Thermal modelling of parabolic trough collectors - Solar Energy Sciences and Engineering Applications - page 192

Nomenclatures
a accommodation coefficient ( − )

b interaction coefficient ( − )

D pi inside diameter of the receiver pipe (m)

D po outside receiver pipe diameter (m)

D gi inside glass envelope diameter (m)

D go outside glass envelope diameter (m)

f pi friction factor for the inside surface of the receiver pipe, D pi ( − )

convection heat transfer coefficient (W/m 2 - ◦ C) h

thermal conductivity (W/m- ◦ C) k

K θ incident angle modifier ( − )

HTF convection heat transfer coefficient at T f (W/m 2 - ◦ C)

h f

9.81 m/s 2 )

g gravitational constant ( =

Nu Nusselt number ( − )

mean (bulk) temperature of the HTF ( ◦ C) T f

inside surface temperature of receiver pipe ( ◦ C)

T pi

P a annulus gas pressure (mmHg)

q sol solar irradiation per receiver length (W/m)

Pr Prandtl number ( − )

Ra Rayleigh number ( − )

ambient air temperature ( ◦ C)

T a

receiver pipe inside surface temperature ( ◦ C)

T pi

receiver pipe outside surface temperature ( ◦ C)

T po

glass envelope inside surface temperature ( ◦ C) T gi

glass envelope outside surface temperature ( ◦ C) T go

T gi )/2 ( ◦ C)

T po-gi average temperature (T po +

T s effective sky temperature (K)

Greek symbols

α abs absorptance of receiver pipe ( − )

thermal diffusivity for air at T go-a (m 2 /s)

α air

α env absorptance of the glass envelope ( − )

β volumetric thermal expansion coefficient (ideal gas) (1/K)

γ ratio of specific heats for the annulus gas ( − )

δ molecular diameter of annulus gas (cm)

−

ε po receiver pipe selective coating emissivity ( )

ε gi glass envelope emissivity ( − )

ε go emissivity of the glass envelope outside surface ( − )

η abs effective optical efficiency at receiver pipe ( − )

η env effective optical efficiency of the glass envelope ( − )

solar incidence angle ( ◦ ) θ

kinematic viscosity for air at T go-a (m 2 /s) ν air

λ mean-free-path between collisions of a molecule (cm)

10 − 8 W/m 2 -K 4 )

σ Stefan-Boltzmann constant ( = 5.67 ×

τ env transmittance of the glass envelope ( − )