Convection In Vertical Tube Research Articles

Numerical investigations on the difference between aiding and opposing flows in the developing regime of laminar mixed convection in vertical tubes

The present article discusses the numerical simulation results of laminar mixed convection flow in vertical tubes. A comparative analysis of the thermal and hydrodynamic features of both buoyancy-assisted and opposed flows was performed for Reynolds number (), Grashof number () and Richardson number () with uniform heat flux boundary condition. 2-D axisymmetric steady state simulations were carried out for a length-to-diameter () ratio of with water as the working fluid. Numerical simulations were performed by employing SIMPLE scheme for pressure–velocity coupling in momentum equations and second order UPWIND scheme for solving energy equations. In case of assisting flow (), at fully developed state the centerline velocity decreases, and velocity is increased near the tube wall due to heat flux induced free convection. With increasing heat flux, the decrement in centerline velocity compared to the no-heat flux condition increases. Further, with increasing heat flux, the increase in friction factor and Nusselt number was observed. Therefore, at the same the variation of heat flux led to unique velocity profiles and temperature gradients. The variation of centerline velocity and temperature in developing region was also studied. While centerline temperature was monotonically increasing with length, the centerline velocity increased up to a maximum in the developing region and then attained the steady state at a lower value in the fully developed state. Subsequently we studied the dependence of on the hydrodynamic and thermal features. For constant friction factor and Nusselt number was observed to increase with increase in from 0.1 to 1.5 range. At fixed variation of heat flux leads to variation of or Hence, the buoyancy effect has a significant role in the entrance length development. The hydrodynamic entry length after an initial increase, attained an almost constant value with increasing On the other hand, the thermal entry length exhibited a decreasing trend with increasing Similarly, at constant Nusselt number increased with increasing for a range of 100–1000. It was evident that for a given and the heat transfer in the developing flow is always higher as that of the fully developed flow. Contrasting observations were observed for buoyancy-opposed flow. Velocity is accelerated at the center as compared to the tube wall in case of opposing flow for same and For a fixed the friction factor and Nusselt number decreased with increasing the Both the hydrodynamic and thermal entry length increases for opposing flows. Finally, we have developed correlations for fully developed friction factor () with as well as and Nusselt number () with for buoyancy-assisting and buoyancy-opposing flows. Two independent correlations are also produced for with Graetz number () for developing and fully developed regimes in both assisting as well as opposing flows.

Two regimes of flux scaling in axially homogeneous turbulent convection in vertical tube

From experiments of axially homogeneous turbulent convection in a vertical tube using heat (Prandtl number Pr 6 ) and brine (Pr 600 ) we show that at sufficiently high Rayleigh numbers (Ra-g), the Nusselt number Nu(g) similar to (RagPr)(1/2), which corresponds to the so-called ultimate regime scaling. In heat experiments below certain Rag,however,there is transition to a new regime, Nu(g) similar to (RagPr)(0.3). This transition also seems to exist in earlier reported data for Pr = 1 and Pr 600 , at different Ra-g. However, the transition occurs at a single Grashof number, Gr(gc) 1.6 x10(5) , and unified flux scalings for Pr >= 1 , Nug/Pr similar to Gr(g)(0.3), and Nu(g)/Pr similar to Gr(g)(1/2) can be given for the two regimes.

Bouyancy Effect on Forced Convection in Vertical Tubes at High Reynolds Numbers

The complex interaction of forced and natural convections depends on flow regime and flow direction. Aiding flow occurs when both driving forces act in the same direction (heating upflow fluid and cooling downflow fluid), opposing flow occurs when they act in different directions (cooling upflow fluid and heating downflow fluid). To evaluate mixed convection methods, Heat Transfer Research, Inc. (HTRI) recently collected water and propylene glycol data in two vertical tubes of different tube diameters. The data cover wide ranges of Reynolds, Grashof, and Prandtl numbers and differing ratios of heated tube length to diameter in laminar, transition, and turbulent forced flow regimes. In this paper, we focus the buoyancy effect on forced convection of single-phase flows in vertical tubes with Reynolds numbers higher than 2000. Using HTRI data and experimental data in literature, we demonstrate that natural convection can greatly increase or decrease the convective heat transfer coefficient. In addition, we establish that natural convection should not be neglected if the Richardson number is higher than 0.01 or the mixed turbulent parameter Ra1/3/(Re0.8 Pr0.4) is higher than 0.05 even in forced turbulent flow with Reynolds numbers greater than 10,000. High resolution Reynolds-averaged Navier–Stokes simulations of several experimental conditions confirm the importance of the buoyancy effect on the production of turbulence kinetic energy. We also determine that flow regime maps are required to predict the mixed convection heat transfer coefficient accurately.

