# Surface temperature of a radiated plate

1. Jul 29, 2014

### marco75

Hi,
I would like to know what is the surface temperature of a material when it is radiated from another material at a certain distance. In other words: I have a material at 120°C (aluminium) and another parallel plate of area A faced to the first one at 10cm of distance. What is the surface temperature of the faced material?
This problem is general, so all data (emissivity, room temperature, etc.) are free, I would like to have a conceptual response, my numerical data are only to example purposes.

2. Jul 29, 2014

### davenn

the surface temp would depend on at least its colour and type of material

if it was a darker colour then it would absorb more energy and get hotter
think of a white car to a black car in the summer sun

other factors would also come into play

Dave

3. Jul 29, 2014

### marco75

Hi davenn,
many thanks for the answer. Yes, I understand what you say, but I would like to know a mathematical formulation, so we can suppose aluminium for both materials and choose some reflectivity, absorption and transmission values (I don't know if the correct analysis is obtained by means of the Kirchhoff law (thermal...)).

Marco

4. Jul 30, 2014

### 256bits

Is all of the radiation from each plate being exchanged between the 2 plates?

For smaller plates not so, as some radiation from each will bypass and not strike the other.
An assumption of infinite plates can be made, if the seperation distance is much smaller than the area of the plates.

See
http://www.chem.mtu.edu/~fmorriso/cm310/heat_lecture_20.pdf

5. Jul 30, 2014

### Matterwave

Is the 120 degree plate kept at that temperature indefinitely, or does it cool as it radiates its heat away?

6. Jul 31, 2014

### marco75

Hi 256bits and Matterwave,
thank you for the answers. The hot plate remain at 120°C indefinitely and the assumption of infinite plates cannot be made, because we have the following schema: an heater at 120°C has a size of 14cm x 7cm (hot plate) is faced to another aluminium plate (same size) at a distance of 10cm.

Thanks again,
Marco