Purely convective models for tubular reactors with non-Newtonian flow

General pure convection residence time distribution theory of fully developed laminar flows in straight planar and axisymmetric channels

“…Osborne (1975) and GarciaSerna et al (2007) also derived this RTD, 1 however, represented it in terms of the power law velocity profile index q ¼ ðn þ 1Þ=n. For 0 o q r 2 the differential RTD E θ has a finite maximum at θ ¼ 2ðq þ 1Þ=3ðq þ 2Þ while for q 4 2 the maximum is infinite and located at θ c ¼ q=ðq þ 2Þ ¼ θ F (Osborne, 1975). For the cumulative RTD Eq.…”

“…1 Note that in Osborne (1975) and Garcia-Serna et al (2007) the symbol n is not the flow behavior index but the power law velocity profile index, which we here denote as q. (30) and (31) become…”

“…Closed analytical forms of the diffusion-free RTD in laminar flows are known only for very few channel shapes and certain Newtonian, non-Newtonian or generalized velocity profiles, see Table 1. Examples are axisymmetric flows in a circular pipe (Bosworth, 1948;Danckwerts, 1953;Delaplace et al, 2008;Hsu and Wei, 2005;Osborne, 1975;Pegoraro et al, 2012;Sawinsky and Balint, 1984;Sawinsky and Deak, 1995;Wein and Ulbrecht, 1972;Zakharov, 2006), in a planar channel (Asbjornsen, 1961;Levenspiel et al, 1970;Sawinsky and Simandi, 1983;Zakharov, 2006) and in a concentric annulus (Nigam and Vasudeva, 1976). In all these cases the velocity profile is one-dimensional as it depends on one coordinate only.…”

Modeling of continuous thermal processing of a non-Newtonian liquid food under diffusive laminar flow in a tubular system

“…The artificial volumetric heat generation term for this control volume is defined in Eq. (33) in order to consider the heat exchanged between the insulation and the inner tube and the heat exchanged between the insulation and the ambient air. The overall heat transfer coefficient between T t and T a can be calculated through Eq.…”

“…The first term represents the convective transport in the axial direction, the second represents the radial diffusion between parallel layers in laminar flow and the last term is the reaction rate from Eq. (1) [32][33][34]. Variable L is the length of the section (heating, holding or cooling).…”