Heat transfer: All 3 modes together

[chetanladha]

Hi.
How can i find out the temperature rise in a steel plate of known dimensions, when exposed to sunlight, losing heat to air flowing over it by convection, and heat getting transferred to another body by convection?
I hope to hear about the different approaches that could be taken.

Thanks in advance.

 

[edgepflow]

Basically, you will perform an energy balance from radiation absorbed from the sun, radiant energy emitted from the plate, and convection energy loss as follows:

Energy absorbed by sun (Es) = absorptivity X solar radiation power density

For a steel plate, you can use absorptivity = 0.5. A good average value of energy from the sun at the surface of the Earth is 750 watt / m^2.

Now the plate will "re-radiate" energy back into space as follows

Er = emmissivity * Stefan Boltzmann constant X surface area of plate (plate surface temperature ^ 4 - sky temperature ^ 4)

you can use emmissivity = 0.21 for your steel plate and sky temperature (not ambient temperature) = - 5 C. Make sure your temperatures are in Kelvin and Rankine.

Finally, use Newton's law of cooling for the convection:

Econv = A * h * (T-surface - T-ambient)

And you can find h from a vertical plate natural convection correlation.

The solution is trial-and-error. Assume a value of T-surface until:

Es = Er + Econv

 

[chetanladha]

Many Thanks for your response.
Can u please explain why have u used sky temperature radiated energy, and not the ambient temperature.

Er = emmissivity * Stefan Boltzmann constant X surface area of plate (plate surface temperature ^ 4 - sky temperature ^ 4)

Also, is it appropriate to use sky temperature as -5, or should it be 3 Kelvin?

 

[edgepflow]

Many Thanks for your response.
Can u please explain why have u used sky temperature radiated energy, and not the ambient temperature.

Er = emmissivity * Stefan Boltzmann constant X surface area of plate (plate surface temperature ^ 4 - sky temperature ^ 4)

Also, is it appropriate to use sky temperature as -5, or should it be 3 Kelvin?

Atmospheric emmision is often estimated as blackbody, hence the "sky" temperature. You want to use an average temperature for the atmosphere so 3 K is too low (would suggest - 5C to -10C).