## Radiative heat transfer

## Radiative heat transfer

(OP)

Hello,

I'm having difficulties calculating the time to reach a certain temperature caused by radiation. I cannot find any method to get time into my calculations.

Any help?

Specific problem:

Double-walled tank with the outer wall at 700 °C. How long does it take for the inner wall to reach 500 °C?

I've calculated that the conduction trough the walls is so rapid that this does not has to be calculated.

Also the convection of the air between the walls is negligible. So I guess the inner wall is only heated due radiation. Correct?

Thanks!

I'm having difficulties calculating the time to reach a certain temperature caused by radiation. I cannot find any method to get time into my calculations.

Any help?

Specific problem:

Double-walled tank with the outer wall at 700 °C. How long does it take for the inner wall to reach 500 °C?

I've calculated that the conduction trough the walls is so rapid that this does not has to be calculated.

Also the convection of the air between the walls is negligible. So I guess the inner wall is only heated due radiation. Correct?

Thanks!

## RE: Radiative heat transfer

Time is a factor of heat input and mass of metal - heat capacity of the metal. as you say you can assume that the entire wall heats up at the same rate. Caron steel is 0.49 Kj/kg/K.

So at a fairly basic level if you have 10kg of steel and Input of say 1kW (1000J/sec) it will take 49 seconds to go up 10 degrees C assuming no losses from the lump of metal

The other factor is whether any heat then "escapes" from the inner wall or do you ignore those losses?

I'm surprised you think convection isn't a factor care to share how you came to that conclusion?

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Radiative heat transfer

For calculating the overall heat transfer coefficient:

1/U = 1/h + D/k

there isn't much air between the walls, and only natural convection occurs. So let's assume

h = 10 W/m²K (which is an overestimation)

D = 0.02 m

k= 20 W/mK (for steel)

1/U = 0.1 + 0.001 = ... so the walls are thin enough to rule out the conductivity.

Now q = U (T1-T2) + o-(T1^4-T2^4)/(2/e-1) (which is the conduction/convection plus the radiation part)

o- = Boltman constant = 5.67*10^-8

e=0.85 for steel

q = 10*(1000-800) + 5.67E-8*5,904E+11

= 2000 + 33475

So because the radiation part is much larger, we can rule out the convective part.

I know it is an estimation, but that's okay.

## RE: Radiative heat transfer

I assume a fire under a tank. I assume the tank fails when the inner wall reaches 500°C. That's why I need to calculate the time for this to happen.

I assume the surface as infinite, so no masses or surfaces.

The tank is filled with liquid at atmospheric temperature. How can I incorporate this? How can I calculate the time?

## RE: Radiative heat transfer

"In this bright future, you can't forget your past..." Bob Marley

## RE: Radiative heat transfer

however if the inner tank is filled with liquid then I think you're doing this all wrong.

Fire cases are about the change in pressure and potential boiling / over pressure of the tank.

Normally if you have an intense fire under a piece of equipment, you assume it will fail at some point. What you don't want it to do is explode and create further hazards.

You then bund the tank so if the contents come out and catch fire you limit the area of the fire.

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Radiative heat transfer

Matter of the case is really to calculate when (theoretically) the inner wall will fail, not considering any explosions or leaks.

## RE: Radiative heat transfer

Lets go back a bit here.

What sort of fire?

Where has 700C come from?

why fail at 500?

What about outer wall failure?

What is liquid boiling point?

Is the venting system good enough to handle the boiling liquid?

Is there a secondary bund?

Why is this thing double walled in the first place

What sort of fire protection do you have?

All much more important than figuring out when the inner wall fails

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Radiative heat transfer

What sort of fire? just A fire

Where has 700C come from? outer wall temperature when subjected to pool fire

why fail at 500? just an estimation

What about outer wall failure? I assume the vessel as lost

What is liquid boiling point? don't know

Is the venting system good enough to handle the boiling liquid? don't know

Is there a secondary bund? don't know

Why is this thing double walled in the first place? don't know

What sort of fire protection do you have? The question is, which fire protection is needed? That's the whole point of calculating time. Is there enough time to deploy a monitor, or is a fixed cooling system needed?

I don't need a precise calculation, just a rough time like is it 5 sec, 10 min, 1 hr?

## RE: Radiative heat transfer

Use 1m2 as your heat area which also give you your mass of steel to heat up.

Question then will be how much mass do you assume is not affected by the pool fire. - 50%?

If the tank has liquid that boils at your storage pressure a long way from 500C, then I'm pretty sure your issue is not failure of the inner tank, but the amount of vapour being generated and avoidance of the tank / vessel ( which is it - makes a big difference) exploding.

The point about type of fire is whether it is a general fire / heat or a jet fire with impingement onto the surface? The latter will be much quicker to destroy your vessel.

You might find the following guide useful

http://www.hse.gov.uk/pubns/books/hsg176.htm

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Radiative heat transfer

Sanika Patel

http://crbtech.in/CAD-CAM-Training/

## RE: Radiative heat transfer

## RE: Radiative heat transfer

epsilon * area * sigma * (T^4 - Tsur^4) = rho * volume * c * dT/dt

Actually, if you only have radiation there is an exact solution to the equation, you don't have to do a numerical solution.

But you really should read the whole chapter to make sure that all the assumptions hold for your system (such as spatial effects).

## RE: Radiative heat transfer

Good luck!

K