Natural convection from plate-fin heat sinks in both horizontal and slightly inclined from horizontal orientations is studied for the inclination angles of +/- 60 degrees, +/- 75 degrees, +80 degrees, +/- 85 degrees, +/- 90 degrees from the vertical. A set of correlations is obtained for both upward (-) and downward (+) facing horizontal cases. The correlations are tested for validity by using large sets of experimental data from literature. By varying the direction of gravitational acceleration for several upward and downward inclinations, the phenomenon is investigated for the purpose of determining the flow structures forming in and around the heat sinks. The chimney flow structures forming in the upward facing horizontal case are investigated. The extents of validity of the horizontal case correlations for the average Nusselt number are investigated by modifying the dimensionless body force terms with the sine of the inclination angle. It is observed that the modified correlations are valid in ranges, from -60 degrees to -90 degrees (upward) and +80 degrees to +90 degrees (downward). A complete set of Nusselt number correlations covering all possible inclination angles is suggested and shown to be accurate with less than 20% error for the cases with fin spacing values close to the determined optima. (C) 2013 Elsevier Ltd. All rights reserved.