A cylindrical reflecting lens focuses direct solar light on a collector pipe through which fluid…

A cylindrical reflecting lens focuses direct solar light on
a collector pipe through which fluid circulates. The heated fluid is used as
the heat source for a heat engine producing mechanical power. The collector
tube is surrounded by a glass tube to reduce heat loss to the ambient
atmosphere. The collector tube diameter is larger than the solar image formed
by the reflecting lens. Use the given data and:

a) Find an analytical expression for the efficiency of the
solar collector (i.e., the ratio of heat collected by the circulating fluid to
the solar flux intercepted by the reflecting lens)
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A cylindrical reflecting lens focuses direct solar light on
a collector pipe through which fluid circulates. The heated fluid is used as
the heat source for a heat engine producing mechanical power. The collector
tube is surrounded by a glass tube to reduce heat loss to the ambient
atmosphere. The collector tube diameter is larger than the solar image formed
by the reflecting lens. Use the given data and:

a) Find an analytical expression for the efficiency of the
solar collector (i.e., the ratio of heat collected by the circulating fluid to
the solar flux intercepted by the reflecting lens) as a function of the ratio
(Tc – Ta)/Qi and the fixed parameters listed
below,

b) if the thermodynamic efficiency of the heat engine is a
fixed fraction of the Carnot efficiency of a reversible heat engine operating
between heat reservoirs having temperatures equal to the collecting fluid
temperature and the ambient temperature, find an analytical expression for the
collector temperature which will maximize the power output of the heat engine,
and determine its nominal value.

Cord of cylindrical lens ( D = 1 m), focal length of cylindrical
lens ( F = 2 m), collector tube outer diameter (d = 0.03 m), design direct
solar flux ( q1 __ = 950 W/m2 ), ambient
atmospheric temperature (Ta = 20 C), temperature of the collecting
fluid (Tc), absorptivity-transmissivity product for the incident solar
radiation focused on the collector tube (__ = 0.75),
reflectivity of lens surface for solar spectrum (_ = 0.9).

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