Piotr Kubski

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.

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.

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.

The limitation of heat losses from horizontal surfaces by a layer of open hexagonal cells

Abstract A study of the limitation of heat transfer from a flat horizontal surface insulated by a layer of cellular material was carried out. A model for heat transfer from a flat horizontal isothermal surface through the insulating layer open at the top is presented, in which conduction and natural convection heat transfer mechanisms are considered. The solution of the model was verified experimentally. The experiment was performed using a round plate of diameter D = 0.07 m covered by panels of cellular material of height expressed as H / D = 0.1, 0.143, 0.371, 0.6, 0.857 and 1.186 for two sizes of cell given by d / D = 0.143 and 0.214. To eliminate the radiation component in the global heat transfer and to provide a low range of heat flux, glycerine was used as a test fluid. Good agreement between theoretical and experimental results was found. The results obtained indicate that with the use of such a material it is possible to reduce the majority of heat loss from a flat horizontal surface. For example the panel with H / D = 0.6 and d / D = 0.143 limits the heat transfer 2.11, 1.97 and 1.87 times for Ra = 10 4 , 10 5 or 10 6 respectively, in comparison with the plate without cellular material. This method of modification of heat losses could be used in solar collectors, civil engineering, chemical technology and in industry.

Natural convection heat transfer from round horizontal plate

A new approach to the model of natural convection from a horizontal, isothermal round plate and a simplified analytical solution of this model have been presented. In this model two separate regions with different fluid motions have been distinguished. In the first region, inside the boundary layer, the fluid flows concentrically towards the centre of the plate, while in the second one (stagnation region) the fluid is motionless. The presented theory has been verified experimentally.ZusammenfassungEin neuer Lösungsweg für das Modell der freien Konvektion an einer isothermen, kreisförmigen, horizontalen Platte und eine vereinfachte analytische Lösung für dieses Modell werden hier vorgestellt. An diesem Modell wird zwischen zwei Bereichen mit verschiedenen Fluidbewegungen unterschieden. Im ersten Bereich, innerhalb der Grenzschicht, strömt das Fluid konzentrisch in Richtung Plattenmitte, während im zweiten Bereich (Stau-Bereich) die Flüssigkeit in Ruhe ist. Diese Theorie wurde experimentell überprüft.

Laminar free convection heat transfer from a horizontal ring

AbstractThe analytical solution of laminar free convective heat transfer in an unlimited space from an isothermal horizontal ring with an adiabatic plug is presented. The results of theoretical considerations are presented as relation of the Nusselt and Rayleigh numbers:

Wrmebergang bei laminarer freier Konvektion von einem horizontalen Ring

Nu_D = 1.151 \cdot (Ra_D )^{1/5} \cdot \Phi (\phi _0 )