The present numerical work delineates the flow and heat transfer characteristics due to the combined convection (free and forced) inside semi-circular, top lid-driven cavity. The flow conditions are assumed to be laminar, steady-state, incompressible, and for non-Newtonian power-law fluids. The curved surface of the cavity is subjugated to constant heat flux (CHF) thermal condition, while the top wall is sliding with uniform velocity (Ulid) along –x-direction. The governing parameters utilized for numerical experimentation are Richardson number (Ri = 0.1–10), non-Newtonian power-law index (n = 0.5–1.5), modified Prandtl number (Pr = 1–100) and Grashof number (Gr = 104). The study is also intended to provide a comparative explanation for the use of adiabatic blockage of varying cross-sections on the flow and thermal patterns in the cavity. In particular, the influence of the shape of blockage in the cavity, viz., circular, square, and triangular investigated. Normalized Nusselt numbers have also plotted to give the idea of heat transfer enhancement/deterioration by the presence of block with that of the absence of block. Empirical correlations are also developed for summarizing the results of the study. The triangular block shows better heat transfer results as compared with the circular and square blocks in the semi-circular cavity. © 2020 Elsevier Ltd