Axial dispersion in laminar flow through coiled tubes

A study has been made on axial dispersion in laminar flow in helical coiled tubes, for conditions in which molecular diffusion plays a dominating role. The axial dispersion coefficients have been calculated for Dean numbers smaller than 16. In this region the ratio of the dispersion coefficient in coiled tubes to that in straight tubes can with good approximation be given as a function of Dn²Sc, provided R/a > 20. This ratio decreases from 1, for Dn²Sc ≈ 100, to ? 0·25 for Dn²Sc ≈ 5000.     

Axial dispersion in laminar flow of polymer solutions through coiled tubes

The results of an experimental study on axial dispersion in laminar flow of non-Newtonian fluids through helical coils are reported. The ranges of variables covered are 10.5 ≤ λ ≤ 220, 0.6 ≤ n ≤ 1.0, 0.1 < N_Regn < 140, and 0.04 < τ > 2.2. The condition for the applicability of Taylor's dispersion model is also reported. It is found that coiling results in a dispersion reduced over that in a straight tube.     

The residence time distribution for laminar flow in helically coiled tubes

Sizable errors exist in previously published studies on the residence time distribution for ideal laminar flow in a helically coiled tubes. The numerical methods used to give corrected results are generally useful for flow situations where the projections of the streamlines on the channel cross-section are closed curves.An asymptotic solution, valid at long residence times, has been obtained. This solution confirms the numerical observation that the tail of the distribution is similar to that for laminar flow in a straight tube. If molecular diffusion is ignored, this form of asymptotic behavior is shown to be a general characteristic of all flow systems involving a fixed wall. When diffusion is considered, the asymptotic residence time distribution will be a decaying exponential in time. This confirms the widespread experimental observation that residence time distributions have exponential tails.     

Non-isothermal pressure-drop in non-newtonian laminar flow

Experimentally-measured pressure-drop data are compared with analytical predictions for laminar flow of non-Newtonian fluids in circular conduits, under constant wall heat flux boundary condition. The non-Newtonian pseudoplastic solutions used in this study were aqueous solutions of Methocel® (0.75% – 2% w/w) and Carbopol 934® (0.15% – 0.50%). The heated section was 0.792″ i.d. × 1″ o.d. × 112.87″ long brass tube with an additional length of 68″ acting as the entrance length. The analytical predicitions on pressure drop have been based on numerically computed or analytically-postulated temperature profiles. The mean deviation of the predicted values from the experimental values is of the order of ±8%.     

Reverse osmosis in laminar flow through curved tubes

A new design for reverse osmosis in a curved tube system takes advantage of the scouring-silting nature of the secondary flow pattern by utilizing a split membrane over the circumference of the tube. The wall concentration and concentration boundary layer thickness at the inside of the bend grow rapidly unless salt is allowed to escape there, whereas at the outside of the bend, the wall concentration and concentration boundary layer thickness remain small compared to straight tubes, thus indicating improved performance.     

RTD for diffusion free laminar flow in helical coils

The results of an experimental investigation of the RTD in the low Reynolds number, low Dean number region for helical coils are reported. It is found that, under the conditions of negligible molecular diffusion, for 0·6 <N_De < 6 and curvature ratio from 0·0036 to 0·0970 coiling results in an essentially unique RTD which is narrower than that for straight tubes confirming the validity of a published theoretical analysis. The results throw light on the conditions for the validity of Dean's analysis. An empirical expression is obtained for taking into account the weak influence of curvature ratio on narrowing the RTD.     

Heat transfer to pseudoplastic fluids in laminar flow in horizontal tubes

Experimental work dealing with the heating and cooling of pseudoplastic solutions in horizontal tubes is described. The solution strengths are chosen in order to either exclude, or permit, the presence of natural convection.In the absence of natural convection, heat transfer increases of up to 20 per cent are obtained as a direct result of the pseudoplastic character of the fluids, and the data obtained in heating runs provide satisfactory verification of an existing heat transfer correlation [7]. The cooling results are not well correlated, however, emphasizing doubt about the general use of empirical correction factors similar to that of Sieder and Tate.The unusual properties of aqueous solutions of Carbopol are shown to have important bearing on the results described in this paper. Both the apparent viscosity and non-Newtonian character of the solutions increase with increasing temperature, the reverse of the normal case.For pseudoplastic fluids, the extent of heat transfer due to natural convection is shown to be controlled by the physical properties of the fluids evaluated under wall temperature conditions, as suggested by Metzner and Gluck [9]. Nevertheless, the equation given by these workers is inaccurate when applied to the present results, most of which are well represented by the equation

This equation applies also to Newtonian fluids provided bulk fluid conditions are used and the consistency indices γ_B and γ_w are replaced by viscosities μ_B and μ_w.Under certain extreme conditions the effects of natural convection can decrease, rather than increase, the extent of heat transfer. It is suggested that this occurs when layers of fluid having a very much higher viscosity than the bulk of the fluid are formed. It is shown theoretically that this may reduce the heat transfer coefficients, but the exact nature of the interplay between such “stratified flow” effects and the normal “circulation” effects are not yet clear. It would appear, however, that the effects of stratified flow on heat transfer can become pronounced only when the temperature differences and shear rates are such as to produce large point to point variations in the effective viscosity of the fluid.     

