Consecutive chemical reactions in an annular reactor with non-newtonian flow

The purpose of this paper is to analyze the homogeneous consecutive chemical reactions carried out in an annular reactor with non-Newtonian laminar flow. The fluids are assumed to be characterized by a Ostwald-de Waele (powerlaw) model and the reaction kinetics is considered of general order. Effects of flow pseudoplasticity, dimensionless reaction rate constants, order of reaction kinetics and ratio of inner to outer radii of reactor on the reactor performances are examined in detail.Nomenclature c _A concentration of reactant A, g.mole/cm³ - c _B concentration of reactant B, g.mole/cm³ - c _A0 inlet concentration of reactant A, g.mole/cm³ - C ₁ dimensionless concentration of A, c _A/c _A0 - C ₂ dimensionless concentration of B, c _B/c _A0 - C ₁ dimensionless bulk concentration of A - C ₂ dimensionless bulk concentration of B - D _A molecular diffusivity of A, cm²/sec - D _B molecular diffusivity of B, cm²/sec - k _A first reaction rate constant, (g.mole/cm³)^1–m /sec - k _B second reaction rate constant, (g.mole/cm³)^1–n /sec - K ₁ dimensionless first reaction rate constant, k _A r ₀ ² c _A0 ^m–1 /D _A - K ₂ dimensionless second reaction rate constant, k _B r ₀ ² c _A0 ^n–1 /D _B - K apparent viscosity, dyne(sec) ^m /cm² - m order of reaction kinetics - n order of reaction kinetics - P pressure, dyne/cm² - r radial coordinate, cm - r _i radius of inner tube, cm - r _max radius at maximum velocity, cm - r _o radius of outer tube, cm - R dimensionless radial coordinate, r/r _o - s reciprocal of rheological parameter for power-law model - u local velocity, cm/sec - u _max maximum velocity, cm/sec - u bulk velocity, cm/sec - U dimensionless velocity, u/u - z axial coordinate, cm - Z dimensionless axial coordinate, zD _A/r ₀ ² /u - ratio of molecular diffusivity, D _B/D _A - ratio of inner to outer radius of reactor, r _i/r _o - ratio of radius at maximum velocity to outer radius, r _max/r _o