Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.     

Computational analysis of heat transfer and pressure drop performance for internally finned tubes with three different longitudinal wavy fins

Turbulent pressure drop and heat transfer characteristics in tubes with three different kinds of internally longitudinal fin patterns (interrupted wavy, sinusoidal wavy and plain) are numerically investigated for Re = 904–4,520. The channel velocity, temperature, and turbulence fields are obtained to discern the mechanisms of heat transfer enhancement. Numerical results indicate that the steady and spatially periodic growth and disruption of cross-sectional vortices occur near the tube/fin walls along the streamwise locations. The thermal boundary layers near the tube/fin surfaces are thereby periodically interrupted, with heat transfer near the recirculation zones being enhanced. The overall heat transfer coefficients in wavy channels are higher than those in a plain fin channel, while with larger pressure drop penalties. At the same waviness, the interrupted wavy fin tube could enhance heat transfer by 72–90%, with more than 2–4 times of pressure drop penalty. Among the fins studied, the sinusoidal wavy fin has the best comprehensive performance.     

Flow boiling heat transfer of R134a and R404A in a microfin tube at low mass fluxes and low heat fluxes

An experimental investigation of flow boiling heat transfer in a commercially available microfin tube with 9.52 mm outer diameter has been carried out. The microfin tube is made of copper with a total fin number of 55 and a helix angle of 15°. The fin height is 0.24 mm and the inner tube diameter at fin root is 8.95 mm. The test tube is 1 m long and is electrically heated. The experiments have been performed at saturation temperatures between 0 and −20°C. The mass flux was varied between 25 and 150 kg/m²s, the heat flux from 15,000 W/m² down to 1,000 W/m². All measurements have been performed at constant inlet vapour quality ranging from 0.1 to 0.7. The measured heat transfer coefficients range from 1,300 to 15,700 W/m²K for R134a and from 912 to 11,451 W/m²K for R404A. The mean heat transfer coefficient of R134a is in average 1.5 times higher than for R404A. The mean heat transfer coefficient has been compared with the correlations by Koyama et al. and by Kandlikar. The deviations are within ±30% and ±15%, respectively. The influence of the mass flux on the heat transfer is most significant between 25 and 62.5 kg/m²s, where the flow pattern changes from stratified wavy flow to almost annular flow. This flow pattern transition is shifted to lower mass fluxes for the microfin tube compared to the smooth tube.     

Unsteady natural convection in an enclosure with vertical wavy walls

In this paper, unsteady heat transfer and fluid flow characteristics in an enclosure are investigated. The enclosure consists of two vertical wavy and two horizontal straight walls. The top and the bottom walls are considered adiabatic. Two wavy walls are kept isothermal and their boundaries are approximated by a cosine function. Governing equations including continuity, momentum and energy were discretized using the finite-volume method and solved by SIMPLE method in curvilinear coordinate. Simulation was carried out for a range of Grashof number Gr = 10³–10⁶, Prandtl number Pr = 0.5–4.0, wave ratio A (defined by amplitude/wavelength) 0.0–0.35 and aspect ratio W (defined by average width/wavelength) 0.5–1.0. Streamlines and isothermal lines are presented to corresponding flow and thermal fields. Local and average Nusselt number distributions are presented. The obtained results are in good agreement with available numerical and experimental data.     

Peristaltic flow and heat transfer in a vertical porous annulus, with long wave approximation

In this paper, we study the interaction of peristalsis with heat transfer for the flow of a viscous fluid in a vertical porous annular region between two concentric tubes. Long wavelength approximation (that is, the wavelength of the peristaltic wave is large in comparison with the radius of the tube) is used to linearise the governing equations. Using the perturbation method, the solutions are obtained for the velocity and the temperature fields. Also, the closed form expressions are derived for the pressure-flow relationship and the heat transfer at the wall. The effect of pressure drop on flux is observed to be almost negligible for peristaltic waves of large amplitude; however, the mean flux is found to increase by 10-12% as the free convection parameter increases from 1 to 2. Also, the heat transfer at the wall is affected significantly by the amplitude of the peristaltic wave. This warrants further study on the effects of peristalsis on the flow and heat transfer characteristics.     

