Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is Nu¯=6.25(1+r)Ra″sinϕ+1.64(Ra″sinϕ)2/5-1/2, where r   is ratio of the heat flux at the top and bottom wall. At inclination angles of 30°≤ϕ≤90°30°≤ϕ≤90°, this correlation predicts the available data base for 10≤Ra″≤10510≤Ra″≤105 and agrees with the analytical solution for 1≤Ra″≤1021≤Ra″≤102.