Heat transfer characteristics of spirally-coiled circular fin-tube heat exchangers operating under frosting conditions

The objective of this study is to investigate the heat transfer characteristics of spirally-coiled circular fin-tube heat exchangers under frosting conditions. The heat transfer rate, pressure drop, frost thickness, and Nusselt number of the heat exchanger were measured and analyzed by varying the fin pitch and number of tube rows under frosting conditions. In addition, the Nusselt number of the spirally-coiled circular fin-tube exchanger was compared with those of flat plate fin-tube heat exchangers with discrete fins. An empirical correlation of the Nusselt number was developed as a function of the Reynolds number, dimensionless fin pitch normalized by the hydraulic diameter, i.e., D_h/F_p, Fourier number, and number of tube rows. The measured Nusselt number was consistent with the predicted value with mean and average deviations of 3.5% and 0.3%, respectively.     

Heat transfer characteristics of oscillating flow regenerators in cryogenic temperature range below 20 K

Linearized thermoacoustic model considering temperature oscillation in the solid wall is applied to analyze the heat transfer characteristics of compressible oscillating flow in parallel-plate and circular-tube regenerators. In particular, the study focus results of heat transfer analysis are applicable in lower cryogenic temperature ranges (<20 K). Complete expression for Nusselt number is derived and it is shown to be the function of six nondimensional parameters when the shape of the regenerator is fixed. These parameters are discussed, respectively. Simplified expressions of the Nusselt numbers for both parallel plates and circular tubes structured regenerators are derived. Heat transfer characteristics can be evaluated via these simple expressions. Possible approaches of enhancing heat transfer in a thermoacoustic regenerator are discussed.     

Heat transfer in turbulent nanofluids: Separation flow studies and development of novel correlations

Convective heat transfer plays a significant role in numerous industrial cooling and heating applications. This method of heat transfer can be passively improved by reconfiguring flow passage, fluid thermophysical properties, or boundary conditions. The broader scope of nanotechnology introduced several studies of thermal engineering and heat transfer. Nano-fluids are one of such technology which can be thought of engineered colloidal fluids with nano-sized particles. In the present study, turbulent forced convection heat transfer to nanofluids in an axisymmetric abrupt expansion heat exchanger was investigated experimentally. During heat transfer investigation, the functionalized multiwalled carbon nanotubes (MWCNT-COOH), polycarboxylate functionalized graphene nanoplatelets (F-GNP), SiO₂ and ZnO water-based nanofluids were used. The convective heat transfer coefficient of fully developed turbulent flow of nanofluids flowing through an abrupt enlargement with the expansion ratio (ER) of 2 was experimentally determined at a constant wall heat flux of 12,128.56 W/m². The experiments were conducted at the Re ranges of 4000–16,000. The observed Nusselt numbers were higher than in the case of fully developed pipe flow indicating the level of the turbulent transport is high even though the recirculating velocities were a few percentages of the bulk mean velocity. The effect of Reynolds number and nanofluid’s volume concentration on heat transfer and friction losses were studied, where all the results reveal that with the increase of weight concentration and Reynolds number, the local Nusselt number enhanced at the increment of axial ratios in all the cases showing greater heat transfer rates than those of the base fluids. Comparison between the examined four types of nanofluids, show that the carbon-based nanofluids have a greater effect on enhancing heat transfer (33.7% and 16.7% heat transfer performance improvement for F-GNP and MWCNT nanofluids respectively at 0.1 wt% concentration) at the downstream of the sudden expansion pipe. There is no reported work dealing with the prediction of the local Nusselt number at the distance equivalent to the axial ratio and flow through sudden expansion. So far, two excellent correlations for the Local Nusselt number are proposed with reasonably good accuracy. Furthermore, a new correlation is developed for the average Nusselt number.     

