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.     

Mixed convection cooling of a heated circular cylinder by laminar upward-directed slot jet impingement

An experimental and numerical study has been carried out to investigate the heat transfer characteristics of a horizontal circular cylinder exposed to a slot jet impingement of air. A square-edged nozzle is mounted parallel with the cylinder axis and jet flow impinges on the bottom of the cylinder. The study is focused on low Reynolds numbers ranging from 120 to 1,210, Grashof numbers up to Gr = 10Re ² and slot-to-cylinder spacing from 2 to 8 of the slot width. The flow field is greatly influenced by the slot exit velocity and the buoyancy force due to density change. A Mach–Zehnder Interferometer is used for measurement of local Nusselt number around the cylinder at 10° interval. It is observed that the average Nusselt number decreases with increasing the jet spacing and increases with rising the Reynolds number. A finite volume method utilizing a curvilinear coordinate transformation is used for numerical modeling. The numerical results show good agreement with the experimental results. The flow and thermal field are seen to be stable and symmetric around the cylinder over the range of parameters studied.     

Vortex motions in stratified wake flows

The vortex wakes of obstacles (circular cylinder and sphere) moving through a linearly stratified fluid have been investigated, by means of flow visualization, at Reynolds numbers smaller than 800 and non-dimensional buoyancy frequencies smaller than 6. Vortex shedding from a horizontally suspended circular cylinder is suppressed when the fluid is stratified. The wake of a sphere is affected by lee waves when the Reynolds number exceeds about 200.     

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.     

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.     

Unsteady mixed convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

A two-dimensional numerical study is carried out to understand the influence of cross buoyancy on the vortex shedding processes behind two equal isothermal square cylinders placed in a tandem arrangement at low Reynolds numbers. The spacing between the cylinders is fixed with five widths of the cylinder dimension. The flow is considered in an unbounded medium, however, fictitious confining boundaries are chosen to make the problem computationally feasible. Numerical calculations are performed by using a finite volume method based on the PISO algorithm in a collocated grid system. The range of Reynolds number is chosen to be 50–150. The flow is unsteady laminar and two-dimensional in this Reynolds number range. The mixed convection effect is studied for Richardson number range of 0–2 and the Prandtl number is chosen constant as 0.71. The effect of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as overall drag and lift coefficients, local and surface average Nusselt numbers and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.     

Heat convection from a cylinder performing steady rotation or rotary oscillation – Part I: Steady rotation

In this paper, the problem of laminar, two dimensional heat convection from a circular cylinder performing steady rotation is investigated. The cylinder is␣placed with its axis horizontal in a quiescent fluid of infinite extent. Because of viscous dissipation, the flow process is confined to the region adjacent to the cylinder and is mainly driven by shear and buoyancy forces. The study is based on the solution of the full conservation equations of mass, momentum and energy for Rayleigh numbers up to 10⁴ and Reynolds numbers (based on surface velocity) up to 400 while Prandtl number ranges between 0.7 and 7.0. For the range of parameters considered, the study revealed that the rate of heat transfer increases with the increase of Rayleigh number and decreases with the increase of speed of rotation. The increase of Prandtl number resulted in an appreciable increase in the average Nusselt number only at low Reynolds numbers. The effect of Prandtl number at high Reynolds number is negligibly small. The resulting flow field in all cases is steady with no vortex shedding. The streamlines and isotherms are plotted for a number of cases to show the details of the velocity and thermal fields. Received on 15 December 1997     

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.     

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     

On the development of Taylor vortices in a vertical annulus with a heated rotating inner cylinder

A numerical study has been conducted to determine the heat transfer characteristics and flow patterns which develop around a rotating, heated vertical cylinder enclosed within a stationary concentric cylinder. A tall annulus (aspect ratio of 10) with fixed, adiabatic horizontal end-plates and a radius ratio of 0·5 has been considered. Furthermore, the effect that the introduction of buoyancy forces by heating the inner cylinder has on the development of the Taylor vortex flow is examined. It is observed that the formation of the Taylor vortices is delayed until the rotational parameter σ = Gr/Re² has a value below unity for any given Reynolds number Re which is above the critical value Re_crit for the formation of Taylor vortices in an isothermal flow. Also, the Taylor cells first appear at the top of the annulus. As σ is gradually decreased below unity, bifurcations to other states are observed. The final structure of the secondary flow is noticeably distorted in the mixed-convection mode, with the size of the Taylor cells varying greatly along the height of the annulus. This distortion diminishes as σ is further decreased, until the isothermal flow pattern is nearly recovered below σ = 0·01.     

