A photovoltaic panel of dimensions 6 m x 5 m is located on top of the roof of a house. Solar irradiation Gs = 900 W/m² is incident on the panel. The panel has an absorptivity to solar irradiation, αₛ of 0.92. The freestream air temperature is Tɪɴꜰ and the surrounding temperature for radiation exchange with the sky is Tsᴜʀʀ. For this particular problem, it is given that Tɪɴꜰ = Tsᴜʀʀ. The convective heat transfer coefficient of air blowing over the panel is h W/m²-K.
The generated electric power is provided by the following expression:
Pᴇʟᴇᴄ = αₛ Gₛ Aᴘ*(A-B*Tᴘ),
where A = 0.61 and B = 0.0014 K⁻¹. The emissivity of the panel and its absorptivity to radiation in the wavelength range of the sky temperature are both equal to 0.7. In the above equation, Aᴘ is the solar panel area and Tᴘ is the panel temperature.
Heat conduction from the panel supports to the roof can be neglected, and so can the heat loss from the back side of the solar panel.
(1) Derive an expression for electrical power generated by the panel as a function of other known quantities.
(2) Plot the electrical power produced as a function of convective heat transfer coefficient h for a fixed air temperature of Tinf = 22 °C over a range of h from 20 to 40 W/m²-K. Provide appropriate reasoning to support the observed trend.
For (2), neglect irradiation from the surroundings. On the same graph as in (2), plot the new electrical power generated as a function of h. Does the electrical power produced change substantially? Comment on why or why not.