Question 6.16: In an experimental plant of a Renewable Energy Laboratory, t......
In an experimental plant of a Renewable Energy Laboratory, three types of solar installations are available:
(1) 5 m² of flat solar collectors that heat a water flow of 76 L/h from 12°C to 40°C.
(2) 2.4 m² of vacuum tube collectors that produce a mass flow of 0.4 g/s of saturated steam at 100°C from water at 35°C.
(3) Some photovoltaic cells of 1.4 m² that generate electricity at 0.50 V and 400 A.
If the solar irradiation is 800 W/m² and the ambient temperature is 15°C, determine
(a) The energy efficiency in each type of solar installation.
(b) The irreversibilities and exergy efficiency in each type of installation.
(a) The incident radiation on flat collectors is 4000 W. The increase in enthalpy of the water is
\Delta\dot{H}_{w}=\dot{m}_{w}c_{w}(T_{o u}-T_{i n})=2.47\,k WThe energy efficiency of flat collectors is
\eta_{c}=\frac{\Delta\dot{H}_{w}}{A_{c}G_{s}}=61.8\%For the vacuum tube collectors, the incident radiation is 1920 W. The change of enthalpy of the water is
\Delta\dot{H}_{\nu}=\dot{m}_{w}(h_{\nu}-h_{w})=\dot{m}_{w}(l_{100^\mathrm{\circ}C}+c_{w}(T_{o u}-T_{i n}))=1,011\,{\mathrm{W}}so that its energy efficiency is
\eta_{c\nu}={\frac{\Delta \dot{H}_{\nu}}{{A_{c}}{G_{s}}}}=52.7\%Finally, the incident radiation in the photovoltaic panels is 1120 W. The electricity produced is 200 W. Therefore, the energy efficiency of the photovoltaic panels is
\eta_{P V}={\frac{\dot{E}}{A_{c}G_{s}}}=17.8\%(b) On the other hand, the exergy change of water in the flat solar collectors is
\Delta{\dot{B}}_{w}={\dot{m}}_{w}c_{w}{\biggl[}(T_{o u}-T_{i n})-T_{0}\:ln{\frac{T_{o u}}{T_{i n}}}{\biggr]}=89\:WThe exergy of the incident radiation is
\dot{B}_{s}=\left[1-\frac{4}{3}\,\frac{T_{0}}{T_{s u n}}+\frac{1}{3}\left(\frac{T_{0}}{T_{s u n}}\right)^{4}\right]\!\!A_{c}G_{s}=3.730\,\mathrm{W}so that the quality factor of the solar radiation is 0.93. The irreversibilities in the collector are
\dot{B}_{s}=\Delta\dot{B}_{w}+\dot{I}_{c}\rightarrow\dot{I}_{c}=3.641\mathrm{{~W}}and the exergy efficiency is
\varphi_{c}={\frac{\Delta\dot{B}_{w}}{\dot{B}_{S}}}=2.4\%The change of exergy of the water as it passes through the vacuum collectors is
\Delta\dot{B}_{\nu}=\dot{m}_{w}(b_{\nu}-b_{w})=\dot{m}_{w}\Biggl[l_{100^{\circ}\mathrm{C}}+c_{w}(T_{o u}-T_{i n})-T_{0}\Biggl(\frac{l_{100^{\circ}\mathrm{C}}}{373}+c_{ag}l n\frac{T_{o u}}{T_{i n}}\Biggr)\Biggr]\\ =230\ \rm WSince the exergy of the incident radiation is \dot{B}_{s}\,=\,1,838\,\mathrm{W}, the irreversibilities in the collector are
\dot{B}_{r.s}=\Delta\dot{B}_{\nu}+{\dot{I}}_{c\nu}\rightarrow{\dot{I}}_{c\nu}=1,608\ \mathrm{W}and the exergy efficiency is
\varphi_{c\nu}={\frac{\Delta{\dot{B}}_{\nu}}{{\dot{B}}_{r,s}}}=14.3\%Finally, the irreversibilities in the photovoltaic panels are
{\dot{B}}_{r.s}=\dot{E}+{\dot{I}}_{P V}\rightarrow\dot{I}_{P V}=844{\mathrm{~W}}and the exergy efficiency is
\varphi_{P V}={\frac{\dot{E}}{\dot{B}_{r,s}}}=19.2\%