Numerical investigation of mixed convection heat transfer from two isothermal circular cylinders in tandem arrangement: buoyancy,spacing ratio,and confinement effects

This paper presents a two-dimensional numerical study for mixed convection in a laminar cross-flow with a pair of stationary equal-sized isothermal cylinders in tandem arrangement confined in a channel. The governing equations are solved using the control volume method on a nonuniform orthogonal Cartesian grid, and the immersed boundary method is employed to identify the cylinders placed in the flow field. The numerical scheme is first validated against standard cases of symmetrically confined isothermal circular cylinders in plane channels, and grid convergence tests were also examined. The objective of the present study was to investigate the influence of buoyancy and the blockage ratio constraint on the flow and heat transfer characteristics of the immersed cylinder array. Using a fixed Reynolds number based on cylinder diameter of \(Re_{D} = 200\), a fixed value of the Prandtl number of \(Pr = 7\), and a blockage ratio of \(D/H = 0.2\), all possible flow regimes are considered by setting the longitudinal spacing ratio (\(\sigma = L/D\)) between the cylinder axes to 2, 3, and 5 for values of the buoyancy parameter (Richardson number) in the range \(-1\le Ri\le 4\). The interference effects and complex flow features are presented in the form of mean and instantaneous velocity, vorticity, and temperature distributions. The results demonstrate how the buoyancy, spacing ratio, and wall confinement affect the wake structure and vortex dynamics. In addition, local and average heat transfer characteristics of both cylinders are comprehensively presented for a wide range in the parametric space.     

Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Mixing of two gases one of which is expelled from a cylindrical space by the other

The flow structure and impurity distribution in an axisymmetric cylindrical space is obtained from the system of equations of convective heat and mass transfer in the Boussinesq approximation for different variants of the gas inflow and outflow conditions. The variation of the average impurity concentration in the space investigated, obtained as a result of numerical calculations, is compared with two limiting cases of expulsion of the contaminated gas: the gas piston case and total mixing. The dependence of the velocity and impurity concentration fields on the regime parameters (Reynolds, Grashof, and Schmidt numbers, velocity profiles at the gas inlet and outlet) and the geometric and design parameters (elongation of cylinder, inflow and outflow geometry) is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 31–38, May–June, 1986.     

Mixed Convection in a Horizontal Channel with Local Heating from Below

Mixed convection induced in the entrance region of a horizontal plane channel by a bottom heat source of finite dimensions is considered. The calculations were performed for the Prandtl number Pr = 1, Grashof numbers ranging from 4 · 10³ to 3.2 · 10⁴, and Reynolds numbers varying from 0 to 10. The dimensions of the heat source and its location were also varied. The results were obtained from a numerical solution of the 2D unsteady Navier-Stokes equations in the Boussinesq approximation, written in vorticity – stream function – temperature variables. The solution was found by the Galerkin finite element method.     

Induced parallel vortex shedding from a circular cylinder at Re of O(10) by using the cylinder end suction technique

In the present work, the objective is to attempt to induce parallel vortex shedding at a moderately high Reynolds number (=1.578 × 10⁴) by using the cylinder end suction method, and measure the associated aerodynamic parameters.We first measured the aerodynamic parameters of a single circular cylinder without end suction, and showed that the quantities measured are in good agreement with equivalent data in the published literature. Next, by using different amount of end suction which resulted in increasing the cylinder end velocity by 1%, 2% and 2.5%, we were able to show that the above corresponded to the situation of under suction, optimal suction and over suction, respectively. With optimal suction, we demonstrated that the end suction method works at Re = 1.578 × 10⁴. The shape of the primary vortex shed became straighter than when there is no end suction, and parameters like cylinder surface pressure distribution, drag force per unit span, as well as vortex shedding frequency all showed negligible spanwise variation. Further careful analyses showed that when compared to the naturally existing curved vortex shedding, with parallel vortex shedding the mid-span drag per unit span became slightly smaller, but the drag averaged over the cylinder span became slightly larger. For cylinder surface pressure, it was found that cylinder end effects mainly influenced the surface pressure in the angular ranges −180°  β < −60° and 60° < β  180°. Without end suction, the cylinder surface pressure in the above ranges was found to increase (become less negative) slightly with |z/d|, but such increase disappeared when optimal end suction was applied, and the cylinder surface pressure distribution became spanwise location independent. As for the vortex shedding frequency (Strouhal number), although the Strouhal number showed spanwise variation when there is no end suction and negligible spanwise variation when optimal suction was applied, the difference between the spanwise averaged Strouhal number was quite negligible. With under suction, the spanwise dependence of various aerodynamic parameters existed, but was found to be not as significant as when no end suction was applied at all. With over suction, the flow situation was found to be practically no change from the optimal suction situation.     

