Direct numerical simulation (DNS) of laminar lean methane-air and n-heptane-air premixed flames with high exhaust gas recirculation (EGR) ratios propagating towards inert walls in a head-on quenching configuration is conducted to investigate flame-wall interactions at relatively high initial pressure conditions. This study considers the flame propagation under isochoric process after ignition while the piston is at top dead center (TDC). The effects of EGR ratio, equivalence ratio, initial pressure and wall temperature on heat loss and quenching distance are investigated. The results showed that change of EGR ratio in fuel mixture significantly affects the maximum wall heat flux and the heat flux induced by the burned gas temperature. The normalized flame-wall interaction time is not influenced over a range of EGR ratios, equivalence ratios and initial chamber pressures for methane-air and n-heptane-air flames at fixed wall temperature conditions. The dimensional flame-wall interaction time is almost constant when the chamber pressure is doubled. The influence of low temperature oxidation in n-heptane flames on wall heat flux induced by temperature differences between the preheated fuel mixture and the wall is found to be insignificant. Moreover, both thermal conductivity near the wall and quenching distance are sensitive to the wall temperature, and have a substantial influence on the wall heat flux. (C) 2016 Elsevier Ltd. All rights reserved.