Question

A solar collector installed on the roof of a SoCal home is used to heat water flowing through ducts attached at the back of the collector. The absorbing surface has an area of 2 m2 with an emissivity of 0.9. The surface temperature of the absorber is 35 °C, and solar radiation is incident on the absorber at 450 W/m2. Temperature of surrounding air is 22 °C. Heat transfer coefficient at the absorber surface is 5 W/m2·K. If water is pumped through the ducts at 5 g/s, determine the temperature rise of the water. Water has a specific heat capacity of 4.2 kJ/kg·K. How does the temperature rise change when conditions become breezy forcing the heat transfer coefficient to increase to 25 W/m2.K?

Answer 1

Overall energy balance

= absorptivity = 1

= incident energy = 450 W/m2 = 450*2 = 900 W

= energy emitted by absorber

= heat transfer by convection to surroundings

Heat transfer by radiation

• 

= emissivity of plate = 0.9

= Stefan-Boltzmann constant = 5.67*10^-8 W/m2-K4

= area of plate = 2 m2

= surface temperature = 35 + 273 = 308 K

= temperature of surrounding = 22 + 273 = 295 K

Q emit = 0.9 x 5.67 x 10^-8 x 2 x (308⁴ - 295⁴) = 145.52 W

Q convection = h x A x ( - ) = 5 x 2 x (35-22) = 130 W

Overall energy balance

900 - 145.52 - 130 = E system

E system = 624.48 W

= mass of water x Cp water x temperature rise

624.48 = 5 x 10^-3 kg/s x 4.2 x 10^3 J/kg-K x temperature rise

temperature rise of water = 29.73 K

when conditions become breezy

Q convection = h x A x ( -   ) = 25 x 2 x (35-22) = 650 W

Overall energy balance

900 - 145.52 - 650 = E system

E system = 104.48 W

= mass of water x Cp water x temperature rise

104.48 = 5 x 10^-3 kg/s x 4.2 x 10^3 J/kg-K x temperature rise

temperature rise of water = 4.975 K