Optimum depth for PV cooling ducts

A theoretical foundation is given for a previously-reported design rule for the geometry of PV cooling ducts. It is confirmed that the temperature rise of the face of the duct near its exit, and hence of the PV array in contact with it, is minimised when the ratio L/D of the duct length to its hydraulic depth is around 20. Choosing this proportion will minimise the loss of efficiency of the cells of the array, due to a raised operating temperature. It is further shown that the optimum proportion is practically independent of the slope of the array.A straightforward first-order analysis is employed, which might also be suitable for teaching purposes.