A numerical study is performed to investigate the influence of geometrical factors on the performance characteristics of a laminar thermally developing flow of phase change nano-suspensions in a rectangular minichannel considering axial wall conduction effects. The phase change material dispersed in the pure water is considered N-eicosane with the onset point of melting of 34.7 degrees C, latent heat of fusion of 243 J/g, and particle size of 200 nm. The volume fractions of the phase change nano-suspensions are 2% and 10%, and the Reynolds number is in the range of 200 to 1500. To evaluate the influences of geometrical parameters on the cooling performance of the minichannel heat sinks, five minichannels are investigated, with aspect ratios (ration between channel height and width) AR(ch) of 1, 1.25, and 1.5 and bottom wall thicknesses H-bw of 0.5, 1, and 1.5. The results reveal that the axial wall conduction significantly affects the heat transfer process of a flow in a minichannel at a low Reynolds number, and this effect is more remarkable with a shallower channel and a thicker bottom wall. Five performance indicators are used to systematically evaluate the heat transfer characteristics of the minichannels, including dimensionless heat flux at the bottom wall, temperature suppression, heat transfer effective ratio, heat dissipation of the extended wall, and figure of merit.