Solar energy conversion with thermal cycles - Solar Energy Sciences and Engineering Applications - page 415

can be representative of a Rankine cycle 2 , the conversion efficiency (

η carn )isas

follows:

T amb
T max

η = 1 − (14.2.2)

Carn

where T amb is the ambient temperature and T max is the maximum temperature in the
cycle.
From this formula, it can be deduced that the higher the maximum temperature of
the cycle, the higher the ideal conversion efficiency from thermal power to electricity.
For example, moving from a maximum temperature of 600 K to 1000 K, the Carnot
efficiency increases from 50% to 70%.
Moving on to the second term of ideal conversion efficiency, η th represents the

.
Q ABS , and the heat concentrated

ratio between the net heat absorbed by the collector,

.
Q CONCENTRATED :

on the collector itself

· Q ABS
· Q CONCENTRATED

η th = (14.2.3)

In a CSP plant, solar energy is concentrated on an absorber by a collecting structure;
the entire system is designed to capture most of the solar energy and transfer it to a fluid
inside the absorber. In order to produce useful heat for the power cycle, the absorber
must be at a high temperature and consequently it will emit energy to the environment
as infrared emissions 3 . Therefore the net heat absorbed by the collector ( . Q ABS ) can be
written as the difference between the energy received from the collecting system and
the energy emitted to the environment, as expressed by the following equation:

· Q ABS = · Q CONCENTRATED − · Q EMITTED =

( T abs − T amb )

α · C · G − σ · ε · (14.2.4)

where α is the hemispherical absorptivity of the absorber, C is the geometrical con-
centration ratio of the collector, G is the direct normal irradiance [W/m 2 ], epsilon is
the hemispherical emissivity of the absorber, sigma is the Stefan-Boltzmann constant
[5.67e-08 W/m 2 K 4 ], T abs is the average temperature of the absorber and T amb is the
sky temperature or the temperature viewed by the absorber [K].
With regard to the non-dimensional coefficient, the thermal efficiency of a collector

( η th ) can be expressed as the ratio between the net heat absorbed by the collector and the

heat concentrated on the collector itself (all these formulae assume a unitary surface):

· Q ABS
· Q CONCENTRATED =

· Q ABS
C

· Q EMITTED
C

( T abs − T amb ) σ · ε ·

η th =

G −

= α −

· · G CG

(14.2.5)

2 See section 14.5 for a detailed discussion of a Rankine cycle.
3 Any body at a temperature above 0 K emits radiation energy expressed by the Stefan-Boltzmann
Law (Incropera & DeWitt, 2007).