Experimental correlation of combined heat and mass transfer for NH3–H2O falling film absorptionCorrélation expérimentale entre le transfert de chaleur et de masse pour de l'absorption au NH3–H2O à film tombant

In this article, experimental analysis was performed for ammonia–water falling film absorption process in a plate heat exchanger with enhanced surfaces such as offset strip fin. This article examined the effects of liquid and vapor flow characteristics, inlet subcooling of the liquid flow and inlet concentration difference on heat and mass transfer performance. The inlet liquid concentration was selected as 5%, 10% and 15% of ammonia by mass while the inlet vapor concentration was varied from 64.7% to 79.7%. It was found that before absorption started, there was a rectification process at the top of the test section by the inlet subcooling effect. Water desorption phenomenon was found near the bottom of the test section. It was found that the lower inlet liquid temperature and the higher inlet vapor temperature, the higher Nusselt and Sherwood numbers are obtained. Nusselt and Sherwood number correlations were developed as functions of falling film Reynolds Re₁, vapor Reynolds number Re_v, inlet subcooling and inlet concentration difference with ±15% and ±20% error bands, respectively.     

Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements

Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements has been studied using numerical simulations for wide ranges of parameters, Reynolds numbers (1?≤?Re?≤?50), Richardson numbers (0?≤?Ri?≤?2), Prandtl numbers (0.7?≤?Pr?≤?50) and confinement ratios (0.2?≤?β?≤?0.8). A hot semi-circular cylinder is symmetrically kept in a 2D rectangular confinement. The circular side of the cylinder faces the upstream flow and the fluid flows against gravity in the channel. The governing equations are numerically solved using FLUENT and the results obtained are presented in the form of isotherms, streamlines, pressure coefficients, drag coefficients, Nusselt numbers, etc. The highest value of pressure coefficient increases with blockage ratio for all cases. The drag coefficient decreases with Re and shows complex phenomena with change in Ri and blockage ratio of the channel. Pressure drag has contributed more as compared with viscous drag in all cases. The curved surface showed more heat transfer than the flat surface of the semi-circular cylinder. The value of β also has great influence at large value of Peclect numbers (=?2500). Overall average heat transfer in terms of average Nusselt number is a function of Ri, Re, Pr and β.     

Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Steady-state and quasi-steady-state flows in a round pipe with constant temperature on the wall

An integral method is suggested for the calculation of heat transfer and drag under conditions of flow of dropping liquid and gas in a pipe with constant wall temperature. It is found that the kind of thermal conditions on the wall (T _wall = const or q _wall = const) has insignificant effect on the Nusselt number and coefficient of friction drag for a steady-state flow of dropping liquid of variable viscosity. For a quasi-steady-state pulsating flow of dropping liquid, the thermal boundary conditions have an appreciable effect on the Nusselt number alone; in so doing, the degree of this effect increases with the oscillation amplitude and hardly depends on the temperature factor. For steady-state and quasi-steady-state flows of gas at high temperature factors, the values of heat transfer and drag at T _wall = const differ significantly from those at q _wall = const.     

Heat transfer asymptote in laminar flow of non-linear viscoelastic fluids in straight non-circular tubes

