A study of two-phase Jeffery Hamel flow in a geothermal pipe

Abstract

In this paper a two-phase convergent Jeffrey-Hamel flow in a geothermal pipe concentrated with silica particles and thermophoresis has been studied. The governing equations are equation of mass, momentum, heat transfer and concentration. These equations are transformed into nonlinear ordinary differential equations by introducing a similarity transformation. The resulting equations are then solved using the bvp4c collocation method. Results for velocity, temperature and concentration are presented for various parametric conditions. It is established that the unsteadiness parameter significantly influences the velocity, temperature and concentration in both the gaseous and the liquid phase, secondly the Reynolds’number effect in the gaseous phase velocity is more significant incomparison to the liquid phase, thirdly the variation in heat transfer as a result of the Prandtl number is more significant in comparison to the liquid phase, fourthly there is a significant effect of the control factor introduced in the concentration equation to counter silica polymerization . In conclusion, the gaseous and the liquid phase have to be accounted separately. Further, the control mechanisms used for preventing silica deposition need to be factored in the concentration equations with their ranking specification so as to monitor the growth of silica deposits.