A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes

A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes is proposed. In order to overcome the effect of flow pattern on heat transfer, a flow pattern factor (effective wetted-perimeter) is developed and introduced into our proposed correlation. To verify the correlation, local heat transfer coefficients and flow parameters were measured for air–water flow in a pipe in the horizontal position with different flow patterns. The test section was a 27.9 mm ID stainless steel pipe with a length to diameter ratio of 100. A total of 114 data points were taken by carefully coordinating the liquid and gas superficial Reynolds number combinations. The heat transfer data were measured under a uniform wall heat flux boundary condition ranging from about 3000 W/m² to 10,600 W/m². The superficial Reynolds numbers ranged from about 820 to 26,000 for water and from about 560 to 48,000 for air. These experimental data including different flow patterns were successfully correlated by the proposed general two-phase heat transfer correlation with an overall mean deviation of 5.5%, a standard deviation of 11.7%, and a deviation range of −18.3% to 37.0%. Ninety three percent (93%) of the data were predicted within ±20% deviation.     

Cross-flow heat transfer in fixed bed

Radial flow reactor operated at cross-flow heat transfer is focused for large scale methanol synthesis. The effects of operating conditions including the reactor inlet air temperature, the heating pipe temperature and the air flow rate on the cross-flow heat transfer were investigated and results show that the temperature profile of the area in front of the heating pipe is slightly affected by all the operating conditions. The main area whose temperature profile is influenced is located behind the heating pipe. The heat transfer direction is related to the direction of the flow. In order to obtain the basic parameters for radial flow reactor designing calculation, the dimensionless number group method was used for data fitting of the bed effective thermal conductivity and the wall heat transfer coefficient which were calculated by the mathematical model with the product of Reynolds number and Prandtl number. The comparison of experimental data and calculated values shows that the calculated values fit the experimental data satisfactorily and the formulas can be used for reactor designing calculation.     

Flow of couple stress fluid with variable thermal conductivity

The steady flow and heat transfer of a couple stress fluid due to an inclined stretching cylinder are analyzed. The thermal conductivity is assumed to be temperature dependent. The governing equations for the flow and heat transfer are transformed into ordinary differential equations. Series solutions of the resulting problem are computed. The effects of various interested parameters, e.g., the couple stress parameter, the angle of inclination, the mixed convection parameter, the Prandtl number, the Reynolds number, the radiation parameter, and the variable thermal conductivity parameter, are illustrated. The skin friction coefficient and the local Nusselt number are computed and analyzed. It is observed that the heat transfer rate at the surface increases while the velocity and the shear stress decrease when the couple stress parameter and the Reynolds number increase. The temperature increases when the Reynolds number increases.     

Turbulent heat transfer in circular tube flows of viscoelastic fluids

The effects of thermal entrance length, polymer degradation and solvent chemistry were found to be critically important in the determination of the drag and heat transfer behavior of viscoelastic fluids in turbulent pipe flow. The minimum heat transfer asymptotic values in the thermally developing and in the fully developed regions were experimentally determined for relatively high concentration solutions of heat transfer resulting in the following correlations: $$\begin{gathered} j_H = 0.13\left( {\frac{x}{d}} \right)^{ - 0.24} \operatorname{Re} _a^{ - 0.45} thermally developing region \hfill \\ x/d< 450 \hfill \\ j_H = 0.03 \operatorname{Re} _a^{ - 0.45} thermally developed region \hfill \\ x/d< 450 \hfill \\ \end{gathered} $$ For dilute polymer solutions the heat transfer is a function ofx/d, the Reynolds number and the polymer concentration. The Reynolds analogy between momentum and heat transfer which has been widely used in the literature for Newtonian fluids is found not to apply in the case of drag-reducing viscoelastic fluids.     

Turbulent heat transfer characteristics of water flow in a rotating pipe

Large-Eddy-Simulation of turbulent heat transfer for water flow in rotating pipe is performed, for various rotation ratios (0 ≤ N ≤ 14). The value of the Reynolds number, based on the bulk velocity and pipe diameter, is Re = 5,500. The aim of this study is to examine the effect of the rotating pipe on the turbulent heat transfer for water flow, as well as the reliability of the LES approach for predicting turbulent heat transfer in water flow. Some predictions for the case of non-rotating pipe are compared to the available results of literature for validation. To depict the influence of the rotation ratio on turbulent heat transfer, many statistical quantities are analyzed (distributions of mean temperature, rms of fluctuating temperature, turbulent heat fluxes, higher-order statistics). Some contours of instantaneous temperature fluctuations are examined.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

Effect of particles on turbulent thermal field of channel flow with different Prandtl numbers

