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 Mike June 5, 2003 04:04

time steps in transient heat transfer in solids

Hello,

Is there any criteria for the time steps doing transient calculation with heat transfer in solids?

I found one for the convective mass transport saying

2*dt*nu/rho < L^2

L ... mean mesh size dt ... time step rho ... density nu ... dynamic viscosity

Is that criteria correct?

Is it possible to compare the energy-equation with the one for mass transport, so that I get a similar criteria for heat transport in solids?:

2*dt*lambda/(rho*cp) < L^2

L ... mean mesh size dt ... time step rho ... desnity lambda ... heat conduct. of solid cp ... spec. heat

 gorka June 5, 2003 04:58

Re: time steps in transient heat transfer in solid

Hi,

It depends on whether you use an explicit or implicit method for time discretization. Usually:

Explicit: 2*dt*lambda/(rho*cp) < L^2 (as you have pointed out)

Implicit: No restrictions for convergence (only for accuracy)

Semi-implicit (Crank-Nicolson): No retrictions for convergence but a restriction to avoid unphysical results:

dt*lambda/(rho*cp) < L^2

Hope this helps,

Gorka

 Mike June 5, 2003 05:30

Re: time steps in transient heat transfer in solid

Hello,

Thank you very much - that really helps a lot, Gorka.

I have an implicit scheme, so it should be only a question of accuracy.

Do you have any advice how I can measure or see accuracy without having experimental data? Or is there any hint how to choose the time steps in fully imclicit scheme?

Mike

 gorka June 5, 2003 05:47

Re: time steps in transient heat transfer in solid

Hi,

The Implicit scheme is first order accurate unless you use results from the two previous time-steps (n and n-1, being n+1 the new time step, in which you evaluate the terms). Therefore, you should use small time steps if you want to obtain accurate results. Sorry but I donīt know any specific criterium.

Gorka

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