A note on unsteady impinging jet heat transfer

Reported are the results of experiments on a regular in-line-jet that was modified prior to its impingement to improve heat transfer on the plate. Modifications consisted of insertion of two bluff bodies and a streamlined body in the jet. The improvement in transport coefficients was attributed to the periodicity in the flow which caused the attachment point to sweep the reattachment region and the turbulence created was distributed over a large area compared to simple attachment.     

Prediction of stagnation point heat transfer for a slot jet impinging on a flat surface

The fluid flow and heat transfer for a slot jet impinging on a flat plate has been analysed for different nozzle-to-plate spacing. The available potential flow solution has been used to solve the boundary layer and energy equations by using the Blasius-Frossling series solution method. The friction factor and Nusselt number have been evaluated as a function of the dimensionless distance from the stagnation point. Correlation for the Stanton number at the Stagnation point, is obtained in terms of velocity gradient at the stagnation point and Reynolds number.

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Berechnung des Wärmeübergangs am Staupunkt für einen Strahl, der senkrecht auf eine ebene Fläche trifft

Zusammenfassung Für einen Fluidstrahl, der senkrecht auf eine ebene Platte trifft, wurden für verschiedene Anordnungen von Düse und Platte Strömung und Wärmeübertragung untersucht. Die beschreibende Potentialtheorie wurde verwendet, um die Grenzschicht und Energiegleichungen mit Hilfe der Blasius-Frossling-Reihenentwicklung zu lösen. Reibungsfaktor und Nusseltzahl sind als eine Funktion des dimensionslosen Abstandes vom Staupunkt dargestellt. Die Beziehung für die Stanton-Zahl am Staupunkt ist in den Ausdrücken des Geschwindigkeitsgradienten am Staupunkt und der Reynoldszahl enthalten.

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Nomenclature A ₁ dimensionless coefficient - a dimensionless parameter - b dimensionless parameter - C _f friction factor,C _f= ₀/(1/2w ² ) - C _p specific heat at constant pressure - F ₀ function ofPr and - G ₄ function ofPr and - f ₁ function of - h heat transfer coefficient - k thermal conductivity - l half-width of slot nozzle - Nu Nusselt number,Nu=hl/k - Pr Prandtl number,Pr=v/ - Re Reynolds number,Re=w l/v - St Stanton number,St=Nu/(Re · Pr) - t temperature - t _w wall temperature - t ambient temperature - U dimensionless velocity,U=u/w - U _f dimensionless free-stream velocity,U _f =u _f /w - U _s dimensionless mainstream velocity along the plate,U _s =u _s /w - u velocity component inx-direction - u _f free stream velocity - u _s mainstream velocity along the plate - w velocity component inz-direction - w velocity at the nozzle exit - x coordination along the plate - X dimensionless distance from the stagnation point along the plate,X=x/l - Y ratio ofU _s andU _f ,Y=U _s /U _f - z coordinate perpendicular to the plate - z _n height of the nozzle above the plate - Z dimensionless height of the nozzle above the plate,Z=z _n /l - thermal diffusivity,=k/( C _p) - dimensionless parameter - dimensionless coordinate perpendicular to the plate - viscosity - kinematic viscosity - ₀ shear stress at the wall - stream function     

Prediction of stagnation point heat transfer for a slot jet impinging on a concave semicylindrical surface

A systematic procedure has been laid out for assessment of fluid flow and heat transfer parameters for a slot jet impinging on a concave semicylindrical surface. Based on Walz's modifications of the Karman-Pohlhausen integral method, expressions have been derived for evaluation of the momentum thickness, boundary layer thickness and the displacement thickness at the stagnation point. The work then has been extended for the estimation of thermal boundary layer thickness and local heat transfer coefficients. A correlation has been presented for the Nusselt number at the stagnation point as a function of the Reynolds number for different non-dimensional distances from the exit plane of the jet to the impingement surface.