Flow about yawed,stranded cables

The development of a steady lift force on a stranded cable, which is yawed with respect to a flow, is a unique characteristic of a cable when compared to a circular cylinder. Comparisons of lift and normal drag coefficients and wake characteristics were made between stranded cable models and the cylinder. These were based upon surface pressure and hot-wire measurements and flow visualization studies conducted in a low speed wind tunnel on rigid cables and cylinders. The models were yawed to four different yaw angles and tested within the Reynolds number range of 5,000 and 50,000. Pressure profiles for the yawed cables indicated that the lift force is directed towards the side where the primary strands are more nearly aligned with the flow. The pressure profiles also indicated that the lift force is generated by asymmetric separation. The small scale irregularities associated with wires within individual strands also appeared to have an effect on the cable's lift and drag characteristics. Results show that cables have significantly different shedding characteristics and near-wake shear layer structure when compared to the circular cylinder. For the flow regime tested, the Strouhal number showed no dependence on Reynolds number nor spanwise position along the cable.List of symbols C _dn normal drag coefficient - C _l lift coefficient - C _p pressure coefficient - D actual diameter, based on circumscribing circle for the cable - f _v shedding frequency - L/D length to actual diameter ratio - ppd peak-to-peak distance, unit span - Re Reynolds number based on actual diameter - S Strouhal number, - V free stream velocity - cable angle - azimuthal angle     

Flow around a porous cylinder subject to continuous suction or blowing

In the present experimental investigation the surface pressure distribution, vortex shedding frequency, and the wake flow behind a porous circular cylinder are studied when continuous suction or blowing is applied through the cylinder walls. It is found that even moderate levels of suction/blowing (5% of the oncoming streamwise velocity) have a large impact on the flow around the cylinder. Suction delays separation contributing to a narrower wake width, and a corresponding reduction of drag, whereas blowing shows the opposite behaviour. Both uniform suction and blowing display unexpected flow features which are analysed in detail. Suction shows a decrease of the turbulence intensity throughout the whole wake when compared with the natural case, whilst blowing only shows an effect up to five diameters downstream of the cylinder. The drag on the cylinder is shown to increase linearly with the blowing rate, whereas for suction there is a drastic decrease at a specific suction rate. This is shown to be an effect of the separation point moving towards the rear part of the cylinder, similar to what happens when transition to turbulence occurs in the boundary layer on a solid cylinder. The suction/blowing rate can empirically be represented by an effective Reynolds number for the solid cylinder, and an analytical expression for this Reynolds number representation is proposed and verified. Flow visualizations expose the complexity of the flow field in the near wake of the cylinder, and image averaging enables the retrieval of quantitative information, such as the vortex formation length.     

Heat transfer between an impinging jet and a continuously moving flat surface

Experiments have been carried out to determine heat transfer rates from a continuously moving belt to an air jet impinging normally. The parameters that were varied included the jet velocity (4 < V_N < 40 m/s), the jet width (4.8 < B < 19 mm), the nozzle-to-plate distance (3 < H/2B < 11) and the belt speed (0. 15 < V_B < 5. 5 m/s). An infrared thermometer was used for the measurement of temperature of the moving belt. The average heat transfer coefficients increase with belt speed steeply initially to a maximum value and then remain almost constant for all higher belt speeds. The maximum heat transfer coefficients are about 1.5 to 2.0 times higher than those predicted for the stationary surface. The present data on continuously surface in still air and in impinging jet flow are well compared with the data on rotating cylinders reported in the literature.

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Wärmeübergang zwischen einem senkrecht auftreffenden Strahl und einer bewegten Oberfläche

Zusammenfassung Experimentell bestimmte Wärmeübergangskoeffizienten für Düsengeschwindigkeiten zwischen 4 m/s und 40 m/s, sowie Düsenbreiten zwischen 4,8 mm und 19 mm lagen bei Bandgeschwindigkeiten zwischen 0, 15 m/s bis 5, 5 m/s ca. 50 % bis 100 % höher als bei unbewegtem Band. Die gemessenen Daten bei bewegtem wie bei unbewegtem Band schließen gut an bekannte Werte aus der Literatur an.

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Nomenclature A Heat transfer area - B Width of the nozzle - D Diameter of the cylinder or equivalent diameter of the flat surface (D=L/) - k Thermal conductivity - Gr Grashof number - h Heat transfer coefficient - H Height of the nozzle from the surface - i Number of nozzles - L Heat transfer length of a flat surface - Nu_D Nusselt number hD/k - Re_DB Belt Reynoldsnumber, DV_B/ - Re_DN Nozzle Reynolds number, DV_N/ - Re_SN Nozzle Reynolds number, SV_N/ - S Hydraulic diameter of the nozzle, 2B - V_B Belt velocity or circumferential velocity of a cylinder - V_N Nozzle celocity - Kinematic viscosity     

Supersonic viscous perfect gas flow past a circular cylinder

The complete Navier-Stokes equations are used to calculate supersonic perfect gas flow past a circular isothermal cylinder by the method described in [1]. The effects of the Mach number M=2.5–10 and the Reynolds number Re=30-10⁵ on the flowfield structure and heat transfer to the cylinder wall are investigated. Special attention is paid to the study of the near wake and the local characteristics on the leeward side of the cylinder.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 107–115, November–December, 1993.