The fully developed thermal field in constant pressure gradient driven laminar flow of a class of non-linear viscoelastic fluids with instantaneous elasticity in straight pipes of arbitrary contour ∂D with constant wall flux is investigated. The non-linear fluids considered are constitutively represented by a class of single mode, non-affine constitutive equations. The driving forces can be large. Asymptotic series in terms of the Weissenberg number Wi are employed to expand the field variables. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D₀. The analytical method presented is capable of predicting the velocity and temperature fields in tubes with arbitrary cross-section. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is to a very large extent the result of secondary flows in the cross-section but there is a component due to first normal stress differences as well. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its Newtonian counterpart. Order of magnitude larger enhancements are possible even with slightly viscoelastic fluids. The coupling between inertial and viscoelastic non-linearities is crucial to enhancement. Isotherms for the temperature field are discussed for non-circular contours such as the ellipse and the equilateral triangle together with the behavior of the average Nusselt number Nu, a function of the Reynolds Re, the Prandtl Pr and the Weissenberg Wi numbers. Analytical evidence for the existence of a heat transfer asymptote in laminar flow of viscoelastic fluids in non-circular contours is given for the first time. Nu becomes asymptotically independent from elasticity with increasing Wi, Nu = f(Pe, Wi) → Nu = f(Pe). This asymptote is the counterpart in laminar flows in non-circular tubes of the heat transfer asymptote in turbulent flows of viscoelastic fluids in round pipes. A different asymptote corresponds to different cross-sectional shapes in straight tubes. The change of type of the vorticity equation governs the trends in the behavior of Nu with increasing Wi and Pe. The implications on the heat transfer enhancement is discussed in particular for slight deviations from Newtonian behavior where a rapid rise in enhancement seems to occur as opposed to the behavior for larger values of the Weissenberg number where the rate of increase is much slower. The asymptotic independence of Nu from elasticity with increasing Wi is related to the extent of the supercritical region controlled by the interaction of the viscoelastic Mach number M and the Elasticity number E, which mitigates and ultimately cancels the effect of the increasingly strong secondary flows with increasing Wi to level off the enhancement. The physics of the interaction of the effects of the Elasticity E, viscoelastic Mach M, Reynolds Re and Weissenberg Wi numbers on generating the heat transfer enhancement is discussed.     

Heat analogy in langmuir probe theory

Mathematical equivalence of the problems of determining the Langmuir, probe saturation current and the Nusselt number is shown in the heat transfer of a body of the same shape. Numerical results of the solution to these two problems obtained in various works are compared for a cylinder.Notation Re, Re _e gasdynamical and electrical Reynolds numbers - Pr Prandtl number - Pe Peclet number - Nu average Nusselt number - Nu _D local Nusselt number determined from the diameter - Debye screening distance to the proble radius ratio - _D Debye screening distance - R probe radius - u velocity field of a neutral gas - kinematic viscosity factor - D _i ion diffusion coefficient - n dimensionless concentration of charged particles - r radial coordinate - j dimensionless density of the saturation current - i dimensional integral saturation current - I dimensional saturation current - e electron charge - N concentration of charged particles in the incoming flow - L probe length N. E. Zhukovskii Central Aerohydrodynamic Institute, Zhukovskii-3. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 4, pp. 629–632.     

贝克利数对圆管流道交变流动传热的影响分析

从可压缩黏性流体的一般控制方程出发,通过数值模拟,研究管内可压缩层流交变流动传热现象,重点关注贝克利数对于传热的影响.采用离散傅立叶级数的形式表征管内交变流动传热特性,研究表明采用五阶级数拟合值与原始数据的相对误差可小于10%.给出了贝克利数为2和300时,一个周期内交变流动传热过程的计算结果,并进行了对比分析.根据模...     

Power-law fluids flow and heat transfer over two tandem square cylinders: effects of Reynolds number and power-law index

The low-Reynolds numbers free-stream flow of power-law fluids and forced convection heat transfer around a square cylinder and two square cylinders in a tandem arrangement are numerically investigated. In the single cylinder case, the power-law index and Reynolds numbers range from n = 0.7 ? 1.4 and Re = 60 ? 160 at Pr = 0.7. In the tandem case, the spacing between the cylinders is four widths of each cylinder side and the power-law index ranges from 0.7 to 1.6 at Re = 40, 100, 160 and Pr = 0.7. All simulations are performed with a finite volume code based on the SIMPLEC algorithm and a non-staggered grid. The effect of spatial resolution on the results is also studied for a single cylinder and tandem cylinders. The mean and instantaneous streamlines, vorticity and temperature contours, the global quantities such as pressure and friction coefficients, the rms lift and drag coefficients, Strouhal and Nusselt numbers are determined and discussed for various power-law indexes at different Reynolds numbers. A comparison between the results of the single cylinder case and the two cylinders in tandem arrangement shows that there are relatively similar results for the single cylinder and the upstream cylinder of the tandem case.     

