Significantly improved mixing and heat transfer between two nanofluid streams in a Y-shaped sinusoidal microchannel have been achieved via geometric modifications and changes in pulsatile flow conditions. As a result a new mass-and-heat transfer correlation has been obtained as well. The geometry modification was done in two distinct parts. First, the phase shift (phi) between the wavy walls of the Y-channel was varied for three different shift values (0 degrees, 90 degrees, 180 degrees). Once the shift that yielded the highest degree of mixing was determined, the included angle (alpha) between the input streams was varied (30 degrees, 45 degrees, 60 degrees). The numerical results show that alpha = 60 degrees and phi = 90 degrees yield best results. The inlet streams are pulsatile with a velocity of the form V + delta Vsin(omega t + Phi) where V, delta V, omega, Phi are the average velocity, pulse amplitude, pulse frequency and phase shift respectively. Flow variations have been implemented via different phase shifts (45 degrees, 90 degrees, 135 degrees, 180 degrees), different phase amplitudes and different phase frequencies. For the sake of comparison and ease of plotting, non-dimensional parameters have been used. The frequency has been captured by the non-dimensional Strouhal number (St) and the amplitude by the amplitude ratio (delta V/V). The average degree of mixing (zeta), which is observed to undergo spatial variations along the exit channel as well as temporal fluctuations over one pulsation cycle is shown to be most sensitive to the amplitude and frequency of pulsations. For a fixed amplitude, the average degree of mixing increases with elevated Strouhal numbers. It reaches a peak at a particular St value and then decreases with further increase in St. The St where the degree of mixing peaks depends on the amplitude of pulsations. For delta V/V >= 5, the degree of mixing peaks at St approximate to 0.5. For delta V/V <= 5, the degree of mixing peaks at St approximate to 2. Unlike mixing, the heat transfer rate, characterized by the non-dimensional Nusselt number (Nu) peaks at higher frequency values for all delta V/V ratios. To generate higher amplitudes in the pulsating flow, a larger pumping power would be required. Hence, to minimize energy cost, low amplitude and high frequency pulsations are most suitable for optimal mixing and heat transfer. Finally, a microchannel with optimized geometry and inlet flow conditions is proposed, which takes advantage of the flow instabilities created by the modified geometry and pulsating flow to yield the highest degree of mixing and heat transfer within the listed constraints. Functional dependencies have been established, based on computer experiments, between non-dimensional parameters such as St, delta V/V, zeta, Nu. As a result, a correlation between mixing and heat transfer was developed which allows studying one quantity, say, the Nusset number Nu, to readily obtain the average degree of mixing zeta. (C) 2018 Elsevier Ltd. All rights reserved.