The study deals with the effect of pressure gradient on the onset of Darcy-Bénard convection of water-copper nanoliquidsaturatedporous layer and on amount of heat transport. The present study assumes thermal non-equilibrium (LTNE) betweensolid and liquid phases. The LTNE assumption results in advanced onset of convection and increase in heat transportwhen compared to that of local thermal equilibrium (LTE) assumption. Free-Free, isothermal boundaries are consideredfor investigation. Critical Rayleigh number and Nusselt number as functions of various parameters are analysed and this isdepicted graphically. The influence of pressure gradient, inter-phase heat transfer coefficient, ratio of thermal conductivities onthe onset of convection as well as on heat transport has been presented graphically and discussed in detail. The effect ofincreasing the value of porosity modified thermal conductivities advances the onset of convection and enhances the amount ofheat transport whereas the remaining parameters have an opposing influence on both onset of convection as well as heattransport. The classical results of LTE case are obtained as a limiting case of LTNE case for small values of H and large valuesof H, γ and γH.