In this experimental investigation, the heat transfer and pressure drop analysis of a shell and helically coiled tube heat exchanger by using $Al_2O_3$/water nanofluids have been carried out under turbulent flow condition. The $Al_2O_3$/water nanofluids of 0.1%, 0.4%, and 0.8% particle volume concentration have been prepared by using two step method. The tube side experimental Nusselt number of 0.1%, 0.4% and 0.8% nanofluids were found to be 28%, 36% and 56%, respectively higher than water. These enhancements are due to higher thermal conductivity of nanofluid, better fluid mixing and strong secondary flow formation in coiled tube. The pressure drop of 0.1%, 0.4% and 0.8% were found to be 4%, 6%, and 9%, respectively higher than water. The increase in pressure drop is due to increase in nanofluid viscosity while adding nanoparticles. The measurement of nanofluid thermal performance factor is found to be greater than unity. It is concluded that the $Al_2O_3$ nanofluid can be applied as a coolant in helically coiled tube heat exchanger to enhance heat transfer with negligible pressure drop.