The vibration of Heat Exchange Tubes due to hydrodynamic fluid coupling is an international problem for Nuclear fuel assemblies etc. on account of frequent failure of Heat exchanger tube, which causes not only expensive repair but a great loss to the plant. Thus, several studies in this field have been made so far. But here, a study of three circular cylindrical tubes in a liquid is done on the analytical approach. The author also describes the various parameters for maximum efficiency of heat transmission from Heat Exchanger's, which is defined as; nH =F (G/R, V) = Heat transmission efficiency of the heat exchanger, where G=gap between two adjoining tubes, R= Radius of cylindrical tubes (if considered of same diameters) and V= fluid flow velocity and geometry of tubes. The relations amongst the above parameters are yet to derive to solve this problem.