Evaporation of pure liquids with increased viscosity in a falling film evaporator

The present study investigated fluid dynamics and heat transfer of viscous pure liquids in a falling film evaporator. This is of special benefit as it avoids mass transfer effects on the evaporation behaviour. Experiments at a single-tube glass falling film evaporator were conducted. It allowed a full-length optical film observation with a high-speed camera. Additionally the evaporator was equipped with a slotted weir distribution device. Test fluids provided viscosities ranging from μ = 0.3 to 41 mPa s. The Reynolds number was between 0.7 and 1,930. Surface evaporation and the transition to nucleate boiling were studied to gain information about the film stability at maximum wall superheat. A reliable database for laminar and laminar-wavy viscous single component films was created. The experimental results show a significant enhancement in the wave development due to the film distribution. A wavy flow with different wave velocities was superposed to the film in each liquid load configuration without causing a film breakdown or dry spots on the evaporator tube. It was found that nucleate boiling can be allowed without causing film instabilities over a significant range of wall superheat.     

Modelling of heat flux received by a bubble pump of absorption-diffusion refrigeration cycles

In the present study, the heat flux received by a bubble pump, which was simulated to a vertical tube 1 m long and with a variable diameter, was optimized. A numerical study was carried out in order to solve balance equations concerning the water-ammonia mixture in the up flow. The two-fluid model was used to derive the equations. A numerical study was carried out on a heat flux between 1 and 70 kW m⁻² and the liquid velocity was determined. The optimum flux was determined for a tube diameter equal to 4, 6, 8 and 10 mm and a mass flow rate ranging from 10 to 90 kg m⁻² s⁻¹. The optimum heat flux was correlated as a function of the tube diameter and mass flow rate, while the minimum heat flux required for pumping was correlated as a function of the tube diameter.     

Experimental research on transient critical heat flux in vertical tube under oscillatory flow condition

The transient critical heat flux (CHF) experiments with forced sinusoidal inlet flow oscillation (oscillation period in 1–11 s, normalized amplitude of inlet flow oscillation in 0–3.0) were conducted in a vertical tube under low pressure condition. To analyze the triggering mechanism and aftermath of periodic dryout, the wall temperature fluctuation characteristics at the onset of periodic dryout and during post-periodic dryout were investigated. Under inlet flow oscillation condition, periodic dryout would be triggered at the wave trough of liquid film oscillation as wall heat flux far below the stable-flow CHF. The transient periodic dryout would give rise to temperature fluctuations on the tube wall, the amplitude of which increased with oscillation period and heat flux. The large wall temperature fluctuation during long-playing periodic dryout could significantly pre-trigger continuous dryout. The changing trends of the periodic dryout heat flux show a reasonable agreement with Okawa’s theoretical model, in which the liquid film oscillation was supposed be weakened by the axial mixing of liquid film. Moreover, the droplet entrainment at the oscillatory interface also has noticeable influence on the oscillation characteristics of liquid film. Based on the analysis of parameter effects on periodic dryout, a semi-empirical correlation was proposed to predict the periodic dryout heat flux under inlet flow oscillation condition.     

An experimental investigation on the airside performance of fin-and-tube heat exchangers having sinusoidal wave fins

The heat transfer and friction characteristics of the heat exchangers having sinusoidal wave fins were experimentally investigated. Twenty-nine samples having different waffle heights (1.5 and 2.0 mm), fin pitches (1.3–1.7 mm) and tube rows (1–3) were tested. Focus was given to the effect of waffle configuration (herringbone or sinusoidal) on the heat transfer and friction characteristics. Results show that the sinusoidal wave geometry provides higher heat transfer coefficients and friction factors than the herringbone wave geometry, and the difference increases as the number of row increases. The j/f ratios of the herringbone wave geometry, however, are larger than those of the sinusoidal wave geometry. Compared with the herringbone wave geometry, the sinusoidal wave geometry yielded a weak row effect, which suggests a superior heat transfer performance at the fully developed flow region for the sinusoidal wave geometry. Possible reasoning is provided considering the flow characteristics in wavy channels. Within the present geometric variations, the effect of waffle height on the heat transfer coefficient was not prominent. The effect of fin pitch was also negligible. Existing correlations highly overpredicted both the heat transfer coefficients and friction factors. A new correlation was developed based on the present data.     

