Natural convection inside a bounded space is often vital for designing the flow dynamics of high-energy dense systems, namely, the thermal management systems of electronic devices, nuclear reactor cores, crude generation, and so on. In the present exploration, numerical investigation of buoyancy-motivated thermal energy flow patterns inside an inclined quadrantal enclosure has been conducted. The curved wall, bottom wall, and left wall have null heat flux, higher temperature, and lower temperature, respectively. The influence of the inclination angle phi has been critically scrutinized with the support of the flowfield (stream function), temperature distribution (isotherms), Nusselt number Nu, and entropy generation within the enclosure. phi is varied from 15 to 60 deg under dissimilar Rayleigh numbers (103 <= Ra <= 106) and Prandtl numbers (0.7 <= Pr <= 1000). One crucial insight deduced from the study is that the power of circulation roll alters radically with the inclination angle and Ra. The local heat transport rate has been found to increase with Ra and decrease with an escalation in phi. The cavity tilted at 30 deg with the horizontal direction has been found to be the optimal design condition due to the maximum average Nusselt number along both the walls and the total value of entropy generation.