A parabolic trough collector has a tubular steel receiver. The receiver has an outside

diameter of $8$ cm and an inside diameter of $6$ cm with a total length of $17$ m$.$ The receiver surface

is selective with $\backslash$epsi $=0\mathrm{.}14$ and is at $245\backslash$deg C$.$ The glass cover with an emissivity of $0\mathrm{.}90$ and

diameter of $10$ cm is at temperature of $39\backslash$deg C$.$ The space between the receiver and the glass is

evacuated. The environmental temperature is $23\backslash$deg C and the wind speed is $1\mathrm{.}4$ m$/$s$.$

a$)$ determine the heat loss coefficient of the receiver $($UL$)$

b$)$ Given the collector aperture is $4\mathrm{.}9$ m$,$ the inside convection coefficient is $270$ W$/$m$2$

$-$K$,$

and the absorbed solar radiation $($S$)$ is $540$ W$/$m$2$ of aperture area. The circulating fluid

$($specific heat of $1\mathrm{.}4$ kJ$/$kg$-$K$)$ enters the receiver at a temperature of $205\backslash$deg C and at a mass

flow rate of $1\mathrm{.}32$ kg$/$s$,$ determine:

i$.$ The collector efficiency factor

ii$.$ The heat removal factor

iii. The useful energy gain of the collector

iv$.$ The circulating fluid outlet temperature