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Non-isothermal reaction-diffusion (RD) systems control the behavior of many transport and rate processes in physical, chemical, and biological systems. A considerable work has been published on mathematically coupled nonlinear differential equations of RD systems by neglecting the possible thermodynamic couplings among heat and mass fluxes, and reaction velocities. Here, the thermodynamic coupling refers that a flux occurs without its primary thermodynamic driving force, which may be gradient of temperature, or chemical potential, or reaction affinity. This study presents the modeling equations of non-isothermal RD systems with coupled heat and mass fluxes excluding the coupling of chemical reactions using the linear non-equilibrium thermodynamic approach. For a slab catalyst pellet, it shows the dynamic behavior of composition and temperature profiles obtained from the numerical solutions of non-linear partial differential equations by Mathematica for two industrial reaction systems of synthesis of vinyl chloride and dissociation of N2O.