6. A solar flux of 700 W/m² is incident on a flat-plate solar collector used to heat water.
The area of the collector is 3 m², and 90% of the solar radiation passes through the
cover glass and is absorbed by the absorber plate. The remaining 10% is reflected
away from the collector. Water flows through the tube passages on the back side of
the absorber plate and is heated from an inlet temperature Ti to an outlet temperature
To. The cover glass, operating at a temperature of 30 °C, has an emissivity of 0.94
and experiences radiation exchange with the sky at -10 °C. The convection
coefficient between the cover glass and the ambient air at 25 °C is 10 W/m² K. (30
points)
Cover glass
Air space
Absorber plate
Water tubing
Insulation
(a) Perform an overall energy balance on the collector to obtain an expression for the
rate at which useful heat collected per unit area of the collector, q" u. Determine the
value of q" u.
(b) Calculate the temperature rise of the water, To-Ti, if the flow rate is 0.01 kg/s.
Assume the specific heat of the water to be 4179 J/kg K.
(c) The collector efficiency n is defined as the ratio of the useful heat collected to the
rate at which solar energy is incident on the collector. What is the value of n?

The rate of heat transfer from the sun into the metal plate by radiation must be equal to the rate of heat loss from the plate to the surrounding air by convection.

What is the rate of heat transfer?

The temperature difference divided by the total thermal resistance between two surfaces equals the rate of heat transfer between two surfaces.

The rate at which an object transfers energy by heating is determined by the following factors: the object's surface area, volume, and material, as well as the nature of the surface with which the object is in contact.

We know that,

qᵃ = qᵇΔT

where

a is the Radiation energy source

b is the Convection energy source

ΔT = Tp - Ta = Temperature difference between the plate and the surrounding air under equilibrium conditions.

Given that,

qᵃ = 700 W/m2

qᵇ = 10 W/m2K - 100 W/m2K

So the qᵇ = 10 W/m2K,

ΔT = qᵃ / qᵇ

ΔT = 700/10 = 70K

Also, for qᵇ = 100 W/m2K

ΔT = 700/100 = 7K

Under equilibrium conditions, the temperature change of the plate ranges from 7K to 70K.

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