A mathematical modeling and numerical simulation study has been carried out for a liquid hydrocarbon production system using syngas from biomass gasification. The system is based on a Fischer-Tropsch packed bed reactor with an external heat removal sink. To ensure the accurate prediction of exothermic heat release, the chemical reaction kinetics is modeled with a comprehensive product distribution scheme based on a novel carbon number dependent chain growth concept and stoichiometric relationship between the syngas and hydrocarbons produced. The Fischer-Tropsch synthesis involves a three-phase phenomenon: gaseous phase-syngas, water vapor and light hydrocarbons; liquid phase-heavy hydrocarbon; solid phase-catalyst. A porous medium model has been used for the two-phase flow through an isotropic packed bed of spherical catalyst pellets. An Eulerian multiphase continuum model has been applied to describe the gas-liquid flow through the porous medium. Heterogeneous catalytic chemical reactions convert syngas into hydrocarbons and water. Intraparticle mass transfer limitation has also been considered in this model. Two independent validation cases have been demonstrated to show a successful implementation of the computational schemes. In this study, major attention has been paid to reactor temperature profiles because thermal management is highly important for the current exothermic catalytic reaction. We believe that our model could provide optimum operating conditions for achieving the maximum yield for desired products, liquid hydrocarbon fuels, without the thermal deactivation of the catalyst.