Question

A metal plate is on an advance and receives 950 W m2 of radiant energy that falls from the sun . The plate absorbs 80 % of the incident solar energy and has an emissivity of0.05 Consider that the lower surface is thermally insulated from the surface of the avenue. If the air temperature is 20 C and the natural convection coefficient of heat transfer between the surface of the plate and the surrounding air is 10 W Im2 K, determine the temperature of the plate

Answer 1

answer : given that -

incident radiant energy = 950 w/m²

radiant energy absorb by plate = 950x 80/100

=760 w/m²

emissivity of metal plate = 0.05

so, thermal radiation from the surface of metal plate = 0.05 x 760

=38 w/m² (since emmisivity is the ratio of thermal radiation from surface to the radiation from a black body at the same temperature and black body radiate as much as it absorb. here, in this case, it is 760 w/m² )

air temperature T₀ = 20 c

= 293 k

natural convection coefficient h = 10 w/m² k

so, heat transfer rate   ...........................1

(NOTE : convective cooling is generally describe by newton 's law of cooling )

from equation 1 :

  

temperature of plate K

...............................................................................................................................QED