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.     

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.     

Numerical investigation of mixed convection heat transfer past an in-line bundle of cylinders

Two dimensional unsteady Navier-Stokes and the energy equations are solved using finite element method for the case of flow past five row deep in-line bundle of circular cylinders with pitch to diameter ratios (PDR) of 1.5 and 2.0. Numerical solutions of governing equations have been obtained using Euler's explicit algorithm. Analysis have been made for Reynolds number of 100 and Prandtl number of 0.71. The effect of Richardson number (Ri=Gr/Re ²) on the flow and heat transfer have been investigated forRi=?1.0, ?0.5, 0.0, +0.5 and +1.0. Streamlines, isovorticity lines, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distribution around the cylinders are presented. Results obtained for forced convection (Ri=0.0) agree well with the available experimental and numerical results. There is considerable effect of buoyancy over tube bundles both in buoyancy aiding and opposing flows.     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Adverse and favorable mixed convection heat transfer in a two-side heated square channel

Experimental heat transfer measurements and analysis for mixed convection in a vertical square channel are presented. Water flow directions are selected such that buoyancy assists or opposes the bulk flow pressure gradient. Unlike most previous experiments with symmetrically heated circular tubes, the present configuration uses an asymmetric heating condition (two sides heated and two sides insulated) and shows significant increase in the Nusselt number for both assisted and opposed flow conditions. Observed heat transfer coefficient distributions are different from the symmetrically heated channels; and this difference in heat transfer coefficient is attributed to the formation of buoyancy driven large-scale flow structures. In general, opposed flow shows higher heat transfer coefficients, and the Nusselt number ratio is observed to increase as Gr/Re or Gr/Re² ratios increase for both assisted and opposed flow conditions. A correlation based on the buoyancy parameter predicts the heat transfer pattern well in both assisted and opposed mixed convection. The range of Reynolds numbers discussed (Re=400–10,000) is of importance for direct numerical simulations and the details provided here can serve as the benchmark data required for complicated buoyancy affected turbulence simulations.     

Heat transfer performance comparison of steam and air in gas turbine cooling channels with different rib angles

Using steam as working fluid to replace compressed air is a promising cooling technology for internal cooling passages of blades and vanes. The local heat transfer characteristics and the thermal performance of steam flow in wide aspect ratio channels (W/H = 2) with different angled ribs on two opposite walls have been experimentally investigated in this paper. The averaged Nusselt number ratios and the friction factor ratios of steam and air in four ribbed channels were also measured under the same test conditions for comparison. The Reynolds number range is 6,000–70,000. The rib angles are 90°, 60°, 45°, and 30°, respectively. The rib height to hydraulic diameter ratio is 0.047. The pitch-to-rib height ratio is 10. The results show that the Nusselt number ratios of steam are 1.19–1.32 times greater than those of air over the range of Reynolds numbers studied. For wide aspect ratio channels using steam as the coolant, the 60° angled ribs has the best heat transfer performance and is recommended for cooling design.     

Experimental investigation of mixed convection heat transfer in a horizontal and inclined rectangular channel

 Mixed convection heat transfer in rectangular channels has been investigated experimentally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Experiments were conducted for Pr=0.7, aspect ratios AR=5 and 10, inclination angles 0° ≤ θ ≤ 30°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr*=7.0 × 10⁵ to 4.0 × 10⁷. From the parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results related to the buoyancy affected secondary flow and the onset of instability have been discussed. Some of the results obtained from the experimental measurements are also compared with the literature, and a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number and increasing aspect ratio. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle. Received on 19 March 2001 / Published online: 29 November 2001     

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd.     

Natural convection heat transfer from a long heated vertical cylinder to an adjacent air gap of concentric and eccentric conditions

In this work, the natural convection heat transfer from a long vertical electrically heated cylinder to an adjacent air gap is experimentally studied. The aspect and diameter ratios of the cylinder are 55.56 and 6.33, respectively. The experimental measurements were obtained for a concentric condition and six eccentricities from 0.1 to 0.92 at five different heat fluxes. The surface temperature of the heated rod is measured at different heights, and the Nusselt number is calculated at the temperature measurement locations. A correlation is suggested to determine the Nusselt number based on the variation of the eccentric ratio values. The experimental results show a good agreement with other studies.     

