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# Modelling heat transfer through a slab

## Modelling heat transfer through a slab

(OP)
Hi all, I am trying to model 1d, transient heat conduction through a slab.

Basically, one side of the slab is exposed to 200C and the other side is insulated and starts at -20C.
I want to model this in MATLAB by solving the 1d transient heat equation with no heat generation.
How do I go about doing this assuming I know the thermal diffusivity of the slab?

I have looked for many resources on the internet but have no found anything that describes what I want to do in a clear way.
If anyone could point me in the right direction it would be much appreciated.

Cheers.

### RE: Modelling heat transfer through a slab

A long time ago, I performed an ANSYS transient analysis of a concrete slab subject to a relatively quick heating event.... It was a study for protection of electrical equipment in a nuclear power plant.

What I discovered is that concrete will heat up, but very, very slowly. Before the first four inches of the slab could heat up, the event was long over.

MJCronin
Sr. Process Engineer

### RE: Modelling heat transfer through a slab

depends on your required accuracy - but you could get pretty far by relying on the std. heat transfer theory

### RE: Modelling heat transfer through a slab

see:

Conduction of Heat in Solids by H.S. Carslaw & J.C. Jaeger, 2nd Ed., Oxford University Press, Section 5.6.III, p.173. HIH.

### RE: Modelling heat transfer through a slab

"the other side is insulated" ... ?

You mean you are going to assume the far side of the slab (horizontal of vertical ?) is NOT going to transfer ANY heat energy at all, or that it is insulated (by real world insulation) and that insulation is going to only reduce heat transfer out the far side.

Is the heated side "suddenly heated to 200 degrees (as if a hot liquid were poured on the top of a slab of ???) and then cools off itself and the fluid to some middle temperature?
or the slab underneath a constantly replenished constant-temperature flow of a fluid or gas at 200 degrees - so that the end state of the slab is at approximately 200 deg F?
Or it the 200 degrees a momentary thing that then "goes away" somehow - so that the slab ends up back at some final temperature after it loses the 200 deg "bump"?

This is so far-fetched it sounds like a homework problem. No real world problem works like this.

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