Fully developed laminar flow and heat transfer in curved tubes

Zapryanov, Z.; Christov, C. I.; Toshev, Evtim

doi:10.1016/0017-9310(80)90042-3

Cited by 34 publications

(9 citation statements)

References 11 publications

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“…Since the inner cylinder is rotating, the vortex cannot split into two counter-rotating eddies, hence for = 2.5 and = 2.7, a pattern known as 'Kelvin's cat's eye' develops. If it were a primary flow, the appearance of the cat's eye is a clear indication of pending instability, but in secondary streaming, it is quite a standard situation to have a streaming of a type of cat's eye (see, for instance [15] for the flow in rotating annulus and [16] for the secondary flow in the cross section of a curved pipe).…”

Section: Role Of the Aspect Ratiomentioning

confidence: 98%

Numerical implementation of Aristov–Pukhnachev's formulation for axisymmetric viscous incompressible flows

Moshkin

Poochinapan

Christov

2009

Numerical Methods in Fluids

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SUMMARYIn the present work a finite-difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49(2):112-115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross-flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross-flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions.The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in-depth investigations of the bifurcation phenomena in rotating flows.

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Section: Role Of the Aspect Ratiomentioning

confidence: 98%

Numerical implementation of Aristov–Pukhnachev's formulation for axisymmetric viscous incompressible flows

Moshkin

Poochinapan

Christov

2009

Numerical Methods in Fluids

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“…The effect of the different kinds of boundary conditions is shown to be small. Fully developed laminar flow and heat transfer was studied numerically by Zapryanov et al [42]. Their work focused on the case of constant wall temperature and showed that Nu increased with increasing Pr, even for cases at the same De.…”

Section: Introductionmentioning

confidence: 99%

Experimental Investigation of Coil Curvature Effect on Heat Transfer and Pressure Drop Characteristics of Shell and Coil Heat Exchanger

Salem

Elshazly

Sakr

et al. 2014

Journal of Thermal Science and Engineering Applications

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The present work experimentally investigates the characteristics of convective heat transfer in horizontal shell and coil heat exchangers in addition to friction factor for fully developed flow through the helically coiled tube (HCT). The majority of previous studies were performed on HCTs with isothermal and isoflux boundary conditions or shell and coil heat exchangers with small ranges of HCT configurations and fluid operating conditions. Here, five heat exchangers of counter-flow configuration were constructed with different HCT-curvature ratios (δ) and tested at different mass flow rates and inlet temperatures of the two sides of the heat exchangers. Totally, 295 test runs were performed from which the HCT-side and shell-side heat transfer coefficients were calculated. Results showed that the average Nusselt numbers of the two sides of the heat exchangers and the overall heat transfer coefficients increased by increasing coil curvature ratio. The average increase in the average Nusselt number is of 160.3–80.6% for the HCT side and of 224.3–92.6% for the shell side when δ increases from 0.0392 to 0.1194 within the investigated ranges of different parameters. Also, for the same flow rate in both heat exchanger sides, the effect of coil pitch and number of turns with the same coil torsion and tube length is remarkable on shell average Nusselt number while it is insignificant on HCT-average Nusselt number. In addition, a significant increase of 33.2–7.7% is obtained in the HCT-Fanning friction factor (fc) when δ increases from 0.0392 to 0.1194. Correlations for the average Nusselt numbers for both heat exchanger sides and the HCT Fanning friction factor as a function of the investigated parameters are obtained.

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“…Kalb and Seader [11] numerically studied the heat transfer in helical coils in the case of uniform heat flux using an orthogonal toroidal coordinate system. Fully developed laminar flow and heat transfer was studied numerically by Zapryanov et al [12] using a method of fractional steps for a wide range of Dean (10-7000) and Prandtl (0.005-2000) numbers. The effect of pitch on heat transfer and pressure drop was studied by Austen and Soliman [13] for the case of uniform wall heat flux.…”

Section: Literature Surveymentioning

confidence: 99%

Optimisation of Double Pipe Helical Tube Heat Exchanger and its Comparison with Straight Double Tube Heat Exchanger

Kareem

2016

J. Inst. Eng. India Ser. C

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Optimization of double pipe helical coil heat exchanger with various optimizing parameters and its comparison with double pipe straight tube are the prime objectives of this paper. Numerical studies were performed with the aid of a commercial computational fluid dynamics package ANSYS FLUENT 14. In this paper the double pipe helical coil is analysed under turbulent flow conditions for optimum heat exchanger properties. The parameters used for optimization are cross-sectional shape and taper angles. Optimization analysis is being carried out for finding best cross sectional shape of heat exchanger coils by using rectangular, square, triangular and circular crosssections. The tapered double pipe helical coil is then analysed for best heat transfer and pressure drop characteristics by varying the angle of taper. Finally, an optimum coil on the basis of all the analysis is selected. This optimized double pipe helical coil is compared with double pipe straight tube of equivalent cross-sectional area and length as that of unwounded length of double pipe helical coil.

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Fully developed laminar flow and heat transfer in curved tubes

Cited by 34 publications

References 11 publications

Numerical implementation of Aristov–Pukhnachev's formulation for axisymmetric viscous incompressible flows

Numerical implementation of Aristov–Pukhnachev's formulation for axisymmetric viscous incompressible flows

Experimental Investigation of Coil Curvature Effect on Heat Transfer and Pressure Drop Characteristics of Shell and Coil Heat Exchanger

Optimisation of Double Pipe Helical Tube Heat Exchanger and its Comparison with Straight Double Tube Heat Exchanger

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