Heat transfer and fluid flow analysis of artificially roughened ducts having rib and groove roughness

Artificially roughness is one of the well known methods of enhancing heat transfer from the heat transfer surface in the form of repeated ribs, grooves or combination of ribs and groove (compound turbulators). The artificial roughness produced on the heat transferring surface is used in cooling of gas turbine blades, nuclear reactor, solar air heating systems etc. Solar air heaters have wide applications in low to moderate temperature range, namely, drying of foods, agricultural crops, seasoning of wood and space heating etc. Solar air heaters have low value of convective heat transfer coefficient between the working fluid (air) and the heat transferring surface, due to the formation of thin laminar viscous sub-layer on its surface. The heat transfer from the surface can be increased by breaking this laminar viscous sub layer. Hence, in the present work compound turbulators in the form of integral wedge shaped ribs with grooves are used on the heat transfer surface, to study its effect on the heat transfer coefficient (Nusselt number) and friction factor in the range of Reynolds number 3,000–18,000. The roughness produced on the absorber plate forms the wetted side of upper broad wall of the rectangular duct of solar air heater. The relative groove position (g/p) was varied from 0.4 to 0.8 and the wedge angle (Φ) was varied from 10° to 25°, relative roughness pitch (p/e) and relative roughness height (e/D) was maintained as 8.0 and 0.033 respectively. The aspect ratio of the rectangular duct was maintained as 8. The Nusselt number and friction factor of the artificially roughened ducts were determined experimentally and the corresponding values were compared with that of smooth surface duct. It is observed that wedge-groove roughened surface shows more enhancement in heat transfer compared to only rib roughened surface arrangement. The investigation revealed that Nusselt number increases 1.5–3 times, while the friction factor increases two to three folds that of the smooth surface duct in the range of operating parameters. It is also observed that in rib–groove roughness arrangement with relative groove position of 0.65 shows the maximum enhancement in the heat transfer compared to the other rib-groove roughness arrangements. Statistical correlations for the Nusselt number and friction factor have been developed by the regression method in terms of the operating and roughness parameters. A program was also developed in MATLAB for the calculation of thermal efficiency and thermal effectiveness. It was observed that the thermal efficiency is more for wedge angle of 15° and relative groove position of 0.65 and its value ranges from 42 to 73 %. The uncertainties in the measurements due to various instruments for the Reynolds number, Nusselt number, and friction factor have been estimated as ±3.8, ±4.54 and ±7.6 % respectively in the range of investigation made.     

Experimental study of combined free and forced laminar convection in an asymmetrically heated two-dimensional aiding flow

An experimental study of mixed convection in an asymmetrically heated two-dimensional flow of water has been made. Experiments in fully developed turbulent flow (Re maximum=9000) were made initially to establish the satisfactory operation of the equipment. In the mixed convection laminar flow tests to determine local Nusselt numbers, the Reynolds number range was from about 100 to 1000 with the Rayleigh number based on heat flux varying from about 10 to 300. The data, which are presented graphically, have been compared with the results of the theoretical analyses of other workers. The effect of buoyancy in the immediate entry of the flow [(x/de)/Re Pr <.05] was found to be negligible, but at greater distances there were significant increases in the heat transfer coefficient with the larger values of Rayleigh number.     