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Berechnung des Wärmeübergangs im Staupunkt eines Strahles, der aus einer rechteckigen öffnung auf eine konkave halbzylindrische Fläche auftrifft

Zusammenfassung Es wurde eine systematische Prozedur für die Abschätzung von Strömungs- und Wärmeübergangsparametern für einen Strahl, der auf eine konkave halbzylindrische Fläche auftrifft, aufgestellt. Basierend auf Walz's Modifikationen der Karman-Pohlhausen Integral-Methode, wurden Ausdrücke für die Berechnung der Impulsdicke, der Grenzschichtdicke und die Versetzungsdicke am Staupunkt abgeleitet. Die Arbeit wurde dann auf die Abschätzung der thermischen Grenzschichtdicke und der lokalen Wärmeübertragungskoeffizienten ausgedehnt. Es wird eine Beziehung für die Nusselt-Zahl am Staupunkt als eine Funktion der Reynolds-Zahl für verschiedene dimensionslose Abstände von der Austrittsfläche des Schlitzes bis zur Aufprallfläche aufgestellt.

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Nomenclature c _p specific heat at constant pressure - h ₀ heat transfer coefficient at the stagnation point - H distance from the exit plane of the jet to the impingement surface - k thermal conductivity - Nu _.5 Nusselt number based on impinging jet quantities =h _0.50/k - Nu _.5,0 stagnation point Nusselt number =h _{0 0.50}/k - p pressure - p _a ambient pressure - p ₀ maximum pressure or stagnation pressure - p(x) static pressure at a distancex from the stagnation point - p(x*) static pressure at nondimensional distancex* from the stagnation point - Re _J jet Reynolds number =U _J W/ - Re _0.5 Reynolds number based on impinging jet quantities =u _{m0 0.50}/ - T temperature - T* nondimensional temperature =(T–T _W)/(T _J–T _W) - T _a room temperature - T _J jet temperature - T _W wall temperature - u velocity component inx andx directions - u _m jet centerline (or maximum) free jet velocity: external (or maximum) boundary layer velocity aty = _m - u _m0 arrival velocity defined as the maximum velocity the free jet would have at the plane of impingement if the plane were not there - U _J jet exit velocity - W jet nozzle width - x* nondimensional coordinate starting at the stagnation point =x/2 _0.50 - x, y rectangular cartesian coordinates - y coordinate normal to the wall and starting at the wall - ratio of thermal to velocity boundary layer thickness = _T/ _m - ₀ ratio of thermal to velocity boundary layer thickness at the stagnation point - * inner layer displacement thickness - _.50 jet half width at the plane of impingement if the plate were not there - d_.5 free jet (half width) thickness whereu=u _m/2 - _m inner boundary layer thickness atu =u _m - _T thermal boundary layer thickness - nondimensional coordinate normal to wall =y/ _m - _T nondimensional coordinate normal to wall =y/ _T - Pohlhausen's form parameter - dynamic viscosity - kinematic viscosity = / - fluid density - momentum thickness - ₀ momentum thickness at the stagnation point     

Effects of temperature-dependent fluid properties on heat transfer due to an axisymmetric impinging gas jet normal to a flat surface

Heat transfer due to an axisymmetric laminar gas jet impinging onto a flat solid surface of uniform temperature is studied numerically, taking into account the temperature dependence of all fluid physical properties. Numerical solutions are obtained for the jet Reynolds numbers 200–2000, jet mouth-to-surface distances 1–4 times the jet nozzle diameter, and for helium-4, air, and carbon dioxide. Effects of the temperature dependence of the fluid properties are investigated using various kinds of reference temperatures and a viscosity correction method. A method of estimating the values of the local Nusselt number for temperature-dependent fluid from the constant-property solutions is proposed.Die Wärmeübertragung durch einen auf eine flache Oberfläche gleichförmiger Temperatur achsensymmetrisch auftreffenden Gasstrahl wird numerisch unter Berücksichtigung der Temperaturabhängigkeit der physikalischen Eigenschaften von Fluiden untersucht. Die numerischen Lösungen werden für die Reynoldschen Strahlzahlen von 200 bis 2000, für die Abstände vom Düsenmund zur Oberfläche vom 1- bis 4-fachen des Düsenstrahldurchmessers und für Helium-4, Luft und Kohlendioxyd erhalten. Die Wirkungen der Temperaturabhängigkeiten von Fluideigenschaften werden unter Verwendung verschiedener Bezugstemperaturen und einer Viskositätskorrekturmethode untersucht. Ausgehend von der Lösung für konstante Stoffwerte wird eine Methode zur Schätzung der Werte der lokalen Nusseltzahl für temperaturabhängige Fluide vorgeschlagen.     

