The influence of slight inclination, 'α' (i.e., 10°, 15°, and 20°) of the channel comprised of shrouded vertical rectangular non-isothermal fin array has been computationally investigated. Simulations are performed to obtain the convective coefficient of heat transfer for the different dimensionless fin spacing (S * = 0.2, 0.3, 0.5), non-dimensional fin tip to shroud clearances (C * = 0.1, 0.2 and 0.3), Grashof numbers (Gr= 1.08×10 5 , 4.42×10 5 and 11.5×10 5 ), fin lengths (L= 0.25m and 0.5m) and fin heights (H= 0.025m, 0.04m, and 0.055m). Hydrodynamic behavior of the fluid indicates that a significant amount of flow reversal occurs near the entrance of the channel at very low inclination which vanishes with the increase in inclination. Further, at higher length, reverse flow is found to occur only in the clearance zone. An increase in the value of 'α' from 10° to 20°, results in enhancement of convective coefficient up to a maximum of 161%. An increase in the value of fin spacing from 0.2 to 0.5 results in the enhancement of the convective heat transfer coefficient. At α= 15° and 20°, the heat transfer is enhanced by 84.1% and 101.6%, respectively, while at α=10°, the same is reduced by 33.3%. At lower fin spacing (S * <0.3) increase in C * tends to reduce the efficiency. Further, the efficiency of the finite conductive fin is found to reduce by almost 8% with an increase in Grashof number.