A solar radiation flux of 700 W/m2 is absorbed in a metal plate that is perfectly insulated on the back surface. The convection heat transfer coefficient may vary from 10 W/m2K up to 100

Calculate the temperature of the plate under equilibrium conditions.

The main solution to this problem is to note that under equilibrium conditions, the rate at which heat is transferred into the metal plate from the sun by radiation must be equal to the rate at which heat is lost from the plate to the surrounding air by convection.

Explanation:

Therefore, qᵃ = qᵇΔT

where

a = Radiation energy source

b = Convection energy source

ΔT = Tp - Ta = Temperature change between the plate and the air under equilibrium condition

Given,

qᵃ = 700 W/m2

qᵇ = 10 W/m2K - 100 W/m2K

Hence, for qᵇ = 10 W/m2K,

ΔT = qᵃ / qᵇ

ΔT = 700/10 = 70K

Similarly, for qᵇ = 100 W/m2K

ΔT = 700/100 = 7K

The temperature change of the plate under equilibrium conditions range from 7K to 70K.