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Ojiambo, Viona; Kimathi, Mark; Kinyanjui, Mathew

A mathematical model of angular two-phase Jeffery Hamel flow in a geothermal pipe. (English) Zbl 1468.76070

Int. J. Adv. Appl. Math. Mech. 6, No. 2, 1-13 (2018).
Summary: A model of an annular two-phase Jeffrey Hamel flow in a geothermal pipe is designed with silica particles present in the effluent. Thermophoresis is singled out as the source of movement for the particles. The phenomena is also used to determine the growth of silica particles. The power law model has been used to express vicosity in both phases whereby viscosity is a non-linear function of wedge angle in the gaseous phase while a function of wedge angle and temperature in the liquid phase. Equations of mass, momentum, heat transfer and species transfer are the governing equations for this fluid flow. These equations are transformed into nonlinear ordinary differential equations by introducing a similarity transformation. The resulting equations are then solved using the bvp4c MATLAB solver. This method saves on computational time but still provides accurate and convergent results. Skin friction, Nusselt number, Sherwood number, non-dimensional thermophoresis velocity and non-dimensional thermophoresis deposition velocity are determined. The effect of the flow parameters on the flow variables is examined and it is established that changes in velocity and temperature does affect the concentration of silica. An increase in the Reynolds number implies an increase in the fluid velocity which increases the non-dimensional thermophoresis velocity VTW of both the liquid and the gaseous phases. Increase in the VTW implies increased concentration of colloidal silica particles which deposit on the walls of the geothermal pipe.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
76T15 Dusty-gas two-phase flows
76M99 Basic methods in fluid mechanics
80A19 Diffusive and convective heat and mass transfer, heat flow
86A60 Geological problems

Keywords:

gas-liquid flow; silica particle; non-linear viscosity; thermophoresis; mass deposition rate; similarity transform; collocation method; skin friction

Software:

bvp4c; Matlab
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\textit{V. Ojiambo} et al., Int. J. Adv. Appl. Math. Mech. 6, No. 2, 1--13 (2018; Zbl 1468.76070)
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