燃气射流冲击传热特性的数值模拟

针对射流传热问题,利用基于RNGk-ε湍流模型的数值方法模拟了射流垂直冲击平板的流动过程,并与实验数据比较,验证了模型的可行性。在此基础上,以火箭喷管入口参数为入口条件,建立了超音速燃气射流垂直冲击平板和冲击浸没平板的计算模型,分析了不同冲击条件下努塞尔数分布规律和温度分布规律, 论述了超音速射流传热的特性及影响传热特性的因素。得到了冲击距离为(14~18)D的努塞尔数取值范围,并表明冲击距离和射流温度是影响传热效率的关键因素;冲击距离增加,传热效率降低,冲击平板表面的射流温度越高,传热效率越高。     

Prediction of stagnation point heat transfer for a single round jet impinging on a concave hemispherical surface

This paper deals with a systematic procedure for assessment of fluid flow and heat transfer parameters for a single round jet impinging on a concave hemispherical surface. Based on Scholkemeier's modifications of the Karman-Pohlhausen integral method, expressions are derived for evaluation of the momentum thickness, boundary layer thickness and the displacement thickness at the stagnation point. This is followed by the estimation of thermal boundary layer thickness and local heat transfer coefficients. A correlation is presented for the Nusselt number at the stagnation point as a function of the Reynolds number for different non-dimensional distances from the exit plane of the jet to the impingement surface.

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Bestimmung des Staupunktes bei der Wärmeübertragung für einen einzelnen Strahl, der auf eine konkave halbkugelige Oberfläche trifft

Zusammenfassung Diese Arbeit beschäftigt sich mit dem systematischen Verfahren der Bewertung von Fluidströmungen und Wärmeübertragungsparametern für einen einzelnen runden Strahl, der auf eine konkave halbkugelförmige Oberfläche trifft. Das Verfahren beruht auf Scholkemeiers Modifikation des Karman-Pohlhausen Integrationsverfahrens. Ausdrücke sind für die Berechnung der Impuls-Dicke, der Grenzschichtdicke und der Verschiebungsdicke am Staupunkt hergeleitet worden. Dies ist aus der Berechnung der thermischen Grenzschichtdicke und des lokalen Wärmeübertragungskoeffizienten abgeleitet worden. Es wird eine Gleichung für die Nusselt-Zahl am Staupunkt als Funktion der Reynolds-Zahl für verschiedene dimensionslose Abstände vom Strahlaustrittspunkt bis zum Auftreffpunkt auf die Oberfläche vorgestellt.

