The natural convection and conduction heat transfer in inclined rectangular enclosures with honeycomb structure attached to the heated wall is numerically studied. The boundary conditions were constant heat flux on the wall and fins, isothermal on the bounding long sides and adiabatic on the short sides. The governing parameters are the Rayleigh number (10(4) less than or equal to Ra less than or equal to 10(8)), the aspect ratio of the enclosures (2.5 less than or equal to A = H’/L’ less than or equal to 10), the dimensionless lengths of the partitions (0 less than or equal to B = I’lL’(1); less than or equal to 1), the aspect ratio of the micro-cavities (0.25 less than or equal to C = h’/L’ less than or equal to 2.5), the inclination angle (5 less than or equal to phi less than or equal to 90 degrees), the wall thickness (0 less than or equal to w = w’/L’ less than or equal to 1). The fin thickness was (e = e’/H’ = 0.08). The Prandtl number was constant (Pr = 0.72) and the conductivity ratio varied as (10(-3) less than or equal to k(r) less than or equal to 10(5)). Local and average Nusselt numbers along the long sides are calculated as a function of various parameters. Streamlines and isotherms are produced.