We report magnetization and resistivity studies on polycrystalline BaFe2As2 prepared by solid-state reaction, in the temperature range of 5-350 K, upto the field of 9 T. Low-field susceptibility exhibits multi-phase transitions with two new magnetic phase transitions beside the well-known transition at T approximate to 140 K from paramagnetic/antiferromagnetic-tetragonal/orthorhombic transitions. The phase at T similar to 40 K is attributed to the phase transition from antiferromagnetic-orthorhombic (C2-phase) to antiferromagnetic-tetragonal phase (C4-phase), while the phase transition at higher temperatures remains unsolved. Making an analogy to the antiferromagnetic nanosized particles, we suggest that BaFe2As2 consists of smaller but similar nanosized clusters. We have analyzed the magnetization data using the modified Langevin function on the basis of thermally activated induced uncompensated spins (thermoinduced moments). The nanosized clustering in this compound is evidenced by the exchange bias and coercivity stemming from the exchange coupling interactions between weak ferromagnetic bulk magnetization in clusters and spin-glass-like phase interface layers surrounding the clusters. We also observe that annealing enhances the superconductivity, similar to the effect of pressure on the superconductivity.