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Nomenclature c _p specific heat at constant pressure - d diameter of single round nozzle - h ₀ heat transfer coefficient at the stagnation point - H distance from the exit plane of the jet to the impingement surface - k thermal conductivity - Nu _0.5 Nusselt number based on impinging jet quantities=h _0.50/k - Nu _{0.5, 0} stagnation point Nusselt number=h _{0 0,50}/k - p pressure - p _a ambient pressure - p ₀ maximum pressure or stagnation pressure - p(x) static pressure at a distancex from the stagnation point - R radius of curvature of the hemisphere - Re _J jet Reynolds number=U _Jd/ - Re _0.5 Reynolds number based on impinging jet quantities=u _{m0 0.50}/ - T temperature - T _a room temperature - T _J jet temperature - T _W wall temperature - u velocity component inx andx directions (Fig. 1) - u _m jet centerline (or maximum) free jet velocity: external (or maximum) boundary layer velocity aty= _m - u _m0 arrival velocity defined as the maximum velocity the free jet would have at the plane of impingement if the plane were not there - U _J jet exit velocity - x* non-dimensional coordinate starting at the stagnation point=x/2 _0.50 - x, y rectangular Cartesian coordinates - y coordinate normal to the wall starting at the wall - ratio of thermal to velocity boundary layer thickness= _T/_m - ₀ ratio of thermal to velocity boundary layer thickness at the stagnation point - * inner layer displacement thickness - _0.50 jet half width at the plane of impingement if the plate were not there - _m inner boundary layer thickness atu=u _m - Pohlhausen's form parameter - dynamic viscosity - kinematic viscosity=/ - fluid density - momentum thickness - ₀ momentum thickness at the stagnation point     

Numerical simulation of convective heat transfer to a radial free surface jet impinging on a hot solid

The convective heat transfer between a circular free surface impinging jet and a solid surface has been studied numerically. The thin liquid film formed on the surface has been assumed to be in non-turbulent free surface flow. The effects of surface tension, viscosity, gravity and heat transfer between the film flow and the solid surface have been taken into account. The flow structure on a non-heated surface has been investigated first. Next, the steady-state flow structure in the liquid film as well as the heat transfer has been examined. The predicted results have been compared with experimental data for the purpose of validating the analysis. The hydrodynamics of the liquid film and the heat transfer processes have been investigated numerically to understand the physics of the phenomena. Received on 5 October 1998     

Unsteady flow and heat transfer analysis of an impinging synthetic jet

The present paper focuses on the analysis of unsteady flow and heat transfer regarding an axisymmetric impinging synthetic jet on a constant heat flux disc. Synthetic jet is a zero net mass flux jet that provides an unsteady flow without any external source of fluid. Present results are validated against the available experimental data showing that the SST/k − ω turbulence model is more accurate and reliable than the standard and low-Re k − ε models for predicting heat transfer from an impinging synthetic jet. It is found that the time-averaged Nusselt number enhances as the nozzle-to-plate distance is increased. As the oscillation frequency in the range of 16–400 Hz is increased, the heat transfer is enhanced. It is shown that the instantaneous Nu distribution along the wall is influenced mainly by the interaction of produced vortex ring and wall boundary layer. Also, the fluctuation level of Nu decreases as the frequency is raised.     

Heat transfer and pressure distributions of an impinging jet on a flat surface

Experiments were conducted to determine the heat transfer and surface pressure characteristics of a round jet impinging normal on isothermal flat plate. Three nozzles of exit diameters 3, 5 and 7?mm have been used. The local heat transfer rates have been estimated from the outputs of three-wire differential thermocouple heat flux sensors. The results cover a Reynolds number range of 3400 to 41?000 and dimensionless separation distances varies from 6 to 58. The static pressure distributions along the impingement surface are found to be similar and closer to the heat transfer variations at the same configurations. A simple correlation is derived for the average heat transfer coefficients within ±10% deviation from the output data covering the complete range of experimental limits. The predicted values of Nusselt number have also been compared with the results obtained from the literature. The agreement was generally good.     

Heat transfer from a flat surface to an inclined impinging jet

An experimental study was carried out to investigate the effect of the inclination jet on convection heat transfer to horizontal flat plate. Local heat transfer determined as a function is of three parameters including inclination angle of the air jet relative to the plate in range of 90° ≤ θ ≤ 45°, jet-to-plate spacing in range of 2 ≤ L/D ≤ 8 and Reynolds number in range of 1,500 ≤ Re ≤ 30,000. The results show that the maximum heat transfer point moves towards the uphill side of the plate and the maximum heat transfer decreases as the inclination angle decreases. The correlations were conducted to predict maximum and local Nusselt number as a function of Re, θ, L/D, and x/D for a specific three regions.     

