Numerical modeling studies have been performed for a methane dry reforming using a shell and tube type packed-bed reactor and a membrane reactor both with a heating tube as heat source in the center of a reactor. Mathematical models for a reformer bed, a heating tube, and an insulating jacket coupled with reaction kinetics were proposed to investigate axial and radial temperature and concentration profiles within both reactors with a reformer temperature of 923 K and heating tube temperatures from 1023 to 1223 K. 3-D visualizations of temperature, CH4 conversion, CH4 concentration, and H-2 concentration profiles were possible by COMSOL Multiphysics modeling software and significant variations within both reactors were observed providing a critical guideline for an efficient reactor design. Further studies for the effect of hydrogen mass flux on a hydrogen yield enhancement revealed that a threshold hydrogen mass flux in a membrane reactor to outperform a packed-bed reactor exists with a trend of a lower threshold hydrogen mass flux for a higher heating tube temperature