Predicted effects of inlet turbulent intensity on mixed convection in vertical tubes with uniform wall heat flux

Simultaneously developing upward mixed convection of air in vertical tubes with uniform wall heat flux was studied numerically using the three-dimensional elliptic conservation equations. The coupled hydrodynamic and thermal fields were predicted using both laminar and turbulent formulations (the latter was based on the Launder and Sharma low Reynolds number k – ɛ turbulence model) for Re = 1000 and three different values of the inlet turbulent intensity over a wide range of Grashof numbers ( Gr ⩽ 10 8 ). The turbulent formulation is more versatile since it can predict turbulent as well as laminar fully-developed flow fields. The effects of inlet turbulent intensity on the axial evolution of the hydrodynamic and thermal fields as well as on the developed velocity and temperature profiles are presented. It is also shown that the increase of the inlet turbulent intensity causes a significant decrease of the wall temperature and of the skin friction coefficient at certain Re – Gr combinations.

Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux

Upward mixed convection of air in a long, vertical tube with uniform wall heat flux has been studied numerically for Re=1000, Re=1500 and Gr⩽10 8 using a low Reynolds number k– ε model. The results for the fully developed region identify two critical Grashof numbers for each Reynolds number, which correspond to laminar–turbulent transition and relaminarization of the flow. They also distinguish the Re– Gr combinations that result in a pressure decrease over the tube length from those resulting in a pressure increase. A correlation expressing the fully developed Nusselt number in terms of the Grashof and Reynolds numbers is proposed. It is valid for laminar and turbulent flows in the range 1000⩽ Re⩽1500, Gr⩽5×10 7.

Numerical Study of Mixed Convection in Vertical Tubes under Conditions of Unstable Stratification

The present numerical study was performed using a three-parameter turbulence model supplemented by the thermogravitational terms and the transport equation for the transverse turbulent heat flux. The results obtained are compared with the few available experimental data for downward water and air flows through vertical heated tubes and with calculations for upward flow.

95/00711 Laminar natural convection in vertical tubes with one end open to a large reservoir: A numerical solution

95/00711 Laminar natural convection in vertical tubes with one end open to a large reservoir: A numerical solution

Heat transfer by combined free and forced convection in vertical tubes

The influence of free convection on forced convection heat transfer becomes important in laminar flows. Numerical methods have been applied for a study of mixed convection in vertical tubes for the following conditions: temperature-dependent fluid density, constant wall temperature and parabolic profile of axial velocity at the tube entrance. Both cases: heating and cooling have been considered.

Combined Free and Forced Convection in Vertical Tubes with Radial Internal Fins

An analysis is made of the fully developed laminar flow and heat transfer in vertical tubes with radial internal fins to determine the influence of the buoyancy forces. The governing equations for velocity and temperature are solved by a finite difference technique which incorporates a special scheme for treating the two coupled variables. Results are presented for a range of the Rayleigh number and for various values of the fin height and the number of fins. The buoyancy force is found to increase significantly both friction and heat transfer in the finned tube; augmentation factors in the range of 5 to 10 are encountered. The effect of buoyancy is particularly strong when the number of fins is small and the fins are short.

Computational Methods for Entry Length Heat Transfer by Combined Laminar Convection in Vertical Tubes

Numerical techniques for the calculation of velocity and temperature distributions in heated ducts have proved accurate but expensive in computer time and capacity. It is worth investigating to what extent simplification is possible without loss of accuracy. Entry-length heat transfer to upward laminar flow with combined convection in a vertical tube is taken as typical. Comparison is made between measured values and, first, a full numerical solution for constant thermophysical properties (viscosity and thermal diffusivity), secondly, the same solution but allowing for their individual and combined variation with temperature and, thirdly, a solution which assumes a series of truncated versions of the fully developed temperature distribution to establish corresponding velocity profiles, allowing for temperature-dependent properties.

Thermal convection in vertical tubes with application to geysers

Thermal convection in vertical tubes with application to geysers

Thermal convection in vertical tubes with application to geysers

Thermal convection in vertical tubes has been studied theoretically as an initial value problem using numerical techniques. The thermal and viscous boundary layers at the wall are taken into account approximately. Special emphasis is placed on the Geophysical application of this problem, particularly in examining the convective theories of geyser eruptions from a hydrodynamic point of view and determining the forms of convection during the preliminary stage before boiling starts. The proper time scales and other associated properties are explained through determining the appropriate eddy coefficients. DOI: 10.1111/j.2153-3490.1969.tb00417.x

Laminar dispersion in capillaries: Part V. Experiments on combined natural and forced convection in vertical tubes

AbstractAn approximate theory for transient dispersion with combined free and forced convection in vertical tubes is developed and tested experimentally. It is found that the dispersion coefficient in such systems depends on a parameter α, which is defined by Equation (38). The analytical expression developed for the dispersion coefficient, Equation (33), is found to be a reasonably good approximation in the range −50 < α < 300.Experimental results are reported for a rather wide range of parameters for tubes with both 1 1/2 and 5 mm. diameters.It is found that the extent of dispersion is enhanced significantly when lighter fluid is on the bottom and displaces a heavier one. On the other hand, the dispersion coefficient is inhibited when the situation is reversed. It is found that these effects are not symmetrical with respect to the absolute magnitude of the parameter α as is illustrated in Figure 12.