The effect of the mass flow rate at constant velocity on the convective heat transfer coefficient of an incompressible fluid in a turbulent flow regime is presented with the help of dimensional analysis. The heat transfer coefficient decreases by ~10% with a threefold increase in the mass flow rate under these conditions, based on the commonly used Dittus-Boelter correlation for estimation of the heat transfer coefficient. On the other hand, an increase in the heat transfer coefficient is observed if the area is maintained constant. Doubling the mass flow rate will result in a 92% increase in the heat transfer coefficient. However, there is a concomitant increase in the pressure drop, proportional to the mass flow rate raised to 0.95. The pressure drop is predicted to decrease for the constant velocity case with an inverse dependence on the mass flow rate. The pressure drop considerations may be critical in certain situations (elevation of boiling point in case of a boiling heat transfer medium), and any benefit derived from the higher heat transfer coefficient may be lost because of the higher pressure drop across the heat exchanger in the constant area case.