Effect of heater size on ultrasonic enhancement of boiling in water and surfactant solutions

Experiments were performed to study enhancement of heat transfer from the wire of d = 50 µm and the tube of d = 1.5 mm in subcooled pool boiling by ultrasonic waves. The working fluids are clean water and Alkyl (8-16) Glucoside surfactant solutions of different concentrations and bulk temperature 30 °C. The wire resistance was translated to the temperature, using the calibration data, the temperature of the tube was measured by thermocouple. The differences between effect of ultrasonic field on boiling in water for heaters of d = 50 µm and d = 1.5 mm may be summarized as follows: for boiling on the wire of d = 50 µm in subcooled water, T_b = 30 °C, enhancement of heat transfer coefficient due to applied ultrasonic field is about 70% and 20% at heat flux q = 620 kW/m² and q = 1350 kW/m², respectively. For boiling in surfactant solutions at the same boiling conditions enhancement of heat transfer coefficient is in the range of 5–10% at heat flux q = 620 kW/m² and 10–16% at heat flux q = 1350 kW/m² depending on solution concentration. For boiling on the tube of d= 1.5 mm in subcooled water, T_b= 30 ℃, enhancement of heat transfer coefficient due to applied ultrasonic field is about 50% and 45% at heat flux q = 500 kW/m² and q = 2500 kW/m², respectively. The same values are obtained for boiling in surfactant solution of concentration C = 250 ppm. For the wire of d = 50 µm the heat transfer enhancement due to acoustic vibrations in surfactant solutions is not as strong as in water. This fact may be considered as evidence of significant role of relationship between jet flow and ultrasonic field.     

The influence of oil on nucleate pool boiling heat transfer

The influence of various oil contents in R134a is investigated for nucleate pool boiling on copper tubes either sandblasted or with enhanced heating surfaces (GEWA-B tube). Polyolester oils (POE) (Reniso Triton) with medium viscosity 55 cSt (SE55) and high viscosity 170 cSt (SE170) were used. Heat transfer coefficients were obtained for boiling temperatures between −28.6 and +20.1°C. The oil content varied from 0 to 5% mass fraction. For the sandblasted tube and the SE55 oil the heat transfer coefficients for the refrigerant/oil-mixture can be higher or lower than those for the pure refrigerant, depending on oil mass fraction, boiling temperature and heat flux. In some cases the highest heat transfer coefficients were obtained at a mass fraction of 3%. For the 170 cSt oil there is a clear decrease in heat transfer for all variations except for a heat flux 4,000 W/m² and −10.1°C at 0.5% oil content. The heat transfer coefficients are compared to those in the literature for a smooth stainless steel tube and a platinum wire. For the enhanced tube and 55 cSt oil the heat transfer coefficients are clearly below those for pure refrigerant in all cases. The experimental results for the sandblasted tube are compared with the correlation by Jensen and Jackman. The calculated values are within +20 and −40% for the medium viscosity oil and between +50% and −40% for the high viscosity oil. A correlation for predicting oil-degradation effects on enhanced surfaces does not exist.     

Mass transfer enhancement by capillary waves at a liquid–vapour interface

We present experimental results showing that large amplitude capillary waves at a liquid–vapour interface substantially enhance the interfacial heat and mass transfer. The experiments have been conducted in a circular cylinder that is partially filled with a wetting liquid of low boiling point temperature and pressurized by its vapour. The interfacial capillary waves are sub-harmonically excited by oscillating the circular cylinder at 50 Hz with forcing amplitude A in the direction normal to the liquid surface. The upper part of the test cell containing the vapour is heated to a temperature slightly below the boiling point temperature at the operating pressure. When the interface is at rest, the pressure decrease due to condensation is small. However, in the presence of interfacial capillary waves the rate of pressure decrease is substantial. The results show that the vapour condensation rate with respect to the diffusive vapour flux at an undisturbed interface, which is a Nusselt number, increases with the square of the wave amplitude that is proportional to the forcing amplitude. A model is developed that expresses the pressure variation in terms of Jacob number, the temperature gradient in the liquid at the interface and the capillary wave motion. This model allows extrapolation of the results to other fluids and configurations.     

