The application of fluid and heat transfer in electronic and nuclear technology is gaining popularity, particularly in equipment's life span and risk management. However, further study is required for applications involving rectangular cylinders placed inside a square cavity. This study investigates the effects of height ratio (𝐻𝑅), and width ratio (𝑊𝑅) for Prandtl number 𝑃𝑟=0.71 on natural convective heat transfer and the flow field around the annulus of a square domain fitted internally with a heated rectangular cylinder. The square enclosure and the inner rectangular cylinder walls were respectively maintained at cold and hot isothermal conditions. COMSOL Multiphysics (Version 5.6) software was adopted to implement the governing equations and boundary conditions. The results are presented in the form of streamlines, isothermal contours, and Nusselt number (Nu). The study reveals that the combined average Nu of the rectangular cylinder walls improves with 𝐻𝑅, 𝑊𝑅, and Rayleigh number (Ra). The maximum Nu occurred at 𝐻𝑅=0.7, and 𝑊𝑅=0.7; however, height variation at peak average Nu was 37.7% greater than width variation at peak average Nu. This study finds applications in the cooling of electronic chips and aerospace engines.