A numerical analysis is conducted to examine the effects of non-uniform and asymmetric heating on the conjugate thermal transport characteristics for laminar forced convective flow of nanofluid through a rectangular minichannel. The Eulerian-Lagrangian formulation.is employed to model the nanofluid as one single fluid with two phases. The exteriors of both the walls are subjected to a sinusoidal heat flux profile with a phase difference. The theoretical model under negligible wall thickness condition always underestimates the overall rate of heat transfer. There exists an intricate interplay between the non-uniform asymmetric heat flux profiles imposed on the walls and the physico-thermal properties of the fluid and walls to characterize the thermal transport dynamics. The average heat transfer rate is higher for the non-uniform asymmetric heating as compared to uniform heating and moreover, the impact of asymmetric non-uniform heating is higher than the effect of non-uniform heating alone. (C) 2020 Elsevier B.V. All rights reserved.