Flow boiling heat transfer in a vertical spirally internally ribbed tube

 Experiments of flow boiling heat transfer and two-phase flow frictional pressure drop in a spirally internally ribbed tube (φ22×5.5 mm) and a smooth tube (φ19×2 mm) were conducted, respectively, under the condition of 6×10⁵ Pa (absolute atmosphere pressure). The available heated length of the test sections was 2500 mm. The mass fluxes were selected, respectively, at 410, 610 and 810 kg/m² s. The maximum heat flux was controlled according to exit quality, which was no more than 0.3 in each test run. The experimental results in the spirally internally ribbed tube were compared with that in the smooth tube. It shows that flow boiling heat transfer coefficients in the spirally internally ribbed tube are 1.4–2 times that in the smooth tube, and the flow boiling heat transfer under the condition of smaller temperature differences can be achieved in the spirally internally ribbed tube. Also, the two-phase flow frictional pressure drop in the spirally internally ribbed tube increases a factor of 1.6–2 as compared with that in the smooth tube. The effects of mass flux and pressure on the flow boiling heat transfer were presented. The effect of diameters on flow boiling heat transfer in smooth tubes was analyzed. Based on the fits of the experimental data, correlations of flow boiling heat transfer coefficient and two-phase flow frictional factor were proposed, respectively. The mechanisms of enhanced flow boiling heat transfer in the spirally internally ribbed tube were analyzed. Received on 1 December 1999     

Laminar film condensation from downward flowing superheated vapors onto a non-isothermal sphere

 A model is developed for the study of mixed convection film condensation from downward flowing superheated vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, including effects of superheated vapor, pressure gradient and wall temperature variation can be solved numerically by the fourth-order Runge–Kutta technique. By the present numerical approach, the mean heat transfer is evaluated up to the critical angle of the condensate layer, φ_c. In general, the result of mean heat transfer shows that, as A, the wall-temperature amplitude, increases, the value of with inclusion of P, the pressure gradient effect, goes down slightly, however, the value of with the pressure gradient effect ignored will remain almost uniform. Further, for P=2.0, the mean heat transfer coefficient increases significantly, by 8.6–23.9%, depending on A, as the superheat parameter, S p, increases within a practical range. Received on 7 September 2000     

Stratified flow boiling heat transfer study of a HFC/HC refrigerant mixture in smooth horizontal tubes

The flow boiling heat transfer coefficients of R-134a/R-290/R-600a (91%:4.068%:4.932% by mass) refrigerant mixture are experimentally arrived in two tubes of diameter 9.52 and 12.7 mm. The tests are conducted to target the varied heat flux condition and stratified flow pattern found in evaporators of refrigerators and deep freezers. The varied heat flux condition is imposed on the refrigerant using a coaxial counter-current heat exchanger test section. The experiments are performed for mass flow rates of the refrigerant mixture between 3 and 5 g s⁻¹ and entry temperature between −8.59 and 5.33°C which are bubble temperatures corresponding to a pressure of 3.2 and 5 bar. The influences of heat flux, mass flow rate, pressure, flow pattern, tube diameter on the heat transfer coefficient are discussed. The profound effects of nucleate boiling prevailing even at higher vapor qualities in evaporators are highlighted. The heat transfer coefficient of the refrigerant mixture is also compared with that of R-134a.     

