND IS VERYING WITH TIME. Becoz of higher K (43 W/m-K) value of steel, I am in need to use very small time step. I used dy=0.5mm/3=0.167mm=1.67e-4 m.. dt=0.01sec ... But results are not converged.. I am using fully implicit scheme to solve the transient cond eq... Do I need to worry abt Courant number?? Is there any other way that I can solve this problem with higher time step???

julien.decharentenay · February 2, 2010, 22:22

Hi,

Can you clarify what do you mean by q (which I take as a heat flux at one end) is "VERYING WITH TIME"?

I understand the need for very small time-step as the plate is both thin and has a high thermal diffusivity. But considering that you are using an implicit integration scheme (and we are talking about diffusion only), I would think that the time-step should relate to the time variation of "q". The courant number is a limitation related to the convection term (Co = Dt * U/ Delta) and is not relevant to a diffusion only problem.

Regards,
Julien

February 2, 2010, 11:09	time step!!!	#1
vijeshjoshi23 New Member Vijesh Joshi Join Date: Mar 2009 Posts: 10 Rep Power: 17	Hello friends, I am solving 1-d transient heat conduction equation by FVM. I am trying to analyze "heat flow through a very thin sheet of steel". Sheet thickness is 0.5mm. q on one side is given AND IS VERYING WITH TIME. Becoz of higher K (43 W/m-K) value of steel, I am in need to use very small time step. I used dy=0.5mm/3=0.167mm=1.67e-4 m.. dt=0.01sec ... But results are not converged.. I am using fully implicit scheme to solve the transient cond eq... Do I need to worry abt Courant number?? Is there any other way that I can solve this problem with higher time step???

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February 2, 2010, 22:22		#2
julien.decharentenay Senior Member Julien de Charentenay Join Date: Jun 2009 Location: Australia Posts: 231 Rep Power: 17	Hi, Can you clarify what do you mean by q (which I take as a heat flux at one end) is "VERYING WITH TIME"? I understand the need for very small time-step as the plate is both thin and has a high thermal diffusivity. But considering that you are using an implicit integration scheme (and we are talking about diffusion only), I would think that the time-step should relate to the time variation of "q". The courant number is a limitation related to the convection term (Co = Dt * U/ Delta) and is not relevant to a diffusion only problem. Regards, Julien