Problem statement: The combustion processes in the interior of the earth during the gravitational differentiation and radioactive decay processes are characterized by ignition and explosion. The two heat sources are in this paper, considered as time-dependent. Approach: The study investigates the existence of unique solution of the new model and examines the effect of activation energies ratio on the reaction. The criteria for a similarity solution of the resulting equations are established. The resulting ordinary differential equations are solved numerically by shooting method. Results and Conclusion: The results show that with time-dependent gravitational differentiation and radioactive decay processes, the problem has a unique solution and the activation energies ratio has an implication on the reactions in terms of heat release.
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