To determine the mean temperature of the absorber plate is a complicated function of the conductivity of the material, heat transfer inside of the channels and geometric configuration. To consider these factors along with the energy collected at the
absorber plate and heat loss, the collector efficiency factor and the collector heat removal factor are introduced.

The collector efficiency factor, F, represents the temperature distribution along the absorber plate between channels. This collector efficiency factor F’ is defined in the familiar Hottel-Willier-Bliss model, where

The collector heat removal factor, FR, is the ratio of the actual useful energy gain of a collector to the maximum possible useful gain if the whole collector surface were at the fluid inlet temperature. It is defined as [1]:

Fr = mCp (To — Ti )

Ap [S — Ul’ (Ti — Ta)] (3.2.3)

By introducing the collector heat removal factor and the modified overall heat transfer coefficient into Equation 3.1.1, the actual useful energy gain Qu can be represented as

Qu = Ap Fr [S — Ul’ (Ti — Ta)] + (3.2.4)

Since Sc = S (Ap/ Ac) and Ul’ = Ul(Ac/ Ap) implies equation 3.2.1 can be expressed as

Qu = Ac Fr [Sc — Ul (Ti — Ta)] + (3.2.5)

This allows, the useful energy gain to be calculated as a function of the inlet fluid temperature not the mean plate temperature.

For accurate predictions of collector performance, it is necessary to evaluate properties of the working fluid to calculate the forced convection heat transfer coefficients inside the tubes and the overall loss coefficient. The mean fluid temperature Tfm at which the fluid properties are evaluated can be obtained by [1]:

Tfm = Ti + [(Qu / Ap)/ (Fr Ul’)] ( 1 — F”) (3.2.6)

Where the collector flow factor F” defined as the ratio of FR to F’, is given by

F”= Fr / F’ = (mCp /ApUl’F’) [1 — exp (ApUl’F’/mCp)] (3.2.7)

Equating equations 3.2.4 and 3.2.6 and solving for the mean plate temperature TPM yields:

Tpm = Ti + [(Qu / Ap)/(FR Ul’)] (1- Fr) (3.2.8)