The direct numerical simulation(DNS) of heat transfer in a fully developed non-isothermal particle-laden turbulent channel flow is performed.The focus of this paper is on the modulation of the particles on turbulent thermal statistics in the particle-laden flow with three Prandtl numbers(P r = 0.71,1.5,and 3.0) and a shear Reynolds number(Reτ = 180).Some typical thermal statistics,including normalized mean temperature and their fluctuations,turbulent heat fluxes,Nusselt number and so on,are analyzed.The results show that the particles have less effects on turbulent thermal fields with the increase of Prandtl number.Two reasons can explain this.First,the correlation between fluid thermal field and velocity field decreases as the Prandtl number increases,and the modulation of turbulent velocity field induced by the particles has less influence on the turbulent thermal field.Second,the heat exchange between turbulence and particles decreases for the particle-laden flow with the larger Prandtl number,and the thermal feedback of the particles to turbulence becomes weak.     

Transients in flow and local heat transfer due to a pressure wave in pipe flow

The effect of a pressure wave on the turbulent flow and heat transfer in a rectangular air flow channel has been experimentally studied for fast transients, occurring due to a sudden increase of the main flow by an injection of air through the wall. A fast response measuring technique using a hot film sensor for the heat flux, a hot wire for the velocities and a pressure transducer have been developed. It was found that in the initial part of the transient the heat transfer change is independent of the Reynolds number. For the second part the change in heat transfer depends on thermal boundary layer thickness and thus on the Reynolds number. Results have been compared with a simple numerical turbulent flow and heat transfer model. The main effect on the flow could be well predicted. For the heat transfer a deviation in the initial part of the transient heat transfer has been found. From the turbulence measurements it has been found that a pressure wave does not influence the absolute value of the local turbulent velocity fluctuations. They could be considered to be frozen.Nomenclature A surface area (m²) - D diameter (m) - h heat transfer coefficient (Wm^–2 K^–1) - p pressure drop (Pa) - P pressure (Pa) - Q heat flow (W) - R tube radius (m) - T bulk temperature (K) - T _s surface temperature (K) - t time (s) - u velocity (m/s) - V voltage (V) - y distance from wall (m) - viscosity (N s m^–2) - kinematic viscosity (m^–2 s^–1) - density (kg m^–3) - _w wall shear stress (N m^–2) - Nu Nusselt number - Re Reynolds number     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

Local convective heat transfer for laminar and turbulent flow in a rotor-stator system

Abstract The aim of this work is to show a better comprehension of the flow structure and thermal transfer in a rotor-stator system with a central opening in the stator and without an airflow imposed. The experimental technique uses infrared thermography to measure the surface temperatures of the rotor and the numerical solution of the steady-state heat equation to determine the local heat transfer coefficients. Analysis of the flow structure between the rotor and the stator is conducted by PIV. Tests are carried out for rotational Reynolds numbers ranging from 5.87×10⁴ to 1.4×10⁶ and for gap ratios ranging from 0.01 to 0.17. Analysis of the experimental results has determined the influence of the rotational Reynolds number, the gap ratio and systems geometry on the flow structure, and the convective exchanges in the gap between the rotor and the stator. Some correlations expressing the local Nusselt number as a function of the rotational Reynolds number and the gap ratio are proposed.     

Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary conditions

Direct numerical simulations of heat transfer in a fully-developed turbulent pipe flow with circumferentially-varying thermal boundary conditions are reported. Three cases have been considered for friction Reynolds number in the range 180–360 and Prandtl number in the range 0.7–4. The temperature statistics under these heating conditions are characterized. Eddy diffusivities and turbulent Prandtl numbers for radial and circumferential directions are evaluated and compared to the values predicted by simple models. It is found that the usual assumptions made in these models provide reasonable predictions far from the wall and that corrections to the models are needed near the wall.     

Beitrag zur Rohrströmung kompressibler Fluide mit Reibung und Wärmeübergang

Übersicht Die Strömung eines kompressiblen Fluids aus einem Druckkessel durch ein Rohr konstanten Kreisquerschnitts und mit konstanter Wandtemperatur, in dem Wandreibung wirksam ist, wird nach der Stromfadentheorie untersucht. Gegeben sind der Druck im Kessel und am Ende der Rohrleitung sowie die Temperatur der Rohrwand und im Kessel. Als Wärmeübergangshypothese wird die Reynolds-Analogie benutzt. Die Wandreibung wird durch die Rohrreibungszahl beschrieben. Die sich ergebende Differentialgleichung und das Eigenwertproblem für die Eintrittsmachzahl wird numerisch gelöst in Abhängigkeit von der dimensionslosen Rohrlänge für Austrittsmachzahlen 1. Eine analytische Näherungslösung für kleine Eintrittsmachzahlen und eine asymptotische Entwicklung für große Rohrlängen wird angegeben. Es zeigt sich, daß der Wärmeübergangsprozeß relativ schnell abgeschlossen ist und die End-Machzahl, der Druckverlustfaktor sowie das kritische Druckverhältnis vom Wärmeübergang fast unabhängig sind.

