Numerical study on coupled fluid flow and heat transfer process in parabolic trough solar collector tube

A unified two-dimensional numerical model was developed for the coupled heat transfer process in parabolic solar collector tube, which includes nature convection, forced convection, heat conduction and fluid-solid conjugate problem. The effects of Rayleigh number (Ra), tube diameter ratio and thermal conductivity of the tube wall on the heat transfer and fluid flow performance were numerically analyzed. The distributions of flow field, temperature field, local Nu and local temperature gradient were examined. The results show that when Ra is larger than 10⁵, the effects of nature convection must be taken into account. With the increase of tube diameter ratio, the Nusselt number in inner tube (Nu₁) increases and the Nusselt number in annuli space (Nu₂) decreases. With the increase of tube wall thermal conductivity, Nu₁ decreases and Nu₂ increases. When thermal conductivity is larger than 200 W/(m K), it would have little effects on Nu and average temperatures. Due to the effect of the nature convection, along the circumferential direction (from top to down), the temperature in the cross-section decreases and the temperature gradient on inner tube surface increases at first. Then, the temperature and temperature gradients would present a converse variation at θ near π. The local Nu on inner tube outer surface increases along circumferential direction until it reaches a maximum value then it decreases again.     

An experimental study of thermal performance of shell-and-coil heat exchangers

In the present study an experimental investigation of the mixed convection heat transfer in a coil-in-shell heat exchanger is reported for various Reynolds and Rayleigh numbers, various tube-to-coil diameter ratios and dimensionless coil pitch. The purpose of this article is to assess the influence of the tube diameter, coil pitch, shell-side and tube-side mass flow rate over the performance coefficient and modified effectiveness of vertical helical coiled tube heat exchangers. The calculations have been performed for the steady-state and the experiments were conducted for both laminar and turbulent flow inside coil. It was found that the mass flow rate of tube-side to shell-side ratio was effective on the axial temperature profiles of heat exchanger. The results also indicate that the ? − NTU relation of the mixed convection heat exchangers was the same as that of a pure counter-flow heat exchanger.     

Enhancement of heat transfer in a tube with regularly-spaced helical tape swirl generators

Influence of helical tapes inserted in a tube on heat transfer enhancement is studied experimentally. A helical tape is inserted in the tube with a view to generating swirl flow that helps to increase the heat transfer rate of the tube. The flow rate of the tube is considered in a range of Reynolds number between 2300 and 8800. The swirling flow devices consisting of: (1) the full-length helical tape with or without a centered-rod, and (2) the regularly-spaced helical tape, are inserted in the inner tube of a concentric tube heat exchanger. Hot air is passed through the inner tube whereas cold water is flowed in the annulus. The experimental data obtained are compared with those obtained from plain tubes of published data. Experimental results confirmed that the use of helical tapes leads to a higher heat transfer rate over the plain tube. The full-length helical tape with rod provides the highest heat transfer rate about 10% better than that without rod but it increased the pressure drop. To overcome this, different free-spacing ratio (s = L_s/L_h) of 0.5, 1.0, 1.5, and 2.0 were examined. It was found that the space ratio value should be about unity for Re < 4000. The regularly-spaced helical tape inserts at s = 0.5 yields the highest Nusselt number which is about 50% above the plain tube.     

Heat transfer characteristics of two-phase He I (4.2 K) thermosiphon flow

In the framework of the cryogenic cooling system design of a large superconducting magnet under construction at CERN-Geneva, heat transfer in two-phase He I natural circulation loop has been investigated experimentally. The experiments were conducted on a 2 m thermosiphon loop with copper tube of 10 mm inner diameter uniformly heated over a length of 0.95 m. All data were obtained near atmospheric pressure. Evolution of the exit vapour quality and wall superheat as a function of heat flux are presented and analyzed. A comparison between the two-phase heat transfer coefficient h_TP determined in our study and the most relevant correlations available in literature is made. Further, we predict h_TP with a correlation based on the combining effects of forced convection and nucleate boiling by a power-type asymptotic model. Finally, we present the boiling crisis study and we propose a critical heat flux correlation as a function of channel height to diameter ratio (z/D) to model our experimental results.     

