We study the convective heat transport phenomenon of liquid in a nanoscale straight channel by performing the non-equilibrium molecular dynamics simulation (NEMD). Fundamental heat transfer phenomenon distinctive in a nanoscale is reported by Han and Lee [Phys. Rev. E 70, 061205 (2004)]. It is the significant heat transfer in the upstream direction even in the absence of temperature gradient in the direction. A planar Poiseuille flow is considered in the simulation, where liquid argon in a straight channel of Pt atoms is driven by a gravity-like body force. The intermolecular force and plane peculiar velocity mainly induces the heat transfer, which becomes significant when the velocity gradient is sizable in the range of the intermolecular force. While the simulation results agree well with the prediction by Navier-Stokes (NS) equation and Fourier’s law, the heat transfer remains of a significant amount. The heat transfer depends on the velocity gradient in a nonlinear fashion, which can not be accounted for the third order generalized Fourier’s law in the literature.