Abstract Purpose The purpose of this paper is to investigate conjugate heat transfer of natural convection and entropy generation of nanofluid in the presence of external magnetic field via numerical approach in an inclined square cavity enclosure. Design/methodology/approach Control volume finite volume method with collocated arrangement of grids was used for discretization of continuity, momentum, solid and fluid energy equations. Rhie and Chow interpolation technique was applied to avoid checkerboard problem in pressure field and the well-established SIMPLE algorithm was followed to deal with the pressure and velocity coupling. The cavity is filled with water and nanoparticles of the aluminum oxide (Al2O3). This study has been conducted for the certain pertinent parameters of the volume fraction of nanoparticle (φ = 0–0.08), the angle of inclination (ϴ = 0°–330°), the Ra number (Ra = 103–108), the solid to fluid conductivity ratio (ksf = 1–400), the Ha number (Ha = 0–80) and the wall thickness ratio (δ/L = 0–0.3). Findings The results indicate that averaged Nu number increases by approximately 9% by increasing volume fraction from 0.0 to 0.08. Nu increases with an increasing inclination angle to 40° and decreases abruptly in 90° because of the formation of two weaker vorticity with opposite circulation pattern intensifying the density of isotherm curves in a vertical direction. Nu increases sharply with increasing Ra more than 105. Nu also augments almost 67% by increasing ksf = 1 to ksf = 50 and remains constant by increasing ksf more than 50. Nu number reduction is almost 72% with a variation of wall thickness ratio from d/L = 0 to 0.3. Entropy generation because of fluid flow, magnetic field and heat transfer reduces linearly almost 30%, 19% and 16% by increasing volume fraction, respectively. With increasing ksf, entropy generation because of fluid flow, magnetic field and heat transfer increases asymptotically, but Bejan number decreases. Originality/value A