Heat transfer using a correlation by neural network for natural convection from vertical helical coil in oil and glycerol/water solution

A physical-empirical model is designed to describe heat transfer of helical coil in oil and glycerol/water solution. It includes an artificial neural network (ANN) model working with equations of continuity, momentum and energy in each flow. The discretized equations are coupled using an implicit step by step method. The natural convection heat transfer correlation based on ANN is developed and evaluated. This ANN considers Prandtl number, Rayleigh number, helical diameter and coils turns number as input parameters; and Nusselt number as output parameter. The best ANN model was obtained with four neurons in the hidden layer with good agreement (R > 0.98). Helical coil uses hot water for the inlet flow; heat transfer by conduction in the internal tube wall is also considered. The simulated outlet temperature is carried out and compared with the experimental database in steady-state. The numerical results for the simulations of the heat flux, for these 91 tests in steady-state, have a R ≥ 0.98 with regard to experimental results. One important outcome is that this ANN correlation is proposed to predict natural convection heat transfer coefficient from helical coil for both fluids: oil and glycerol/water solution, thus saving time and improving general system performance.     

Numerical Simulation and Optimization of Enhanced Heat Transfer in Helical Oval Tubes: Effect of Helical Oval Tube Modification,Pitch Ratio,and Depth Ratio

ABSTRACT

Flow and heat transfer behaviors in the helical oval tube, alternate-twisted-direction helical oval tube and regularly spaced helical oval tubes were numerically investigated. The helical oval tubes with eight oval tube depth ratios (0.03, 0.04, 0.05, 0.06, 0.07, 0.10, 0.15, and 0.20) and nine oval tube pitch ratios (0.6, 0.8, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0) were examined in turbulent regime, Reynolds number ranged from 5000 to 20,000. The computational results showed that fully developed periodic flow and heat transfer in helical oval tubes commenced at around entrance length to characteristic diameter of 8–9. The decreasing depth ratio and increasing pitch ratio helped to reduce the pressure loss of the tube heat exchanger. The maximum thermal performance of 1.30 was obtained by the use of the helical oval tube with depth ratio of 0.05 and pitch ratio of 0.6 at the lowest Reynolds number of 5000. At similar conditions, typical helical oval tubes offered better heat transfer rate and thermal performance than helical oval tubes with alternate axes and regularly spaced helical oval tubes.     

Turbulent heat transfer enhancement in a heat exchanger using helically corrugated tube

The augmentation of convective heat transfer in a single-phase turbulent flow by using helically corrugated tubes has been experimentally investigated. Effects of pitch-to-diameter ratio (P/D_H = 0.18, 0.22 and 0.27) and rib-height to diameter ratio (e/D_H = 0.02, 0.04 and 0.06) of helically corrugated tubes on the heat transfer enhancement, isothermal friction and thermal performance factor in a concentric tube heat exchanger are examined. The experiments were conducted over a wide range of turbulent fluid flow of Reynolds number from 5500 to 60,000 by employing water as the test fluid. Experimental results show that the heat transfer and thermal performance of the corrugated tube are considerably increased compared to those of the smooth tube. The mean increase in heat transfer rate is between 123% and 232% at the test range, depending on the rib height/pitch ratios and Reynolds number while the maximum thermal performance is found to be about 2.3 for using the corrugated tube with P/D_H = 0.27 and e/D_H = 0.06 at low Reynolds number. Also, the pressure loss result reveals that the average friction factor of the corrugated tube is in a range between 1.46 and 1.93 times over the smooth tube. In addition, correlations of the Nusselt number, friction factor and thermal performance factor in terms of pitch ratio (P/D_H), rib-height ratio (e/D_H), Reynolds number (Re), and Prandtl number (Pr) for the corrugated tube are determined, based on the curve fitting of the experimental data.     

An experimental study of heat transfer to turbulent separation fluid flow in an annular passage

The effect of step height on heat transfer to a radially outward expanded air flow stream in a concentric annular passage was studied experimentally. Separation, subsequent reattachment and developed air flow occurred in the test section at a constant heat flux boundary condition. The experimental investigation was focused on the effect of separation flow on the local and average convection heat transfer. The experimental set-up consists of concentric tubes to form annular passage with a sudden reduction in passage cross-section created by the variations of outer tube diameter at the annular entrance section (D). The outer tube of test section was made of aluminium having 83 mm inside diameter and 600 mm heated length, which was subjected to a constant wall heat flux boundary condition. The investigation was performed in a Re range of 17050-44545, heat flux varied from 719 W/m² to 2098 W/m² and the enhancement of step heights were, s = 0 (without step), 6 mm, 14.5 mm and 18.5 mm, which refer to d/D = 1, 1.16, 1.53 and 1.80, respectively.For all cases, an increase in the local heat transfer coefficient was obtained against enhanced heat flux and or Re. The effect of step variation is prominent in heat transfer at the separation region which increases with the rise of step height and it shows a little effect in the redevelopment region. In the separation region, the local heat transfer coefficient increases up to the maximum value at the reattachment point and then decreases gradually in the redevelopment region. The results have been correlated and compared with forced convection heat transfer in annular passage and show a maximum enhancement of 18% (S_max = 18.5 mm) within the range of step height. The present results show good agreement with previous works and have followed similar trends.     

