Laminar flow in the entrance region of a cylindrical tube: Part I. Newtonian fluids

Sylvester, N. D.; Rosen, S. L.

doi:10.1002/aic.690160617

Cited by 42 publications

(18 citation statements)

References 11 publications

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“…The pressule drops were measured for a I'ange of Reynolds numbers (10 < Re¿ < Weissberg (1962) and experimentally verified by La Nieve and Bogue (1968) for the "cleeping" flow limit, Astarita and Greco (1968) and Sylvester and Rosen (1970) Astarita and Greco (1968) and Sylvester and Rosen (1970) is the temperatule change in the flow Ioop which affects considelably the acculate determination of these corrections. Dullien and Azz¿m (1973) and Azzam and Dullien (1977).…”

Section: Pressure Distributionmentioning

confidence: 99%

The microscopic analysis of high forchheimer number flow in porous media

Ruth

1993

Transp Porous Med

118

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Section: Pressure Distributionmentioning

confidence: 99%

The microscopic analysis of high forchheimer number flow in porous media

Ruth

1993

Transp Porous Med

118

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“…Computed isothermal-flow predictions of L,, at high N R e are less than 3% lower than the experimental results of Sylvester and Rosen (1970) and less than 4% higher than those of LaNieve (1963) but are much lower than the widely varying experimental results at lower N R e (Christiarisen et al, 1972). Also, isothermal-flow computations using the present program are almost always within L,, = 0.1 of those made with a similar but independent program using the stream-function equations and relaxation (Christiansen et al, 1972).…”

Section: Discussion Of Resultsmentioning

confidence: 79%

“…The results of several more or less definitive experimental studies for the isothermal, laminar flow of Newtonian and some non-Newtonian fluids through an abrupt contraction from a large real tube into a smaller real tube of circular cross section have been reported (Astarita and Greco, 1968;LaNieve, 1963;Michiyoshi et al, 1966;Ramamurthy, 1970;Ramamurthy and Boger, 1971;Sylvester and Rosen, 1970). However, we are not aware of any experimental studies of ST-RT or RT-RT Newtonian tube-entrance flow accompanied by heat transfer to or from the fluid that are sufficiently definitive for critical evaluation of our computations.…”

Section: Discussion Of Resultsmentioning

confidence: 93%

Nonisothermal laminar contracted flow

Christiansen

Kelsey

1972

AIChE Journal

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Temperature and velocity profiles and pressure losses were computed for laminar, temperature-dependent Newtonian flow from a stream tube through an abrupt contraction into and through the entrance region of a smaller coaxial tube, in which the fluid was cooled or heated at constant wall temperature. The equations of motion and energy, including axial diffusion and viscous dissipation, were solved numerically for diameter ratios of one and two, a practical temperature range, and N p e and N R~ up to 100. Entrance temperatures and velocities are far from uniform, and pressure losses are greater than those computed using simplified equations and uniform entrance temperatures and velocities. E. B. CHRISTIANSEN and S. J. KELSEY Department of Chemical EngineeringThe University of Utuh Salt Lake City, Utah 841 12 SCOPEThe purpose of the presently reported study was to provide more accurate means for predicting pressure losses and the nature of the velocity and temperature fields at the entrance of and in the tubes of such equipment as shell-and-tube heat exchangers, chemical and nuclear reactors, and similar devices. Improved means for predicting such pressure losses and temperature and velocity fields should provide a basis for more effective and economical heat-exchanger design. Also, the nature of these temperature and velocity fields has an important influence on the progress of a chemical reaction and is important in the design and analysis of data from tubular chemical reactors.Recent as well as earlier theoretical and experimental studies of flow in a tube accompanied by heat exchange with the tube walls have demonstrated that the dependence of viscosity on temperature can importantly affect pressure losses and heat transfer. In some recent numerical solutions of the equations of motion and energy in which the dependence of viscosity on temperature is accounted for, it was assumed that flow at the tube entrance is parabolic and that radial convection, inertial terms, axial diffusion, and viscous dissipation are negligible. Some improved numerical solutions account for temperature-dependent viscosity, radial flow, and inertial effects but are restricted to uniform tube-entrance velocities and temperatures. Although these solutions approximate some situations, it is known that entrance velocity profiles are not flat in laminar, isothermal flow, particularly in the flow geometry of concern here, and that axial diffusion and viscous dissipation may have important effects. The effects of temperature-dependent flow, combined with those of axial diffusion and viscous dissipation, for the case of interest here have not, to our knowledge, been clearly defined in previous reports.In the presently reported study, flow from the header into the tubes of a shell-and-tube heat exchanger or reactor was approximated by flow from a larger stream tube (a stream tube has a frictionless wall) through an abrupt contraction into and through the flow-and temperaturedevelopment region of a smaller coaxial tube. The wall of the small tube...

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“…Figure 3 shows that stability sepatrices can be found in the (K,, 13) plane corresponding to particular regions of contractive stability. The region in the plane above and to the left of these sepatrices represents combinations of (K,, e) for which stability is insured.…”

Section: P1 Llull I Cmentioning

confidence: 99%

Stability of time‐delay systems

Landis

Perlmutter

1972

AIChE Journal

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= pressure, dynes/sq.cm. = radial distance, cm., or reduced radial distance = reduced radial distance = radius of smaller or downstream tube, diameters = radius of larger or upstream tube, diameters = z-component velocity, uJU0 = area average axial velocity in tube (with one or two exceptions, the downstream tube), cm./sec. = velocity, cm./sec. = r-component velocity, cJU0 = axial distance, cm., or reduced axial distance ( z / = reduced axial distance = entrance length, diameters ( r / R ) D ) G r e e k Letters eter = ratio of large-tube diameter to small-tube diam-5 = transformed axial coordinate p = density, g./cu.cm. + = stream functionSubscripts r = radial direction z = axial direction A direct method is presented for determining both local and regional stability of systems described by nonlinear differential-difference equations. Prediction of stability is with respect to a general class of initial curves. The practical as well as the conservative nature of the procedure is demonstrated by a numerical example.

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Laminar flow in the entrance region of a cylindrical tube: Part I. Newtonian fluids

Cited by 42 publications

References 11 publications

The microscopic analysis of high forchheimer number flow in porous media

The microscopic analysis of high forchheimer number flow in porous media

Nonisothermal laminar contracted flow

Stability of time‐delay systems

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