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The main objective of this parametric study was to examine influence of pertinent thermo-physical parameters on sodium droplet temperature. The generic reaction rate and thermal conductivity of the single droplet are varied as non-linear functions of temperature, whereas the contribution of heat loss mechanisms are based on Newton law of cooling and  P-1 approximation for thermal radiation transfer. An extension of existing models was obtained which was non-linear initial value problem. Theorem on existence and uniqueness of solution was formulated and proved to validate the new model based on some criteria. The differential equation was not amenable to analytical solution due to its non-linearity. Therefore, the non-linear problem was tackled numerically, using a finite difference procedure based on a small step-size. Parametric studies were performed to investigate significant effects of thermo-physical parameters on temperature of the single droplet for typical reaction rates such as Sensitized, Arrhenius and Bimolecular reaction rates. The results show the impacts of different thermo-physical parameters on the single sodium temperature of sensitized, Arrhenius and bimolecular reaction rates.  Keywords: Sodium droplet, non-linear problem, variable thermal conductivity, critical temperature, explosion time, sensitized, Arrhenius and bimolecular reaction rates.