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A note on the viscous pipe flow of a compressible fluid with heat transfer

Summary The flow of a compressible fluid from a pressure reservoir through a pipe with constant circular cross-section and constant pipe-wall temperature has been investigated by means of one-dimensional theory with wall-friction taken into account. The initial stagnation pressure and temperature, the pipe wall temperature and the pipe exit pressure are assumed to be given. The heat transfer is assumed to follow the Reynolds analogy, while wall friction is taken into account by the pipe friction coefficient. The resulting differential equation and the corresponding eigenvalue problem for the inlet Mach number have been solved numerically as function of the dimensionless pipe-length for exit Mach numbers 1. An analytic approximation for small pipe inlet Mach numbers and an asymptotic expansion for large pipe-lengths have been derived. It is found that the heat transfer is restricted to a relatively small distance past the inlet. The final Mach number, the pressure loss factor as well as the critical pressure ratio is approximately independent of any heat transfer.

     

Thermo-mechanical modeling of turbulent heat transfer in gas–solid flows including particle collisions

A thermo-mechanical turbulence model is developed and used for predicting heat transfer in a gas–solid flow through a vertical pipe with constant wall heat flux. The new four-way interaction model makes use of the thermal k_θ–τ_θ equations, in addition to the hydrodynamic k–τ transport, and accounts for the particle–particle and particle–wall collisions through a Eulerian/Lagrangian formulation. The simulation results indicate that the level of thermal turbulence intensity and the heat transfer are strongly affected by the particle collisions. Inter-particle collisions attenuate the thermal turbulence intensity near the wall but somewhat amplify the temperature fluctuations in the pipe core region. The hydrodynamic-to-thermal times-scale ratio and the turbulent Prandtl number in the region near the wall increase due to the inter-particle collisions. The results also show that the use of a constant or the single-phase gas turbulent Prandtl number produces error in the thermal eddy diffusivity and thermal turbulent intensity fields. Simulation results also indicate that the inter-particle contact heat conduction during collision has no significant effect in the range of Reynolds number and particle diameter studied.     

Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries

This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - c_m mass concentration of microcapsules - c_p specific heat, kJ kg^–1 K^–1 - h_fs phase change material heat of fusion, kJ kg^–1 - h_m* modified convective heat transfer coefficient, W m^–2 K^–1 - k thermal conductivity, W m^–1 K^–1 - k_e effective thermal conductivity of slurry, W m^–1 K^–1 - k_b slurry bulk thermal conductivity, W m^–1 K^–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - q_wⁿ wall heat flux, Wm^–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r₀ duct radius, m - r₁ dimensionless radial coordinate - Ste Stefan number - T temperature, K - T₁ lower phase change temperature limit, K - T₂ upper phase change temperature limit, K - T_i slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x₁ dimensionless axial coordinate - thermal diffusivity, m²/s - dimensionless temperature - dynamic viscosity, N·s/m² - kinematic viscosity, m²/s - _t width of thermal boundary, m - degree of heat transfer enhancement, = h_m*/(h_m*)_single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid     

Large-eddy simulation in a mixing tee junction: High-order turbulent statistics analysis

This study analyses the mixing and thermal fluctuations induced in a mixing tee junction with circular cross-sections when cold water flowing in a pipe is joined by hot water from a branch pipe. This configuration is representative of industrial piping systems in which temperature fluctuations in the fluid may cause thermal fatigue damage on the walls. Implicit large-eddy simulations (LES) are performed for equal inflow rates corresponding to a bulk Reynolds number Re = 39,080. Two different thermal boundary conditions are studied for the pipe walls; an insulating adiabatic boundary and a conducting steel wall boundary. The predicted flow structures show a satisfactory agreement with the literature. The velocity and thermal fields (including high-order statistics) are not affected by the heat transfer with the steel walls. However, predicted thermal fluctuations at the boundary are not the same between the flow and the solid, showing that solid thermal fluctuations cannot be predicted by the knowledge of the fluid thermal fluctuations alone. The analysis of high-order turbulent statistics provides a better understanding of the turbulence features. In particular, the budgets of the turbulent kinetic energy and temperature variance allows a comparative analysis of dissipation, production and transport terms. It is found that the turbulent transport term is an important term that acts to balance the production. We therefore use a priori tests to evaluate three different models for the triple correlation.     

