A flat-plate solar collector is used to heat water by having water flow through tubes attached at the back of the thin solar abs
orber plate. The absorber plate has a surface area of 2 m2 with emissivity and absorptivity of 0.9. The surface temperature of the absorber is 35°C, and solar radiation is incident on the absorber at 500 W/m2 with a surrounding temperature of 0°C. The convection heat transfer coefficient at the absorber surface is 5 W/m2 ∙K, while the ambient temperature is 25°C. The net heat rate absorbed by the solar collector heats the water from an inlet temperature (Tin) to an outlet temperature (Tout). If the water flow rate is 5 g/s with a specific heat of 4.2 KJ/kg *K, determine the temperature rise of the water.
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Answer:
a) ΔEC=-23.4kW
b)W=12106.2kW
c)
Explanation:
A)
The kinetic energy is defined as:
(vel is the velocity, to differentiate with v, specific volume).
The kinetic energy change will be: Δ ()=
Δ ()=
Where 1 and 2 subscripts mean initial and final state respectively.
Δ()=
This amount is negative because the steam is losing that energy.
B)
Consider the energy balance, with a neglective height difference: The energy that enters to the turbine (which is in the steam) is the same that goes out (which is in the steam and in the work done).
We already know the last quantity: =
Δ (
)=23400W
For the steam enthalpies, review the steam tables (I attach the ones that I used); according to that,
The exit state is a liquid-vapor mixture, so its enthalpy is:
Finally, the work can be obtained:
C) For the area, consider the equation of mass flow:
where
is the density, and A the area. The density is the inverse of the specific volume, so
The specific volume of the inlet steam can be read also from the steam tables, and its value is: , so: