In this paper, the optimum nanofluid parameters are established for double pipe heat exchanger (DPHE) which are commonly used in sensible heating and cooling of fluids. For the same heat transfer surface area and same fluids temperature difference, performance comparisons are carried out by the use of nanofluid and without nanofluid, that is, base fluid itself. Important parameters of nanofluids such as volume concentrations and nanoparticle diameter are varied with respect to second law thermodynamic non-dimensional performance parameters exergetic efficiency and entropy generation number. Also, heat exchanger parametric study is carried out by variations of hot fluid temperature drop, surface area, and length-to-diameter ratio. Although there is increase in heat transfer and effectiveness of DPHE by the use of nanofluid, this will not guarantee higher performance. Because there will be reduction of exergetic efficiency and increase in irreversibilities of heat exchangers. The reasons for this are investigated in this work, and suggestions are provided to choose the optimum values of nanofluid particles based on second law efficiency analysis.