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Considerable work has been published on mathematically coupled nonlinear differential equations by neglecting thermodynamic coupling between heat and mass flows in reaction-transport systems. The thermodynamic coupling refers that a flow occurs without or against its primary thermodynamic driving force, which may be a gradient of temperature, or chemical potential, or reaction affinity. This study presents the modeling of thermodynamically coupled heat and mass flows of two components in a reaction-transport system with external heat and mass transfer resistances. The modeling equations are based on the linear nonequilibrium thermodynamics approach by assuming that the system is in the vicinity of global equilibrium. The modeling equations lead to unique definitions of thermodynamic coupling (cross) coefficients between heat and mass flows in terms of kinetic parameters and transport coefficients. These newly defined parameters need to be determined to describe coupled reaction-transport systems. Some representative numerical solutions obtained by MATLAB illustrate the effect of thermodynamic coupling coefficients on the change of temperature and mass concentrations in time and space.