A series of rotating convection experiments have been conducted in a novel configuration, which comprises a cylindrical annulus with spot heating on the bottom outer edge and uniform cooling on the inner surface. Such a system provides bi-directional thermal gradients in both radial and vertical directions, thereby reenacting the thermal gradient patterns encountered in the atmosphere. Bulk heat transfer characteristics are studied by quantifying the overall Nusselt number, Nu, for a range of Taylor number, Ta, heating rate, Q, and Rayleigh number, Ra. Temperature measurements are carried out at different locations with the help of thermocouples. The Nusselt number is found to be quite sensitive to the buoyancy and relatively insensitive to the rotation rate. The correlation for Nu as a function of Ra revealed different power law exponents for low and high Ta values. The varying exponent is attributed to the presence of baroclinic eddies at high Ta, which in turn is verified with the help of flow visualization. The heat transfer characteristics in this new configuration are significantly different compared to other conventional rotational convection systems, where thermal gradients are present in only one direction.