Experimental study of pre-swirl flow effect on the heat transfer process in the entry region of a convergent pipe

Experiments have been performed to study the heat transfer process of swirling flow issued into a heated convergent pipe with a convergent angle of 5° with respect to the pipe axis. A flat vane swirler situated at the entrance of the pipe is used to generate the swirling flow. During the experiments, the Reynolds number ranges from 7970 to 47,820, and the swirl number from 0 to 1.2. It is found that the convergence of the pipe can accelerate the flow which has an effect to suppress the turbulence generated in the flow and reduce the heat transfer. However, in the region of weak swirl (S = 0-0.65), the Nusselt numbers increase with increasing swirl numbers until S = 0.65, where turbulence intensity is expected to be large enough and not suppressible. In the region of strong swirl (S > 0.65), where recirculation flow is expected to be generated in the core of the swirling flow, the heat transfer characteristic can be altered significantly. At very high swirl (S ? 1.0), the accelerated flow in the circumferential direction is expected to be dominant, which leads to suppress the turbulence and reduce the heat transfer. The Nusselt number is found proportional to the swirl number. Correlations of the Nusselt numbers in terms of the swirl number, the Reynolds number and the dimensionless distance are attempted and are very successful in both the weak and the strong swirl regions.     

On the Lower Critical Reynolds Number for Flow in a Circular Pipe

Flow in a circular pipe is investigated experimentally at Reynolds numbers higher than that at which the resistance coefficients calculated from the Blasius formula for laminar flow and from the Prandtl formula for turbulent flow are equal. The corresponding Reynolds number based on the mean-flow velocity and the pipe diameter is about 1000. The experiments were performed at a high level of inlet pulsations produced by feeding gas into the pipe through a hole with a diameter several times smaller than the pipe diameter. In our experiments the critical Reynolds number was determined as the value, independent of the distance from the inlet, at which the ratio of the axial to the mean-flow velocity as a function of the Reynolds number deviated from 2. At the maximum ratio of the pipe cross-sectional area to the area of the hole through which the gas entered the pipe, equal to 26, the critical Reynolds number was about 2300. After a fivefold increase in the hole area the critical Reynolds number increased by approximately 4%.At Reynolds numbers below 2000, after at a high level of the inlet pulsations an almost laminar flow had developed in the pipe, a perturbation was introduced by inserting a diametrically oriented cylindrical rod with a diameter 10–20 times smaller than the pipe diameter. In these experiments, at Reynolds numbers higher than 1000, at a distance from the rod equal to 50 pipe diameters the axial to mean-flow velocity ratio was less than 2, approaching this value again at large distances from the rod. The insertion of the rod led to a decrease in the critical Reynolds number by approximately 12%.     

Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 Re_Dh 980, and modified Grashof numbers Gr^* = 9.53 × 10⁵ to 1.53 × 10⁷ . From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit, especially for low Reynolds numbers.     

Performance of RNG Turbulence Modelling for Forced Convective Heat Transfer in Ducts

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in straight ducts using the RNG (Re-Normalized Group) turbulence method.

A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts with different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with the RNG κ?ε model and the RNG non-linear κ-ε model of Speziale. The turbulent heat fluxes are modeled by the simple eddy diffusivity (SED) concept, GGDH and WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models arc implemented for an arbitrary three dimensional duct.

Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non-staggered grid arrangement. The pressure-velocity coupling is handled by using the SIMPLEC-algorithm. The convective terms are treated by the QUICK, scheme while the diffusive terms are handled by the central-difference scheme. The hybrid scheme is used for solving the κ and ε equations.

The overall comparison between the models is presented in terms of friction factor and Nusselt number. The secondary flow generation is also of major concern.     

Structure of near wall turbulence downstream of a wall mounted protrusion: an interesting Reynolds stress suppression phenomena

A local suppression in the generation of near wall Reynolds stress is achieved by modifying the buffer region and sublayer (y ⁺ <30) of a turbulent pipe flow with a 16.4 wall unit high wall mounted protrusion. Multi-component, multi-point, time resolved laser Doppler velocimetry measurements are made in the undisturbed and modified ARL/PSU glycerin tunnel pipe flow at a Reynolds number of approximately 10000. A downstream converging flow field is produced by the divergence of the approaching mean flow around the protrusion. A pair of counter-rotating vortices, 15 wall units in diameter with common flow down, are generated by the protrusion and also contribute to the wall directed flow convergence. The convergence region is 15 wall units high and more than 100 wall units long and appears to decouple the near wall region from the outer turbulent wall layer. Locally, turbulent velocity fluctuations in the form of Reynolds stress producing events, sweeps and ejections, are retarded within this region. This results in a reduction in near wall uv Reynolds stress and local wall shear. Interestingly, the counter-rotating vortices act to increase turbulent diffusion in a manner which is uncorrelated with Reynolds stress generation.