Unglazed transpired collector-2stage (UTC-2stage) is a type of solar air heater constructed of two collectors. The first stage is an unglazed transpired collector (UTC), and the second is a tilted transpired collector covered with a transparent cover. In this paper, a mathematical model has been developed for the purpose of analyzing the system, cover and UTC's height impact on energy and exergy efficiencies are investigated. The model's solution is compared with experimental results in order to be validate. The experimental results manifest acceptable commensurability with the present work results. After validation, the effect of key parameters such as hole diameter, hole pitch, sun radiation, suction velocity, wind velocity, plenum depth and inlet air temperature on the ratio of UTC's height to the total height of the system (H-u/H) at points where the equivalent thermal efficiency or second law efficiency is maximum have been investigated. With regards to the results of this paper, designers should take these key parameters into consideration in selecting the heights of UTC and the cover. (C) 2016 Elsevier Ltd. All rights reserved.