The effect of rotating cylinder on the heat transfer in a square cavity filled with porous medium

The heat transfer in a square cavity filled with clear fluid or porous medium is numerically investigated in the present study. To change the heat transfer in the cavity a rotating circular cylinder is placed at the centre of the cavity. The ratio of cylinder diameter to cavity height is chosen as 0.8. Depending on the angular velocity of the cylinder the convection phenomena inside the cavity becomes natural, mixed, and forced. To keep the number of data low the Grashof number, Gr, is set to 10⁶, while the parameter defining the convection regime in the cavity, Gr/Re², is changing from 0.0625 to 10². The Darcy number in the cavity is set to 10⁻², 10⁻³, and 10⁻⁴. Galerkin finite element method is used to solve the Navier–Stokes equations with Brinkman–Forcheimer extended Darcy’s law, and energy equation in 2-D non-dimensional form. The solution methodology is compared and validated with the literature for a similar problem, and good agreement is achieved. The results are presented in terms of Nusselt numbers, velocity profiles and temperature contours. The results show that rotation is more effective in the forced convection regime than in mixed and natural convection regimes, and at high spin velocities the heat transfer is almost independent from the Darcy number.     

Modeling trans- and supersonic viscid flow over a cone on a ballistic range

The possibilities of ballistic-range experimentation in determining the influence of compressibility and viscosity on the flow over cone-shaped parts of flying vehicles are considered. A nonmonotonic character of the dependence of the near wake flow over cone on the Reynolds number is revealed, which is an important factor under natural flight conditions. Tests have been performed for a right circular cone with a half-angle of 15°. The drag coefficients (C _x ) for acute and blunt cones with an aspect ratio of L/D = 1 at a zero attack angle have been determined. Near wake flow parameters (base pressure p _b and base density ρ _b ) have been experimentally studied in a range of Mach numbers M_∞ = 0.5?4 and at a fixed value of M_∞ = 2.3, but with Reynolds numbers Re_∞D varied from 6 × 10⁴ to 1.5 × 10⁶.     

Investigation of laminar-turbulent transition in supersonic boundary layers in an axisymmetric aerophysical flight complex and in a model in a wind tunnel in the presence of heat transfer and suction of air

Analysis is made of the problems associated with laminar-turbulent transition in wall boundary layers, as well as of scale effects observed in the investigation of laminar-turbulent transition in wind tunnels and laminarization of flow. Flight-performance data are given on the Reynolds number and on the gradient criterion of stability at the beginning of transition on the nose part of the Oblako aerophysical complex in the presence of heat transfer for the numbers Re _{L, ∞} ≤ 2 × 10⁷, M_∞ ≤ 2.0, and acceleration a ≤ 12g. Experimental data are given on laminarization of flow past a porous plate in a wind tunnel under the effect of suction for M_∞ = 2.5. The theory of Emmons turbulent spots is generalized to the flight conditions of flow past the nose part of the Oblako aerophysical flight complex in the presence of heat transfer and to the case of laminar-turbulent transition on a porous plate for M_∞ = 2.5 in the presence of suction of air.     

Experimental and numerical investigation on forced convection heat transfer and pressure drop in helically coiled pipes using TiO2/water nanofluid

In the present article, forced convection heat transfer and pressure drop in helically coiled pipes using TiO₂/water nanofluid as working fluid were investigated experimentally and numerically. The aim is to investigate and provide additional insight about the effects of physical and geometrical properties on heat transfer augmentation and pressure drop in helically coiled tubes. The experiments were conducted in the range of Reynolds number from 3000 to 18,000 and in the nanoparticle concentrations of 0.1, 0.2, and 0.5% for five different curvature ratios. In numerical simulations the thermophysical properties of the working fluid were assumed to be a function of nanofluid temperature and concentration. For turbulent regime the standard k − ε model was used to simulate the turbulent flow characteristics. The numerical results were in good agreement with the experimental data. The results showed that utilization of nanofluid instead of distilled water leads to an enhancement in the Nusselt number up to 30%. Also, four formulas were introduced to obtain the average Nusselt number and friction factor in helically coiled tubes under constant wall temperature condition for both laminar and turbulent flow regimes.     