Heat transfer augmentation in a helical-ribbed tube with double twisted tape inserts

Turbulent convective heat transfer characteristics in a helical-ribbed tube fitted with twin twisted tapes have been investigated experimentally. The experiment was carried out in a double tube heat exchanger using the helical-ribbed tube having a single rib-height to tube-diameter ratio, e/D_H = 0.06 and rib-pitch to diameter ratio, P/D_H = 0.27 as the tested section. The insertion of the double twisted tapes with twist ratio, Y, in the range of 2.17 to 9.39 is to create vortex flows inside the tube. The inserted ribbed tube is arranged in similar directions of the helical swirl of the twisted tape and the helical rib motion of the tube (called co-swirl). Effects of the co-swirl motion of the ribbed tube and the double twisted tapes with various twist ratios on heat transfer and friction characteristics are examined. The results obtained from the ribbed tube and the twin twisted tape insert are compared with those from the smooth tube and the ribbed tube acting alone. The experimental results reveal that the co-swirling inserted tube performs much better than the ribbed/smooth tube alone at a similar operating condition. The co-swirl tube at Y ≈ 8 yields the highest thermal performance at lower Reynolds number (Re). In addition, the correlations of Nusselt number and friction factor as functions of Re, Pr and Y are also proposed.     

Heat transfer effects of chimney height,diameter, and Prandtl number

This study investigates the heat transfer enhancement of a chimney system, both experimentally and numerically, by varying the height and diameter of the chimney, and the Prandtl number of the working fluid. Mass transfer experiments are carried out using a sulfuric acid and copper sulfate electroplating system based on analogy concepts. Numerical simulations are executed using FLUENT 6.3. Natural convection experiments and numerical calculations performed without a chimney showed good agreement with the Le Fevre correlation for natural convection on a vertical plate. As the chimney height is increased, the heat transfer rates are enhanced for all Prandtl numbers, but the enhancement rates decrease as the Prandtl number increases. An optimal chimney diameter is found that maximizes the heat transfer. An increase in heat input or heated length results in an additional enhancement of the heat transfer, increasing the buoyancy force. Numerical results provide visualizations of the temperature and velocity fields in the chimneys, showing their interactions and flow regimes.     

Experimental investigation of natural convection from vertical and horizontal helicoidal pipes in HVAC applications

Natural convection from uniformly heated helicoidal pipes oriented vertically and horizontally is experimentally studied. Four helicoidal pipes of different parameters are presented. The effects of pitch to pipe diameter ratio, coil diameter to pipe diameter ratio and length to pipe diameter ratio on the average heat transfer coefficient are found. The experiments covered a range of Rayleigh number based on tube diameter from 1.5 × 10³ to 1.1 × 10⁵. The results showed that the overall average Nusselt number, Nu_m, increases with the increase in pitch to pipe diameter ratio, coil diameter to pipe diameter ratio and length to pipe diameter ratio for vertical helicoidal pipes. For horizontal helicoidal pipes, the overall average Nusselt number, Nu_m, increases with the increase in pitch to pipe diameter ratio and length to pipe diameter ratio, but it decreases with the increase in coil diameter to pipe diameter ratio. New correlations are presented, and they can be used in HVAC applications.     

Convective heat transfer in helical coils for constant-property and variable-property flows with high Reynolds numbers

Forced convection heat transfer of single-phase water in helical coils was experimentally studied. The testing section was constructed from a stainless steel round tube with an inner diameter of 10 mm, coil diameter of 300 mm, and pitch of 50 mm. The experiments were conducted over a wide Reynolds number range of 40000 to 500000. Both constant-property flows at normal pressure and variable-property flows at supercritical pressure were investigated. The contribution of secondary flow in the helical coil to heat transfer was gradually suppressed with increasing Reynolds number. Hence, heat transfer coefficients of the helical tube were close to those of the straight tube under the same flow conditions when the Reynolds number is large enough. Based on the experimental data, heat transfer correlations for both incompressible flows and supercritical fluid flows through helical coils were proposed.     

Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli

Forced and free convective heat transfer for thermally developing and thermally fully developed laminar air flow inside horizontal concentric annuli in the thermal entrance length has been experimentally investigated. The experimental setup consists of a stainless steel annulus having a radius ratio of 2 and an inner tube with a heated length of 900 mm subjected to a constant wall heat flux boundary condition and an adiabatic outer annulus. The investigation covers Reynolds number range from 200 to 1000, the Grashof number was ranged from 6.2 × 10⁵ to 1.2 × 10⁷. The entrance sections used were long tube with length of 2520 mm (L/D_h = 63) and short tube with length of 504 mm (L/D_h = 12.6). The surface temperature distribution along the inner tube surface, and the local Nusselt number distribution versus dimensionless axial distance Z_t were presented and discussed. It is inferred that the free convection effects tended to decrease the heat transfer at low Re number while to increase the heat transfer for high Re number. This investigation reveals that the Nusselt number values were considerably greater than the corresponding values for fully developed combined convection over a significant portion of the annulus. The average heat transfer results were correlated in terms of the relevant dimensionless variables with an empirical correlation. The local Nusselt number results were compared with available literature and show similar trend and satisfactory agreement.     

Effect of flow geometry parameters on transient heat transfer for turbulent flow in a circular tube with baffle inserts

The effect of the flow geometry parameters on transient forced convection heat transfer for turbulent flow in a circular tube with baffle inserts has been investigated. The characteristic parameters of the tubes are pitch to tube inlet diameter ratio H/D = 1, 2 and 3, baffle orientation angle β = 45°, 90° and 180°. Air, Prandtl number of which is 0.71, was used as working fluid, while stainless steel was considered as pipe and baffle material. During the experiments, different geometrical parameters such as the baffle spacing H and the baffle orientation angle β were varied. Totally, nine types of baffle inserted tube were used. The general empirical equations of time averaged Nusselt number and time averaged pressure drop were derived as a function of Reynolds number corresponding to the baffle geometry parameters of pitch to diameter ratio H/D, baffle orientation angle β, ratio of smooth to baffled cross-section area S_o/S_a and ratio of tube length to baffle spacing L/H were derived for transient flow conditions. The proposed empirical correlations were considered to be applicable within the range of Reynolds number 3000 ⩽ Re ⩽ 20,000 for the case of constant heat flux.     

Heat transfer augmentation in 3D internally finned and microfinned helical tube

Experiments are performed to investigate the single-phase flow and flow-boiling heat transfer augmentation in 3D internally finned and micro-finned helical tubes. The tests for single-phase flow heat transfer augmentation are carried out in helical tubes with a curvature of 0.0663 and a length of 1.15 m, and the examined range of the Reynolds number varies from 1000 to 8500. Within the applied range of Reynolds number, compared with the smooth helical tube, the average heat transfer augmentation ratio for the two finned tubes is 71% and 103%, but associated with a flow resistance increase of 90% and 140%, respectively. A higher fin height gives a higher heat transfer rate and a larger friction flow resistance. The tests for flow-boiling heat transfer are carried out in 3D internally micro-finned helical tube with a curvature of 0.0605 and a length of 0.668 m. Compared with that in the smooth helical tube, the boiling heat transfer coefficient in the 3D internally micro-finned helical tube is increased by 40-120% under varied mass flow rate and wall heat flux conditions, meanwhile, the flow resistance is increased by 18-119%, respectively.     

Natural convective heat transfer of heated packed beds

Natural convection heat transfer of heated packed bed was investigated. Experiments were performed for a single heated sphere buried in unheated packed beds varying its locations and for packed beds with all heated spheres varying the heights of packed beds from 0.02 m to 0.26 m. Mass transfer experiments using a copper electroplating system were performed based upon the analogy between heat and mass transfer. The diameter of sphere was 0.006 m, which corresponds to Ra_d of 1.8 × 10⁷. For the single heated sphere cases, the measured results agreed well with the existing natural convection heat transfer correlations for packed beds and even with those for a single sphere in an open channel. For all heated sphere cases, the average heat transfers decrease with increasing packed bed heights.     