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     

Flow structure and heat transfer characteristics of an unconfined impinging air jet at high jet Reynolds numbers

The flow and heat transfer characteristics of an unconfined air jet that is impinged normally onto a heated flat plate have been experimentally investigated for high Reynolds numbers ranging from 30,000 to 70,000 and a nozzle-to-plate spacing range of 1–10. The mean and turbulence velocities by using hot-wire anemometry and impingement surface pressures with pressure transducer are measured. Surface temperature measurements are made by means of an infrared thermal imaging technique. The effects of Reynolds number and nozzle-to-plate spacing on the flow structure and heat transfer characteristics are described and compared with similar experiments. It was seen that the locations of the second peaks in Nusselt number distributions slightly vary with Reynolds number and nozzle-to-plate spacing. The peaks in distributions of Nusselt numbers and radial turbulence intensity are compatible for spacings up to 3. The stagnation Nusselt number was correlated for the jet Reynolds number and the nozzle-to-plate spacing as Nu _st∝Re ^0.69(H/D)^0.019.     

Heat transfer during transient cooling of high temperature surface with an impinging jet

 An experimental study of transient boiling heat transfer during a cooling of a hot cylindrical block with an impinging water jet has been made at atmospheric pressure. The experimental data were taken for the following conditions: a degree of subcooling of ΔT _sub = 20–80 K, a jet velocity of u _j  = 5–15 m/s, a nozzle diameter of d _j  = 2 mm and three materials of copper, brass and carbon steel. The block was initially and uniformly heated to about 250 °C and the transient temperatures in the block were measured at eight locations in r-direction at two different depths from the surface during the cooling of hot block. The surface heat flux distribution with time was evaluated using a numerical analysis of 2-D heat conduction. Behavior of the wetting front, which is extending the nucleate boiling region outward, is observed with a high-speed video camera. A position of wetting region is measured and it is correlated well with a power function of time. The changes in estimated heat flux and temperature were compared with the position of wetting region to clarify the effects of subcooling, jet velocity and thermal properties of block on the transient cooling. Received on 17 March 2000     

Optimization of an inclined elliptic impinging jet with cross flow for enhancing heat transfer

This work presents a parametric study and optimization of a single impinging jet with cross flow to enhance heat transfer with two design variables. The fluid flow and heat transfer have been analyzed using three-dimensional compressible Reynolds-averaged Navier–Stokes equations with a uniform heat flux condition being applied to the impingement plate. The aspect ratio of the elliptic jet hole and the angle of inclination of the jet nozzle are chosen as the two design variables, and the area-averaged Nusselt number on a limited target plate is set as the objective function. The effects of the design variables on the heat transfer performance have been evaluated, and the objective function has been found to be more sensitive to the angle of inclination of the jet nozzle than to the aspect ratio of the elliptic jet hole. The optimization has been performed by using the radial basis neural network model. Through the optimization, the area-averaged Nusselt number increased by 7.89% compared to that under the reference geometry.     

Effect of variable duty cycle flow pulsations on heat transfer enhancement for an impinging air jet

A series of experiments has been conducted in which a pulsed air jet is impinged upon a heated surface for the purpose of enhancing heat transfer relative to the corresponding steady air jet. Traditional variables such as jet to plate spacing, Reynolds number, and pulse frequency have been investigated. One additional flow variable – the duty cycle – representing the ratio of pulse cycle on-time to total cycle time is introduced and shown to be significant in determining the level of heat transfer enhancement. Specifically, heat transfer enhancement exceeding 50% is shown for a variety of operating conditions. In each case, the duty cycle producing the best heat transfer is shown to depend upon each of the other flow parameters. Recommendations are made for further experimentation into optimizing the duty cycle parameter for any particular application.     