Numerical evaluation of laminar heat transfer enhancement in nanofluid flow in coiled square tubes

Convective heat transfer can be enhanced by changing flow geometry and/or by enhancing thermal conductivity of the fluid. This study proposes simultaneous passive heat transfer enhancement by combining the geometry effect utilizing nanofluids inflow in coils. The two nanofluid suspensions examined in this study are: water-Al2O3 and water-CuO. The flow behavior and heat transfer performance of these nanofluid suspensions in various configurations of coiled square tubes, e.g., conical spiral, in-plane spiral, and helical spiral, are investigated and compared with those for water flowing in a straight tube. Laminar flow of a Newtonian nanofluid in coils made of square cross section tubes is simulated using computational fluid dynamics (CFD)approach, where the nanofluid properties are treated as functions of particle volumetric concentration and temperature. The results indicate that addition of small amounts of nanoparticles up to 1% improves significantly the heat transfer performance; however, further addition tends to deteriorate heat transfer performance.     

Irregularities in steady flow for non-newtonian fluids between cone and plate

Flow irregularities have been visually observed in solutions of polyacrylamide of high molecular weight on shear in a cone-and-plate rheometry (gap angle 2.3°). This anomalous flow was found to depend on molecular weight, concentration, and solvent. The onset of flow irregularities were generally at shear rates < 5 sec^?1. A dimensional analysis shows that the elastic component of the fluid is responsible for the anomalous flow. The onset of flow irregularities has been predicted from measurements of recoverable strain as a function of shear stress.     

Modeling of flow dynamics in laminar aerosol flow tubes

Flow behaviour in laminar aerosol flow tubes was investigated using a Computational Fluid Dynamics (CFD) model. Since these flow tubes are typically operated at low gas velocity, even small temperature gradients produce convection currents strong enough to interfere with laminar flow. This results in recirculation, causing the residence times of aerosol particles to be poorly defined. The situation is exacerbated when temperature inversions are present, or when the flow direction and temperature are changed simultaneously. We analyzed several characteristic flow tube configurations to define the range of experimental conditions that will ensure a laminar flow profile with minimal recirculation. For a laminar flow situation, we evaluated the extent of diffusion-controlled exchange between aerosol and the flow tube wall.     

Calendering of non-newtonian fluids

The calendering of non-Newtonian fluids by two rotating cylinders to produce thin films of fluids finds wide application in polymer sheet-making and food-drying industries. Theoretical work has previouly been devoted to the symmetrical case where the cylinders are of equal diameters rotating at the same speed. The present work proposes a new one-film theory of calendering of power law fluids for unequal radii and surface velocities of the calendering cylinders. The relationship between the dimensionless thickness of the calendered fluid, Δ_e^* and that of the incoming fluid, Δ_i^* is shown to be a function of the ratio of the surface velocities of the cylinders and the power law index. The result further shows that Δ_e^* tends to asymptote after the second decade of Δ_i^*     

The dispersion of solute in turbulent pipe flow of non-newtonian fluids

The dispersion of solute in turbulent pipe flow of power law fluids is investigated theoretically. Results in terms of the intensity of dispersion are compared for the non-Newtonian and purely viscous Newtonian fluids over a wide range of Schmidt numbers. The computed results indicate that the intensity of dispersion at a constant Schmidt and Reynolds number increases with increasing flow behavior index.     

Heat transfer in laminar flow of non-Newtonian fluids

The main objective of this work is the consideration of local heat transfer coefficients for non-Newtonian power-law pseudoplastic liquid in laminar flow in circular conduits. The wall boundary conditions chosen are cases involving uniformly constant heat flux and step change in heat flux.Analytical solutions are developed for the wall temperature profile and compared with experimental data. Additionally, the experimental data have been correlated for comparison with existing relationships, hitherto not verified adequately. The limits of experimental data are:

     

Liquid phase residence time distribution for two phase flow in coiled tubes

The residence time distribution (RTD) of the liquid phase in air-water flow through helical coils has been studied. Upward and downward cocurrent flows have been investigated in three coils with curvature ratios ranging from 11 to 60.7. The ranges of the Reynolds numbers for the gas and the liquid varied from 1500 to 3000 and 620 to 3200, respectively. A model has been proposed that describes the liquid phase RTD as combination of two different residence time distributions applicable for turbulent and laminar liquid flows.