Natural convection in cylindrical porous annuli saturated by a nanoliquid whose inner and outer vertical radial walls are respectively subjected to uniform heat and mass influxes and out fluxes is studied analytically using the modified Buongiorno-Darcy model (MBDM) and the Oseen-linearization technique. Nanoliquid-saturated porous medium made up of water as base liquid, copper nanoparticles of five different shapes, viz., spheres, bricks, cylinders, platelets and blades, and glass balls porous material is considered as working medium for investigation. The thermophysical properties of nanoliquid -saturated porous medium is modeled using phenomenological laws and mixture theory. The effect of various parameters and individual effects of five different shapes of copper nanoparticles on velocity, temperature and heat transport are found. From the study, it is clear that the addition of a dilute concentration of nanoparticles increases the effective thermal conductivity of the system and thereby increases the velocity and the heat transport, and decreases the temperature. In other words, the heat transport is more in the case of heat and mass driven convection compared to purely heat-driven convection. Among the five different shapes of nanoparticles, blade-shaped nanoparticles facilitate the transport of maximum temperature compared to all other shapes. Maximum heat transport is achieved in a shallow cylindrical annulus compared to square and tall circular annuli. The increase of the inner solid cylinder's radius is to decrease heat transport. The results of the KVL single-phase model are obtained from the present study by setting to zero the value of the nanoparticles’ concentration Rayleigh number. Also, neglecting the curvature effect in the present problem, we obtain the results of the rectangular enclosure problem.