Diameter and shape of tube, coil pitch and curvature ratio using 0.2% MWCNT-water nanofluid and 0.2-1% SWCNTwater nanofluid, affect the inner Nu and pressure drop in a shell and helically coiled tube heat exchanger, when numerically investigated. Flow configuration and fluid temperatures of both the nanofluids exhibited enormous change in inner Nu and pressure drop, compared with water at laminar (De 1610-2728) and turbulent (De 3019-4050) regime. When pure water in straight tube at the same Re is compared to 0.8% SWCNT-water nanofluid at 335 K with rectangular coiled copper tube of sides 10 mm and 7.85 mm, stretched length of 650 mm, 15 coil turns, coil pitch 15 mm, curvature ratio 0.24 and De 4025 at counter flow configuration, it had 139% higher inner Nu and 56% higher pressure drop. Very high performance index of 1.53 and Colburn factor of 3.25 were obtained using a single phase model.