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Two-phase flow of a non-Newtonian fluid is presented. Bi-phase suspension is obtained by using Casson fluid as the base liquid and tiny size metallic particles. The transport of Hafnium (Hf) particles through a convergent channel are governed by the electro-osmotic phenomenon. An analytical solution is achieved by solving differential equations for the flow dynamics of electro-osmotic flow (EOF). This prominent feature is owing to the density of the metal that suggests that Hafnium alloy is the most appropriate application in nuclear reactors, as a coolant.