Correction for semi-infinite assumption in the theories of natural convection and determination of average Nusselt number for finite inclined plates

It is established that large errors would be incurred if the average Nusselt number for natural convection above heated horizontal plates of finite size is determined by the similarity or integral theories which assume the plate is semi-infinite. Recognizing that boundary layers grow from both edges of a finite plate, correction factors are mathematically deduced for the isothermal case (Ft=22/5) and for the case of constant heat flux (Fq=21/3). Correction factors are also developed for near-horizontal orientations of the heated plate. The semi-infinite assumption does not alter the computation of the overall heat transfer rate for inclination angles at which the vertical mechanism of natural convection is dominant since then, even in the case of a finite plate, a single boundary layer covers the entire length of the plate. The theoretical rationalization developed in the paper brings the predictions of explicit algebraic expressions for average Nusselt number in line with those determined accurately by computational fluid dynamics (with extensive experimental verification), and provides physical explanation of the subtle thermo-fluid-dynamics of natural convection established by the present CFD simulations. •CFD study of natural convection around heated inclined plates.•Correction of theoretical average Nusselt number for horizontal and near-horizontal orientations.•Corrective theories developed for both isothermal and iso-heat-flux boundary conditions.•Influence of boundary condition on average Nusselt number explained.•Subtle effect of inclination on heat transfer in near-horizontal and near-vertical cases uncovered.