The overall heat transfer coefficient of the heat exchanger will improve with an increase in the flow rate and concentration of nanofluid. But beyond an optimum nanoparticle concentration, the overall effectiveness seems to decrease due to an increase in pressure drop that consequently leads to an increase in pumping power. The novelty of the present work is to find the optimum concentration of CuO-Water nanofluid that exhibits the optimum heat transfer rate and global minimum pumping power, using both experimental and numerical study. The cold nanofluid and hot water entered the counter currently at 303.15 and 333.15 K respectively in the corrugated plate heat exchanger. It was observed from the experimental and numerical results that the values of overall heat transfer coefficient and pressure drop were increased monotonically (454–710 W/(m2-K) and 6–133 Pa respectively), with the increment in the concentration and flow rates of the nanofluid. Because of this trend, it was challenging to figure out the optimum nanofluid concentration using these parameters. Later, a procedure was presented to obtain an optimum concentration of nanofluid, to reduce the hot stream temperature by 288.15 K. The hydraulic power exhibited a global minimum at an optimum concentration of 0.5 vol% of nanofluid.