Natural convection in an open and highly anisotropic cellular material, wire-woven bulk Kagome (WBK) is experimentally characterized. A series of pressure drop and heat transfer experiments are conducted. In particular, effect of inclination angle on the heat transfer rate for porous-cored heat sinks (WBK and metallic foams), as well as smooth plate was experimentally investigated. There exists an optimal inclination angle for smooth plate and porous-cored heat sinks in association with the maximum heat transfer rate (Nusselt number). An advance in optimal inclinational angle was observed in porous media during the full inclination angle range from (horizontal) to (vertical) due to the enhanced lateral conduction and a further advance was found in WBK specimen. A strong anisotropic heat transfer existed in terms of different orientations of WBK specimen: O-B orientation with a bigger cross-sectional surface area density (blockage ratio) reveals a higher heat transfer rate than O-A orientation. Further, in comparison with isotropic metallic foams with a given porosity, the WBK which is positioned at vertical orientation can dissipate more heat than the foams due to the higher permeability resulting from less pressure drop in the WBK formed by an assembly of cylindrical wires.