Witold M. Lewandowski

Natural convection heat transfer from plates of finite dimensions

Abstract A new approach to the model of natural convection from an isothermal inclined plate and a simplified analytical solution of this model are presented In this model two separate regions with different fluid motions are distinguished In the first region, the direction of fluid flow inside the boundary layer and parallel to the plate buoyancy force component converge, while in the second one these directions are opposite The theory presented is verified experimentally

Heat transfer by natural convection from an isothermal downward-facing round plate in unlimited space

A theoretical analysis and experimental study of natural convective heat transfer from an isothermal downward-facing horizontal round plate has been carried out. The results are presented in the form of correlations between the Nusselt and Rayleigh numbers. The correctness of the theoretical model, proposed to describe convective heat transfer from the downward-facing round plate, and the simplifying assumptions introduced, were verified by comparison with contours of static temperature and velocity distributions determined from numerical simulations using the FLUENT/UNS code and estimated by flow visualisations using interferometry, images of particle tracks, and a liquid crystal foil. The experimental measurements were performed in air and water using a plate of diameter D=0.07 m. The theoretical, experimental, and numerical results are all in excellent agreement.

Free convection heat transfer and fluid flow above horizontal rectangular plates

Results are presented from experimental and theoretical investigations of natural convective heat transfers from horizontal, rectangular, isothermal plates having different aspect ratios. Convective flow structures in water were visualized by injecting dye through openings along the edges of the plate for different values of the aspect ratio and Rayleigh number. Based upon these observations and previous studies of horizontal polygonal surfaces, two models for convective flow structures are proposed. In the first model, the direction of flow of the fluid was assumed to be perpendicular to the edges of the rectangle with the streamlines parallel to each other. In the second model, the flow was assumed to form structures in which the fluid flowed inwards radially from the edges. Solutions of these models are presented in the form of Nusselt-Rayleigh relations with the aspect ratio as a parameter. The theoretical solution was verified using water for rectangular plates having aspect ratios (i.e. length/width)=1 (square), 1.81, 2.52, 3.66, and 4.66.

Methodical Investigation of Free Convection from Vertical and Horizontal Plates

This paper attempts of review the literature on free convection from flat surfaces transferring heat in an unlimited space. Data from the references have been presented as final criterial relations both in tabular form and in graphic system, separately for the vertical plates and the horizontal ones. About 45 results of investigations on free convection have been examined and the following mean criterial relations have been calculated:Nu=0.550·(Ra)0.250 for vertical plates,Nu=0.310·(Ra)0.290 for horizontal plates.It has been observed for the vertical plates that divergence of these results relatively to the mean values is constant within the whole variability range of the Rayleigh number and amounts to about ± 15%. In the case of horizontal plates the divergencies are more considerable and vary within ± 50% for the laminar, and within ± 25% for the turbulent range. In the next step the attempt was made to determine the causes of these divergencies and errors. The work was performed because of two main reasons: imperfection of measuring methods and a lack of uniformity in the choice of the characteristic linear dimension.ZusammenfassungIn der Arbeit wird in graphischer und tabellarischer Form die Literatur über natürliche Konvektion zusammengestellt. Von den etwa 45 erwähnten Zusammenhängen zwischen Nusselt- und Rayleigh-Zahl werden Mittelwerte für waagrechte und senkrechte Platten errechnet:Nu=0,550·(Ra)0,250 für senkrechte Platten,Nu=0,310·(Ra)0,290 für waagrechte Platten. Die Ergebnisse verschiedener Autoren weichen von dem Mittelwert ab: für die senkrechte Platte bis ± 15%, für die waagrechte Platten im laminaren Bereich bis ± 50% und im turbulenten Bereich bis ± 25%. Es werden die Hauptgründe, die nach Meinung der Verfasser für den großen Streubereich bei den oben erwähnten Werten verantwortlich sind, dargestellt: Ungenauigkeit der Meßmethode; ungünstige Wahl der charakteristischen Länge.

Theoretical and experimental study of natural convection heat transfer from isothermal hemisphere

Abstract The simplified analytical solution and experimental study of laminar free convection heat transfer from an isothermal hemisphere in unlimited space have been presented. The solution is based on adaptation of the methods used for inclined isothermal plates. In the proposed solution the control surface of the hemisphere was considered as a small inclined surface. Inclination of this surface was not a constant one but it was a function of azimuth angle. The result of theoretical consideration is presented in the relation of Nusselt and Rayleigh numbers: Nu = 0.533 × Ra 1 4 . The comparison of theoretical solutions with experimental results presented in this paper and results of other authors shows good agreement. Copyright

Natural convection heat transfer from complex surface

Abstract The analytical solution of convective heat transfer from an isothermal complex surface in an unlimited space has been presented. The complex surface is represented by a horizontal ring of diameters D and d with hemispherical segment of diameter d in the centre. The shape of the complex surface was expressed by factor p = d/D. The presented solution has been verified experimentally on a set-up of diameter of 0.4 m and height of 0.5 m with surfaces of constant external diameter D = 0.06 m and various shape factor p = 0—round plate, 0.183, 0.233, 0.40, 0.483, 0.554, 0.650, 0.817 and 1.0—hemisphere. The tested fluid was glycerine. The comparison of theoretical and experimental results gives good agreement.