Global modes in a confined impinging jet: application to heat transfer and control

We investigate the stability and control of a plane, laminar jet impinging on a flat plate in a channel, a geometry used to cool down a hot wall with a cold air jet in many industrial configurations. The global stability analysis indicates that, even for a strong confinement, the two-dimensional (2-D) steady flow is unstable to three-dimensional (3-D), steady perturbations. In the simplest limit case where dilatation effects are neglected, we show that the development of the instability induces a significant spanwise modulation of the heat flux at the impacted wall. To control the leading global mode, we propose adjoint-based 3-D harmonic and 2-D steady forcing in the bulk or at the wall. We show for instance that the unstable mode is controllable using a spanwise uniform blowing at the upper wall, in a specific domain corresponding to the footprint of the upper recirculating bubble. These techniques are applied to a novel open-loop control, in which we introduce into the flow a small airfoil, modelled by the lift force it exerts on the flow.     

Heat transfer due to impinging co-axial jets and the jets’ fluid flow characteristics

This investigation had multiple goals. One goal was to obtain definitive information about the heat transfer characteristics of co-axial impinging jets, and this was achieved by measurements of the stagnation-point, surface-distribution and average heat transfer coefficients. These results are parameterized by the Reynolds number Re which ranged from 5000 to 25,000, the dimensionless separation distance between the jet exit and the impingement plate H/D (4–12), and the ratio of the inner diameters of the inner and outer pipes d/D (0–0.55). The d/D = 0 case corresponds to a single circular jet. The other major goal of this work was to quantify the velocity field of co-axial free jets (impingement plate removed). The velocity-field study included both measurements of the mean velocity and the turbulence intensity.It was found that the variation of the stagnation-point heat transfer coefficient with d/D attained a maximum at d/D = 0.55. Furthermore, the variation of the local heat transfer coefficient across the impingement surface was more peaked for d/D = 0 and became flatter with decreasing d/D. This suggests that for cooling a broad expanse of surface, co-axial jets of high d/D are preferable. On the other hand, for localized cooling, the single jet (d/D = 0) performed the best. In general, for a given Reynolds number, a co-axial jet yields higher heat transfer coefficients than a single jet. Off-axis velocity peaks were encountered for the jets with d/D = 0.105. The measurements of turbulence intensity yielded values as high as 18%.     

Local heat transfer distribution between smooth flat surface and impinging air jet from a circular nozzle at low Reynolds numbers

An experimental investigation is performed to study the effect of jet to plate spacing and low Reynolds number on the local heat transfer distribution to normally impinging submerged circular air jet on a smooth and flat surface. A single jet from a straight circular nozzle of length-to-diameter ratio (l/d) of 83 is tested. Reynolds number based on nozzle exit condition is varied between 500 and 8,000 and jet-to-plate spacing between 0.5 and 8 nozzle diameters. The local heat transfer characteristics are obtained using thermal images from infrared thermal imaging technique. It was observed that at lower Reynolds numbers, the effect of jet to plate distances covered during the study on the stagnation point Nusselt numbers is minimal. At all jet to plate distances, the stagnation point Nusselt numbers decrease monotonically with the maximum occurring at a z/d of 0.5 as opposed to the stagnation point Nusselt numbers at high Reynolds numbers which occur around a z/d of 6.     

Heat transfer characteristics of premixed butane/air flame jet impinging on an inclined flat surface

 A series of experiments were carried out to determine the heat transfer characteristics of a round, premixed butane/air flame jet impinging upwards on an inclined flat plate, at different angles of incidence. The flame was fixed with an equivalence ratio of 1.0, a Reynolds number of 2500 and a plate-to-nozzle distance of 5d, while the inclination angles chosen for investigation were 57°, 67°, 80° and 90°. It was found that the location of the maximum heat flux point would be shifted away from the geometrical impingement point by reducing the angle of incidence. Decreasing the angle of incidence also enhanced the maximum local heat flux, while reduced the average heat transfer. The present study presented the effect of angle of incidence on the heat transfer characteristics of an impinging butane/air flame jet, which had been rarely reported in previous similar studies. Received on 11 October 2000 The authors wish to thank The Hong Kong Polytechnic University for the financial support of the present study.