Nonlinear stability theory of channel flow with heat transfer – an asymptotic approach

A fully developed laminar Poiseuille flow subject to constant heat flux across the wall is analysed with respect to its stability behavior by applying a weakly nonlinear stability theory. It is based on an expansion of the disturbance control equations with respect to a perturbation parameter ε. This parameter is the small initial amplitude of the fundamental wave. This fundamental wave which is the solution of the linear (Orr-Sommerfeld) first order equation triggers all higher order effects with respect to ε. Heat transfer is accounted for asymptotically through an expansion with respect to a small heat transfer parameter ε _T . Both perturbation parameters, ε and ε _T , are linked by the assumption ε _T =O(ε²) by which a certain distinguished limit is assumed. The results for a fluid with temperature dependent viscosity show that heat transfer effects in the nonlinear range continue to act in the same way as in the initial linear range. Received on 11 August 1997     

Hydrothermal analysis of non-Newtonian fluid flow (blood) through the circular tube under prescribed non-uniform wall heat flux

The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to non-uniform surface heat flux. After the flow field is determined by solving the continuity and the momentum equations, the energy equation is handled by employing the separation of variables method. The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C. The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length, using Duhamel's Theorem. Furthermore, an approximate analytic solution is determined, employing an integral approach to solve the boundary layer equations. With respect to the comparison, the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%. Interestingly, with decreasing the power-law index, the discrepancy between the two presented methods significantly reduces. Eventually, the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow's thermal characteristics and structure are elaborately discussed. It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation's accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube. In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m²and when the power-law index is 0.25, the maximum arterial wall temperature is found to be about 311.56 K.     

Effect of Discrete Heating on Natural Convection in a Rectangular Porous Enclosure

The main objective of this article is to study the effect of discrete heating on free convection heat transfer in a rectangular porous enclosure containing a heat-generating substance. The left wall of the enclosure has two discrete heat sources and the right wall is isothermally cooled at a lower temperature. The top and bottom walls, and the unheated portions of the left wall are adiabatic. The vorticity–stream function formulation of the governing equations is numerically solved using an implicit finite difference method. The effects of aspect ratio, Darcy number, heat source length, and modified Rayleigh number on the flow and heat transfer are analyzed. The numerical results reveal that the rate of heat transfer increases as the modified Rayleigh number and the Darcy number increases, but decreases on increasing the aspect ratio. The average heat transfer rate is found to be higher at the bottom heater than at the top heater in almost all considered parameter cases except for ε = 0.5. Also, the maximum temperature takes place generally at the top heater except for the case ε = 0.5, where the maximum temperature is found at the bottom heater. Further, the numerical results reveal that the maximum temperature decreases with the modified Rayleigh number and increases with the aspect ratio.     

Effect of vertical heat transfer on thermocapillary convection in an open shallow rectangular cavity

In order to understand the effect of the vertical heat transfer on thermocapillary convection characteristics in a differentially heated open shallow rectangular cavity, a series of two- and three-dimensional numerical simulations were carried out by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and the aspect ratio ranged from 12 to 30. Results show that thermocapillary convection is stable at a small Marangoni number. With the increase of the heat flux on the bottom surface, thermocapillary convection transits to the asymmetrical bi-cellular pattern with the opposite rotation direction. The roll near the hot wall shrinks as the Marangoni number increases. At a large Marangoni number, numerical simulations predict two types of the oscillatory thermocapillary flow. One is the hydrothermal wave, which is dominant only in a thin cavity. The other appears in a deeper cavity and is characterized by oscillating multi-cellular flow. The critical Marangoni number for the onset of the oscillatory flow increases first and then decreases with the increase of the vertical heat flux. The three-dimensional numerical simulation can predict the propagating direction of the hydrothermal wave. The velocity and temperature fields obtained by three-dimensional simulation in the meridian plane are very close to those obtained by two-dimensional simulation.     

Conjugate heat transfer study of incompressible turbulent offset jet flows

In the present case, the conjugate heat transfer involving a turbulent plane offset jet is considered. The bottom wall of the solid block is maintained at an isothermal temperature higher than the jet inlet temperature. The parameters considered are the offset ratio (OR), the conductivity ratio (K), the solid slab thickness (S) and the Prandtl number (Pr). The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then it becomes independent of the Reynolds number. The ranges of parameters considered are: OR = 3, 7 and 11, K = 1–1,000, S = 1–10 and Pr = 0.01–100. High Reynolds number two-equation model (k–ε) has been used for turbulence modeling. Results for the solid–fluid interface temperature, local Nusselt number, local heat flux, average Nusselt number and average heat transfer have been presented and discussed.