Heat transfer by free convection from an isothermal vertical round plate in unlimited space

A theoretical solution of natural convective heat transfer from isothermal round plates mounted vertically in unlimited space, is presented. With simplifying assumptions typical for natural heat transfer process, equations for the velocity profile in the boundary layer and the average velocity were obtained. Using this velocity, the energy flow within the boundary layer was balanced and compared with the energy transferred from the surface of the vertical plate according to the Newtons law. The solution of the resulting differential equation is presented in the form of a correlation between the dimensionless Nusselt and Rayleigh numbers. The theoretical result is compared with the correlation of numerical results obtained using . Experimental measurements of heat transfer from a heated round vertical plate 0.07 m in diameter were performed in both water and air. The theoretical, numerical, and experimental results are all in good agreement.

Effect of the use of the balance and gradient methods as a result of experimental investigations of natural convection action with regard to the conception and construction of measuring apparatus

Measurement apparatus designed and constructed according to conceptions of the authors, enabled a more precise calculation of the heat transfer coefficient with the balance and gradient methods. Construction and use of the apparatus and devices are described below, results of experimental investigations for horizontal and vertical, isothermal, flat plates obtained independently with the balance and gradient methods, are also presented. The following equations were found:Nu=0.612 · (Ra)1/4 104 ≦Ra ≦ 108 for vertical platesNu=0.766 · (Ra)1/5 104 ≦Ra ≦ 107Nu=0.173 · (Ra)1/3 105 ≦Ra≦ 108 for horizontal plates.On the basis of the results obtained from both these methods, differences of natural convection acting from vertical and horizontal plates are discussed. The usefulness of the balance and gradient methods have been considered for qualitative and quantitative investigations of heat transfer by natural convection.ZusammenfassungIn der Arbeit wird die von den Autoren konstruierte Apparatur zur Messung der Wärmeübergangskoeffizienten, die eine höhere Genauigkeit erlaubt, und die Bestimmung mit Hilfe der Wärmebilanz- und Temperaturgradientenmethode beschrieben. Die in den Experimenten erhaltenen Werte für isotherme waagrechte und senkrechte Platten haben folgende Form:Nu=0,612 · (Ra)1/4 104 ≦Ra ≦ 108 für senkrechte Platten,Nu=0,766 · (Ra)1/5 104 ≦Ra ≦ 107Nu=0,173 (Ra)1/3 105 ≦ Ra≦ 108 für waagrechte Platten.Aufgrund der Resultate wird der unterschiedliche Mechanismus der Konvektion an waagrechten und senkrechten Platten besprochen. Es wird die Verwendbarkeit der beiden Methoden — der Wärmebilanzmethode für quantitative und der Temperaturgra-dientenmethode für qualitative Untersuchungen — dargestellt.

Influence of cylindrical screens on free convection heat transfer from a horizontal plate

Abstract Experimental investigations of laminar free convection from horizontal, screened plates to water and glycerine are reported. The screen diameter (D) was equal to the diameter of a heated isothermal plate, while the screen height (H) was varied. The effect of screening on convective heat transfer is determined. Comparison with heat transfer from an unscreened horizontal plate is made.

Heat transfer from polygonal horizontal isothermal surfaces

Abstract Each regular surface can be considered as a sum of isosceles triangles of different apex angle (e). Triangular, square, hexagonal and circular plates consist of three, four, six and an unlimited number of triangles of apex angles e = π/3, π/4, π/6 and ⇒0°, respectively. Simplified theoretical consideration for extracted repeated fragments of the surface, describing it in the form of triangles, suitable for any polygon, has been performed. Two models of fluid flow over heated surfaces are proposed. The fluid flow direction in the first model was perpendicular to the leading edge and stream lines are parallel to each other. In the second one it has been assumed that fluid flows from the leading edge concentrically towards the apex angle of the considered triangular surface. In both models free boundary layers transform into plumes above the center of the plates. The solutions of these models are presented in the form of dimensionless Nusselt-Rayleigh relations with the function of apex angles as a polygon parameter. The results of experimental investigations of horizontal isothermal triangular, square, hexagonal and circular plates are presented. The free convection heat transfer experiments and visualization were carried out using plates of the same diameter d = 0.07 m of the circle inscribed in polygon and glycerine as the test fluid.