Heat transfer and friction factor of turbulent flow through a horizontal semi-circular duct

Forced convection heat transfer and pressure drop characteristics of air flow inside a horizontal semi-circular duct are investigated experimentally. The experiments are carried out on a semi-circular duct of 23 mm inner radius, 2 mm thickness, and 2,000 mm length within a range of Reynolds number (8,242 ≤ Re ≤ 57,794)., under uniform wall heat flux conditions. The friction factor is determined by measuring the axial static pressure at different selected axial stations along the semi-circular duct. The variations of surface and mean air temperatures, local heat transfer coefficient, local Nusselt number, and the friction factor with the axial dimensionless distance are presented. It is observed that, for a given value of Reynolds number, each of the local heat transfer coefficient and the friction factor has a relatively high value near the entrance of the semi-circular duct then it decreases with increasing the dimensionless axial distance until it approaches a nearly constant value at the fully developed region. Also, it is found that, with increasing the Reynolds number the average heat transfer coefficient is increased and the friction factor is decreased. Moreover, empirical correlations for the heat transfer coefficient and friction factor as a function of the Reynolds number are obtained.     

浮力对混合对流流动及换热特性的影响

用热线和冷线相结合的技术测量垂直圆管内逆混合对流流体的平均速度、 温度以及它们的脉动. 较详细地研究了浮力对逆混合对流的流动特性和传热特性的影响. 评 估了实验中采用的冷线测量温度补偿速度探头温度敏感的影响. 逆混合对流的传热结果用无 量纲参数Ω (Ω= Grd / Red2 )来表示，其中，基于管道直 径的雷诺数Red变化范围为900~18000, 浮力参数Ω变化范围为 0.004899~0.5047. 研究结果表明，浮力对逆混合对流的换热有强化作用. 随着葛拉晓夫数Grd的增加，温度脉动，流向雷诺正应力和流向温度通量增 大，并且在靠近壁面的流体区域尤其明显. 热线与冷线相结合的技术适合于研究非绝热的流 动测量，可以用于研究浮力对流动和换热特性的影响.     

Mixed convection adjacent to inclined flat surfaces embedded in a porous medium

An analysis is performed to study the flow and heat transfer characteristics of laminar mixed convection boundary layer flows from inclined (including horizontal and vertical) surfaces embedded in a saturated porous medium with constant aiding external flows and uniform surface temperature. Both the streamwise and normal components of the buoyancy forces are retained in the momentum equations. Nondimensionalization of the boundary layer equations results in the following three governing parameter: (1)Gr/Re, the ratio of the Grashof number to the Reynolds number; (2)Pe _x =Re _x Pr, the Peclet number; (3) φ, the angle of inclination from the horizontal. The resulting nonsimilar equations are solved by an efficient implicit finite-difference scheme. Numerical results are presented for flows with different values ofGr/Re in the range of 0 to 50, over a wide range of the Peclet numbersPe _x, and various values of φ ranging from 0 to 90 degrees. It is found that the local surface heat transfer rate increases with increasing the local Peclet number. In addition, as the plate is tilted from the horizontal to the vertical orientation, the local Nusselt number increases for a given Peclet number and the effect of the buoyancy force on the surface heat transfer rate increases.     

Coupled heat and mass transfer in mixed convection over a vertical flat plate embedded in saturated porous media: PST/PSC or PHF/PMF

A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N ^*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases) the local heat (mass) transfer rate. Received on 8 December 1997     

Experimental studies on mixed convection heat transfer in laminar flow through a plain square duct

This paper reports the findings of experimental studies on combined free and forced convection through a plain square duct in laminar region. The test fluid flows through an inner square duct, hot water at high flow rate circulated through a annular channel formed between square duct and circular tube, in counter current fashion to attain a nearly uniform wall temperature conditions. The importance of mixed convection is judged by the value of the Richardson number (Ri). It was observed that at low Reynolds number, heat transfer was mainly governed by mixed convection. However at higher values of Reynolds number, heat transfer was significantly dominated by forced convection. It was found that Reynolds number higher than 1050 for water and 480 for ethylene glycol resulted in laminar forced convention heat transfer. The empirical correlation developed for Nusselt number in terms of Grashoff number and Graez number, was found to fit with experimental Nusselt number within ±11 and ±12?% for water and ethylene glycol respectively.     