Experimental study of turbulent single-phase flow and heat transfer inside a micro-finned tube

Single-phase heat transfer and pressure drop characteristics of a commercially available internally micro-finned tube with a nominal outside diameter of 7.94 mm were studied. Experiments were conducted in a double pipe heat exchanger with water as the cooling as well as the heating fluid for six sets of runs. The pressure drop data were collected under isothermal conditions. Data were taken for turbulent flow with 3300 ≤ Re ≤ 22,500 and 2.9 ≤ Pr ≤ 4.7. The heat transfer data were correlated by a Dittus–Boelter type correlation, while the pressure drop data were correlated by a Blasius type correlation. The correlation predicted values for both the Nusselt number and the friction factors were compared with other studies. It was found that the Nusselt numbers obtained from the present correlation fall in the middle region between the Copetti et al. and the Gnielinski smooth tube correlation predicted Nusselt number values. For pressure drop results, the present correlation predicted friction factors values were nearly double that of the Blasius smooth tube correlation predicted friction factors. It was also found that the rough tube Gnielinski and Haaland correlations can be used as a good approximation to predict the finned tube Nusselt number and ffriction factor, respectively, in the tested Reynolds number range.     

A minichannel aluminium tube heat exchanger – Part I: Evaluation of single-phase heat transfer coefficients by the Wilson plot method

A prototype liquid-to-refrigerant heat exchanger was developed with the aim of minimizing the refrigerant charge in small systems. To allow correct calculation of the refrigerant side heat transfer, the heat exchanger was first tested for liquid-to-liquid (water-to-water) operation in order to determine the single-phase heat transfer performance. These single-phase tests are reported in this paper. The heat exchanger was made from extruded multiport aluminium tubes and was designed similar to a shell-and-tube heat exchanger. The heat transfer areas of the shell-side and tube-side were approximately 0.82 m² and 0.78 m², respectively. There were six rectangular-shaped parallel channels in a tube. The hydraulic diameter of the tube-side was 1.42 mm and of the shell-side 3.62 mm. Tests were conducted with varying water flow rates, temperature levels and heat fluxes on both the tube and shell sides at Reynolds numbers of approximately 170–6000 on the tube-side and 1000–5000 on the shell-side, respectively. The Wilson plot method was employed to investigate the heat transfer on both the shell and tube sides. In the Reynolds number range of 2300–6000, it was found that the Nusselt numbers agreed with those predicted by the Gnielinski correlation within ±5% accuracy. In the Reynolds number range of 170–1200 the Nusselt numbers gradually increased from 2.1 to 3.7. None of the previously reported correlations for laminar flow predicted the Nusselt numbers well in this range. The shell-side Nusselt numbers were found to be considerably higher than those predicted by correlations from the literature.     

The Effect of the Demagnetizing Field on the NMR Spectra for Liquids Enclosed in a Cylinder

The NMR spectrum of a simple liquid in a cell of size L depends on D, the diffusion constant, G, the applied field gradient, and M ₀, the z-component of magnetization before tipping of the spins. For small tipping angles the shape of the spectrum depends on which of the corresponding frequency scales—ω _D = D/L ²,ω _G = γ FL, and ω _M = γ μ₀ M ₀—is the largest. We explore the evolution of the spectrum between the inhomogeneous broadening regime (ω _G ? ω _D ,ω _M ) and the regime where the spin dynamics is dominated by magnetostatic modes (ω _M ? ω _D ,ω _G )for a liquid confined in a cylinder of length 2L, both for classical liquids, and for liquids which exhibit the Leggett–Rice effect.     

Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using Lattice Boltzmann Method

In this paper the Lattice Boltzmann Method (LBM) is utilized to investigate the effects of uniform vertical magnetic field on the flow pattern and fluid–solid coupling heat transfer in a channel which is partially filled with porous medium. Al₂O₃–water nanofluid as a work fluid with temperature sensitive properties is forced to flow into the channel while the top and bottom walls of the channel is heated and kept at a constant temperature. In the present study, with respect to previous works and experimental data, a new correlation is presented for density of Al₂O₃–water nanofluid as a function of temperature. The result also shows that the step approximation which is used for the complex boundaries of porous medium is reliable. Finally, the effect of various volume fractions of nanoparticles (ϕ = 0%, 3%, 5% and 7%) and different magnitude of magnetic field (Ha = 0, 5, 10 and 15) on the rate of heat transfer are thoroughly explored. In accordance with the results, by raising the nanoparticle volume fraction, average temperature and velocity at the outlet of the channel increase and the average Nusselt number rises dramatically. In addition, the increase the Hartmann number leads to the slow growth in the average Nusselt number, although the outlet average temperature and velocity shows a little drop.     

Entropy generation in a heat exchanger working with a biological nanofluid considering heterogeneous particle distribution

Entropy generation rates considering particle migration are evaluated for a biologically produced nanofluid flow in a mini double-pipe heat exchanger. The nanofluid is used in tube side and hot water flows in annulus side. Silver nanoparticles synthesized through plant extract method from green tea leaves are utilized. Particle migration causes non-uniform concentration distribution, and non-uniformity intensifies by increase in Reynolds number and concentration. The results indicate that at high concentrations and Reynolds numbers, particle migration can have a great effect on entropy generation rates. For water inlet temperature of 308 K, the contribution of friction in nanofluid entropy generation is much more than that of heat transfer. However, as the water inlet temperature increases to 360 K, the heat transfer contribution increases such that at low Reynolds numbers, the thermal contribution exceeds the frictional one. For total heat exchanger, Bejan number is smaller than 0.2 at water inlet temperature of 308 K, while Bejan number has a large value at water inlet temperature of 360 K. Furthermore, entropy generation at the wall has an insignificant contribution, such that for Re = 1000 and φ_m = 1%, the total entropy generation rates for the nanofluid, wall, and water are 0.098810, 0.000133, and 0.041851 W/K, respectively.     

Analysis of steady free convection from an axisymmetric heat-generating body embedded in a semi-infinite porous medium

An analysis is presented for the steady state free convective flow and heat transfer from an axisymmetric heat-generating body that is embedded in a fluid-saturated, semi-infinite, porous medium. The porous medium is assumed to be rigid, homogeneous and isotropic, and be in thermal equilibrium with the fluid. The fluid is assumed to be incompressible, with the density changes contributing only towards the buoyancy forces via the Boussinesq approximation. The governing equations for the fluid consist of the equation of continuity, Darcy's law and the equation of energy. After introducing the stream function concept, the equations governing the stream function and pressure are derived. Using the non-dimensional variables, the non-dimensional equations governing the non-dimensional forms of the temperature, stream function and pressure are dervied and the appropriate boundary conditions are stated. The mathematical formulation contains two parameters; D, the non-dimensional depth of the body from the surface of the porous medium, and a product Raθ_s of Rayleigh number (Ra) and the non-dimensional surface temperature of the body (θ_s). The Galerkin finite element method, with linear, isoparametric, quadrilateral elements, is used to reduce the mathematical formulation into a set of algebraic equations. The expressions to calculate the non-dimensional surface temperature and Nusselt number of the body, and the non-dimensional velocity of the fluid, are derived. A computer code has been developed to solve the algebraic equations, using Gauss elimination procedure, in a banded matrix form. The computer code, in addition to the non-dimensional temperature, stream function and pressure, calculates the isothermal lines, non-dimensional surface temperature of the body, Nusselt number of the body, velocity field and isobars. To demonstrate the application of the code, a spherical heat-generating body is considered as an example. Numerical results are obtained for D = 3 and 6, and Raθ_s = 0.001, 0.1, 1 and 5, and presented.