# Energy balance and collector efficiency factor

Calculation of the thermal and optical characteristics of the transparent cover of an air collector with an under flowed absorber follows the method already described for water collectors, as the geometry of the glazing, the standing air layer and the absorber is identical. The heat transfer between the absorber and the fluid now takes place only perpendicularly to the absorber level. The geometry-dependent collector efficiency factor can thus be deduced from a stationary energy balance of three temperature nodes. glass cover absorber air flow insulation

At node a of the absorber, the irradiance G let through with the transmission coefficient t is absorbed by the absorber sheet metal with the absorption coefficient a. The calorific losses through the transparent cover against the exterior temperature To are calculated by the heat transfer coefficient Uf. Convective heat with the heat transfer coefficient hc, a-f is transferred to the heat distribution medium fluid with temperature Tf, and heat is exchanged by the radiation heat transfer coefficient hr, a – with the rear wall of the flow channel with temperature Tb.

G (та)-Uf (f – T0)-hca_f (f – Tf)-hra_b ( – Tb )_ 0 (3.109)

At node f of the heat distribution medium fluid, the available power Qu is produced over the collector width B and the distance Ax in the direction of flow. This power consists
of the amount of heat transferred convectively from the absorber (with hca-) and from the rear (with hc, b – ).

Qu – hca_fBAx (Ta – Tf)-hcb_fBAx(Tb -Tf ) = 0 (3.110)

At node b of the rear wall of the flow channel, heat is radiated from the absorber sheet metal with a radiative heat transfer coefficient hr, b-l, and at the same time heat is transferred convectively to the fluid. Calorific losses to the ambient air develop via the collector rear with the heat loss coefficient Ub.

Kb-a T – Tb )-hCb-f T – Tf)-Ub (Tb – To ) = 0 (3.111)

Equations (3.109) and (3.111) are solved for the absorber and rear wall temperatures Ta and Tb as a function of the fluid and ambient temperatures Tf and To, and these are inserted into the useful power Equation (3.110). Thus a conditional equation for the available power

Q>u is obtained which depends only on the fluid and ambient temperatures, Q = AF1 (T(та)-Ut ( – T0))   the collector efficiency factor F being given by:

and Ut represents the total of the heat transfer coefficients over the front, back and sides. The functional dependency of all characteristics on temperatures and flow rates is discussed in the following section.

Updated: August 4, 2015 — 5:07 am