Numerical investigation of transient laminar natural convection of air in a tall cavity

Transient laminar natural convection of air in a tall cavity has been studied numerically. The Navier-Stokes and Energy equations were solved by the accurate projection method (PmIII), in which the derived Poisson equation for pressure potential was solved by the approximate factorization one method (AF1). The aspect ratio of the tall cavity is 16, and the Prandtl number of air filled in the tall cavity is 0.71. To obtain the numerical results of heat transfer by natural convection of air in the tall cavity, the second order schemes for the space and time discretizations were utilized. The availability of the numerical algorithm was also assessed by considering the natural convection of air in a square cavity which is differentially heated from side walls. It was found that the overall Nusselt numbers for the Rayleigh numbers covering the range from 1000 to 100000 reveal a good agreement with measured data. When Ra takes the value in the range from 100000 to 600000, the overall Nusselt number have a relative deviation less than 18% from the experimental data. For the suddenly heating mode, the multicellular flow pattern occurs when Rayleigh number belongs to the range of Ra from 7000 to 20000. or greater than 115000. At the critical number of cats' eye instability, the cell distance is just twice of the cavity width. This is rather similar to the observed result for Bénard problem. When Ra is over 115000, a further increase of heat flux across the tall cavity causes serious cell-breaking. There are 8 cells when Ra = 600000.     

Numerical investigation of heat transfer and fluid flow characteristics inside a wavy channel

The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed for Prandtl number 0.7, and Reynolds number ranging from 100 to 1,100 on non-orthogonal non-staggered grid systems, based on SIMPLER algorithm in the curvilinear body-fitted coordinates. Effects of wavy heights, lengths, wavy pitches and channel widths on fluid flow and heat transfer were studied. The results show that overall Nusselt numbers and friction factors increase with the increase of Reynolds numbers. According to the local Nusselt number distribution along channel wall, the heat transfer may be greatly enhanced due to the wavy characteristics. In the geometries parameters considered, friction factors and overall Nusselt number always increase with the increase of wavy heights or channel widths, and with the decrease of wavy lengths or wavy pitches. Especially the overall Nusselt number significantly increase with the increase of wavy heights or channel widths, where the flow may become into transition regime with a penalty of strongly increasing in pressure drop. An erratum to this article can be found at     

Experimental correlation of forced convection heat transfer from a NACA airfoil

The results of an experimental investigation of the heat transfer coefficients for forced convection from a NACA-63421 airfoil are presented. Wind tunnel measurements of convection coefficients are obtained for air flow temperatures from −30 to 20 °C. The experimental data is correlated with respect to the Nusselt and Reynolds numbers. Conduction within the airfoil balances heat transfer by convection from the airfoil surface in steady-state conditions. Both average and spatial variations of the heat transfer coefficients are non-dimensionalized through modifications of a classical Hilpert correlation for cylinders in crossflow. It is shown that the functional form of the Hilpert correlation can effectively accommodate measured data for the NACA airfoil over a range of Reynolds numbers. An uncertainty analysis is performed to yield a 7.34% measurement uncertainty for experimental data correlated with the Nusselt number.     

Numerical study on mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows

Fluid flow and heat transfer of mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows have been simulated based on the projection method with two dimensional exponential stretched staggered cylindrical meshes. Cycle mean temperature and secondary streaming are obtained by the method of partial sums of the Fourier series. Present numerical results are validated by comparing the heat transfer results of free convection and the secondary streaming of pure oscillating flow over a circular cylinder to published experimental and numerical results. The complete structures of the cycle mean temperature and secondary streaming patterns are provided by numerical simulations over wide ranges of the Reynolds number, the Keulegan–Carpenter number and the Richardson number. Based on turning points of the curves of the overall Nusselt numbers versus Reynolds numbers and the characteristics of the cycle averaged temperature and flow patterns, the heat transfer can be divided into three linear regimes (conduction, laminar convection, and turbulent convection dominated regimes) and two non-linear transition regimes. The effects of wave directions, amplitudes, frequencies, and buoyancy forces on the enhancement of heat transfer are also investigated. The effective ranges of the governing parameters for heat transfer enhancement are identified.