# What will be the temperature of surroundings, in radiation heat transfer equation?

1. Aug 24, 2011

Hi.

I want to calculate the heat which will be lost from a body at temperature 't' to the atmosphere through radiation heat transfer. I can use Stephen's Boltzmann equation, but what should i take the temperature of surroundings as?

Should it be the temperature of air or space?

Thanks.

2. Aug 24, 2011

### xts

Re: What will be the temperature of surroundings, in radiation heat transfer equation

It depends on weather conditions and surroundings.
Have you ever parked your car wintertime (clear night) on the open area or under tree or under open sched? It gets more frosted on the open area, as it loses heat to the sky, while under sched you should take the temperatur of sched roof.
Similar effect you may find comparing temperature on clear and cloudy nights - clear nights are much colder, because you lose heat to the sky, why on cloudy nights most of the radiation is reflected.

BTW - using Stefan's law - be careful - most of the objects cannot be treated as black-body. Even if some object is visually black, don't believe it is also 'black' outside visual spectrum.

3. Aug 24, 2011

Re: What will be the temperature of surroundings, in radiation heat transfer equation

That was a good description.
I am giving the value of emmissivity in Stefan's law, so i guess that shouldn't be a problem.

I am calculating the radiation heat loss from a steel plate in open atmosphere clear sky. So, now what should i take the temperature of sky as?

4. Aug 24, 2011

### xts

Re: What will be the temperature of surroundings, in radiation heat transfer equation

Not be that sure. For most substances emissivity depends on a wavelength. So you should rather integrate Planck's law over wavelength, than assuming it is uniform. For many materials results may dramatically differ. Snow is a perfect example - having very small emissivity in visual spectrum, while pretty large in infrared - that's why the weather changes to much colder as soon as first snow covers ground.

As the rough approximation you may just forget about sky temp and assume it is 0K. Error you make will be still much less probably than by assuming uniform emissivity of of your plate.

5. Aug 24, 2011

Re: What will be the temperature of surroundings, in radiation heat transfer equation

Thanks a lot. It was really helpful.

6. Aug 24, 2011

Re: What will be the temperature of surroundings, in radiation heat transfer equation

Hey.. Sorry but 1 more small q.

I calculated the heat flux from sun on my plate to be around 51kW. (assuming solar intensity 1000kW/m2).
The stephen law gives me heat lost to the surroundings in order of 72kW (using constant value of emissivity).

Apart of not using constant value of emissivity, can i assume part of heat is going to air at 30 C and rest to 0 K.
Also m really afraid of integrating Plank's law, unless its a must..

What do u think..??

7. Aug 24, 2011

### xts

Re: What will be the temperature of surroundings, in radiation heat transfer equation

Oh, I see you must live in some place in the world where my examples with car getting frosted in the night and snow emissivity are not so common experience

Probably your steel has lower emissivity in infrared than in visual spectrum. Your result is against my intuition: it absorbs less from Sun than emits. It would mean it is getting colder than surroundings. My intuition tells me that steel (maybe except very shiny polished acidproof steels) gets hot in the sunlight faster than soil, concrete, bricks, etc., so something had to be wrong in your calculations.

Anyway - it is not that easy to model the heatflow with reasonable accuracy. Even if you integrate Planck's law over whole spectrum...
In most cases the experimental approach is used to determine the values used for practical calculations.