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Development of modern electronic devices and heat exchangers is related to the energy transport intensity. For this purpose, it is possible to use the internal fins and nanofluids. The present study is devoted to mathematical simulation of free convective thermal transmission of alumina-water nanoliquid in a semi-open cavity with the complicated fin including the wall-mounted part and internal obstacle. Analysis has been carried out by means of the partial differential transport equations written on the basis of the non-dimensional, non-primitive variables. The special procedure has been developed for description of the stream function value at the body surface within the cavity. The developed code has been validated using the mesh sensitivity analysis and computational results of other researchers. Impacts of the Rayleigh number, internal obstacle position, and nano-sized particles concentration on nanoliquid flow and thermal transmission have been considered. It has been revealed that for the present formulation a growth of the solid particles concentration results in the heat transport degradation, while it is possible to find an optimal position of the inner body for the energy transport intensification.