A design configuration and selection of working fluid for solar absorption remain critical for high performance of energy harvesting process in solar pond. In this study, heating and pressure loss characteristics in a novel designed spiral-coil geometry pertinent to salt-gradient solar pond (SGSP) is examined and the thermal performance of nanofluids in the coil is assessed. Nanofluids possessing graphene, functionalized graphene nanoplatelet (fGnP), and graphene oxide (GO) at 0.06% volume concentration are considered as the working fluids in the system. In order to achieve a novel design of a spiral coil, the circular cross-sectional geometries with aspect ratios (AR) of 0.5, 1, and 2 are incorporated in the analysis. The selection of the aspect ratios of 0.5, 1, and 2 results in elliptic, circular, and oval cross sections of the coil, respectively. The findings reveal that heat transfer enhances and pressure loss reduces via increasing the mass flowrate. This is due to the formation of a stable secondary flow which causes mixing enhancement while shortening the thermal entry length. Circular and elliptic cross sections resulted in the maximum and the smallest normalized average Nusselt numbers, respectively, for low rates of flow. This is because of thermal resistance created under the large surface area-to-volume ratio; however, this effect varnishes for high mass flowrates. Graphene oxide and functionalized graphene nanoplatelet have the highest and the lowest normalized average pressure drops, respectively, for all flow rates.