Cocurrent turbulent mixed convection heat and mass transfer in falling film of water inside a vertical heated tube

A detailed numerical study has been conducted in order to analyse the combined buoyancy effects of thermal and mass diffusion on the turbulent mixed convection tube flows. Numerical results for air-water system are presented under different conditions. A low Reynolds number k-ε turbulent model is used with combined heat and mass transfer analysis in a vertical heated tube. The local heat fluxes, Nusselt and Sherwood numbers are reported to obtain an understanding of the physical phenomena. Predicted results show that a better heat transfer results for a higher gas flow Reynolds number Re, a higher heat flux q_w or a lower inlet water flow Γ₀. Additionally, the results indicate that the convection of heat by the flowing water film becomes the main mechanism for heat removal from the wall.     

Mixed convection heat transfer in horizontal,concentric annuli for transitional flow conditions

Experiments have been performed to determine mixed convection flow and heat transfer in a horizontal, concentric tube annulus for Reynolds numbers in the range 2200 < Re < 5000. Within this range, flow conditions are turbulent and laminar, respectively, in regions of the annulus above and below the heated inner tube. For Reynolds numbers less than a critical value Re₁ which depends on the Rayleigh number, diameter ratio and longitudinal position, flow along the sides of the annulus is laminar and helicoidal. For Re >Re₁, there is a breakdown in the helicoidal motion, with subsequent transition to turbulence in the top and side regions of the annular passage. The local Nusselt number at the top of the inner tube is less than, equal to, and greater than that at the bottom for Re < Re₁, Re = Re₁, and Re >Re₁, respectively. The circumferentially averaged Nusselt number is weakly dependent on longitudinal position and may be correlated in terms of the Rayleigh and Reynolds numbers and the tube diameter ratio.     

Investigation of natural convection induced outer side heat transfer rate of coiled-tube heat exchangers

Natural convection induced heat transfer has been studied over the outer surface of helically coiled-tube heat exchangers. Several different geometrical configurations (curvature ratio δ ε [0.035, 0.082]) and a wide range of flow parameters (60 <= T_tank <= 90, T_in = 19 and 60 <= T_in <= 90, T_tank = 20, 4000 <= Re <= 45000) have been examined to broaden the validity of the results gained from this research. A fluid-to-fluid boundary condition has been applied in the numerical calculations to create the most realistic flow configurations. Validity of the numerical calculations has been tested by experiments available in the open literature. Calculated results of the inner side heat transfer rate have also been compared to existing empirical formulas and experimental results to test the validity of the numerical computation in an independent way from the outer side validation of common helical tube heat exchangers. Water has been chosen to the working fluid inside and outside of the coiled tube (3 < Pr < 7). Outer side heat transfer rate along the helical tube axis has been investigated to get information about the performance of the heat transport process at different location of the helical tube. It was found that the outer side heat transfer rate is slightly dependent on the inner flow rate of any helical tube in case of increasing temperature differences between the tank working fluid temperature and the coil inlet temperature. A stable thermal boundary layer has been found along the axial direction of the tube.In addition to this the qualitative behavior of the peripherally averaged Nusselt number versus the axial location along the helical tube function is strongly dependent on the direction of the heat flow (from the tube to the storage tank and the reversed direction). Inner side heat transfer rate of helical coils have also been investigated in case of fluid-to-fluid boundary conditions and the calculation results have been compared with different prediction formulas published in the last couples of decades.     

The effects of different entrance sections lengths and heating on free and forced convective heat transfer inside a horizontal circular tube

An experimental study was done for hydrodynamically fully developed and thermally developing laminar air flows in a horizontal circular tube has a 30 mm inside diameter and 900 mm heated length (L/D = 30) under a constant wall heat flux boundary condition, with different aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths of 600 mm (L/D = 20), 1200 mm (L/D = 40), 1800 mm (L/D = 60), and 2400 mm (L/D = 80). The Reynolds number ranged from 400 to 1600 and the heat flux is varied from 60 W m^− 2 to 400 W m^− 2. This paper examines the effects of the entrance sections lengths and heating on the free and forced convection heat transfer process. The surface temperature data were measured and heat transfer rates at different heat flux levels as well as different Reynolds numbers were calculated and correlated in the form of relevant parameters. The buoyancy force has a significant effect on the heat transfer and the combined convection factor was approximately varied form 0.13 ≤ Gr/Re² ≤ 7.125. It was found that the surface temperature increases as the entrance section length increases. It was inferred that the heat transfer decreases as the entrance section length increases due to the flow resistance and the mass flow rate. The proposed correlation was compared with available literature and with laminar forced convection and showed satisfactory agreement.