Y. Zvirin

Experiments with a flat plate solar water heating system in thermosyphonic flow

Abstract A typical Israeli water heating system in thermosyphonic-flow was tested. The system consisted of two flat plate collectors painted matt black connected in parallel and a 140 l. storage tank. Total surface area of the collectors, employing the parallel flow pattern, was about 3 m 2 and they were tilted about 35° relative to the horizon. All collector pipes and connecting tubes were made of galvanized steel. The underside collector plate, collector tubes and storage tank were equipped with thermo-couples. A specially designed flow meter was used to measure water flow rate. Results show relatively linear temperature distributions both along the collectors and in the storage tank when no water consumption was allowed. Water flow rate was found to essentially follow solar radiation and reached a maximum of about 950 cm 3 /min. This value was found to be about 33 per cent smaller than the one predicted by an analytical model developed by the authors. It was also observed that shutting the system off during the afternoon hours, when losses to the environment are enhanced, might increase system efficiency.

The natural circulation solar heater-models with linear and nonlinear temperature distributions

L, dimensionless length; L~, overall length of the circulation loop; Q, dimensionless volumetric flow rate; q, dimensionless heat flux per unit length; q0, dimensionless solar radiation heat flux per unit length, absorbed in the collector plate; s, dimensionless coordinate along the circulation loop; T, dimensionless temperature above the ambient; T , dimensionless highest temperature in the system [T~(L~)]; Tin, dimensionless mean temperature of the system; 7~,.~, maximum possible temperature; AT, dimensionless temperature difference along the collector and the tank; U, overall heat-transfer coefficient (per unit length); UL, U, = ^ ~, dimensmnless overall heat-transfer pcpA V coefficient;

The transient, steady state and stability behavior of a thermosyphon with throughflow

Abstract A study has been made of the flow, heat transfer and stability of a natural convection loop when there is an addition and withdrawal of fluid. The loop is a toroid that is oriented in a vertical plane and is heated over the lower half and cooled, by maintaining a constant wall temperature, on the upper half. The results include stable, as well as unstable configurations and also reveal multiple solutions.

Transient behavior of natural circulation loops: Two vertical branches with point heat source and sink

Abstract A theoretical method is presented for the evaluation of the transient behavior of free convection loops. The method is applied to a loop consisting of two vertical branches with a point heat source and sink. The system is represented by a one dimensional model, with the only space coordinate running along the loop. Integral forms of the momentum and energy equations are derived and solved to yield the flow rate and temperatures as functions of the time. It is found that this approximate method cannot reconstruct the stability characteristics of the exact steady state solution.

The instability associated with the onset of motion in a thermosyphon

Abstract A theoretical method is presented for the study of the onset of motion in a symmetrical natural circulation loop. A one-dimensional model is applied to describe the behavior of the flow and linear stability analysis is used for the investigation of its stability. The results show that there exists a critical modified Rayleigh number, R c , below which the rest state is stable and any flow perturbation will decay. The same results have been obtained from a steady-state analysis; there is no steady-state solution when R R c . For a vertical loop composed of two parallel branches heated from below and cooled from above, R c = 6.

The effect of dissipation on free convection loops

Abstract A theoretical evaluation is presented of the effect of dissipation on natural circulation loops, heated from below and cooled from above. A one dimensional model, wherein the only space coordinate runs along the loop, is applied to two types of loops: (I) two vertical branches with point heat source and sink, and (II) a toroidal loop heated by a uniform heat flux at the lower half and cooled by a constant wall temperature at the upper half. It is found that for laminar flow in the first loop, dissipation affects only the temperature distribution but neither the steady state flow rate nor the stability characteristics. For laminar and turbulent flows in the second loop, the steady state velocities are enhanced by dissipation. Curves of marginal stability for various dissipation factors are given.

The relation between the rewetting temperature and the liquid-solid contact angle

FIG. 6. The locus of the position of the triple points for d,, = 2, and for L = 0.2,0.1,0.05, and 0.01. plane between these two curves in which the most unstable modes are oscillatory. The width of this region appears to diminish with decreasing (I and thus may not be discernible in these figures for lower values of cr, but nevertheless it exists. The position of the solid curves in both Figs. 4 and 5 represents an absolute lower bound for the instability region in the first quadrant of the R-Rs plane. This is to say that any basic state contiguration for which both R and Rf fall above that curve is linearly unstable. Thus the location of this curve is valuable as a general stability criteria for double diffusive conv~tion. Figure 6 shows the various envelope curves formed by the loci of the tripie points for four Lewis numbers. Two significant features may be observed in this figure. The first is that all curves shown originate from a single point on the ordinate. This is the location of the critical point for AS = 0. The second is that the inclination of each curve to the abscissa appears to increase with decreasing values of L. It may be concluded on the basis of this figure that the region in which the monotone unstable modes are dominant diminishes with decreasing L for any one value of fi. However, this does not imply an equivalent increase in the stability region since, as was shown earlier, the size of that region is a function of 6. Depending on the value of a there could be a substantia1 inl..?. Heut Mass

Determination of the quench velocity and rewetting temperature of hot surfaces. Part I: analytical solution of the micro-scale hydrodynamic model

Abstract The hydrodynamic micro-scale model, developed previously, is used to solve the non-isothermal interface equation. The complex interface equation is simplified in a coordinate frame that moves with the three-phase contact line. This equation accounts for effects of evaporation, thermo-capillary and intermolecular forces. The new non-isothermal interface equation provides generalization of de Gennes’ equation that applies to the isothermal case. The simplified third-order differential equation is solved numerically, and the effect of numerical parameters and selection of boundary conditions on solution convergence are established for a wide range of properties of solid–liquid pairs. In contrast to the smooth isothermal interfaces, non-isothermal interfaces are characterized by an undulating or wavy geometry. This behavior is a reflection of evaporation and mass transfer occurring across the interface, and unique capillary and thermocapillary effects that arise under non-isothermal conditions. A parametric study of the interface solution shows that increase of the capillary, C, and thermocapillary, Cθ02/F numbers produces steeper interface profiles, whereas the factor N, evaporation coefficient S, and the Hamaker constant Ā, produce the reverse effect. Larger values of N, S and Ā result in higher undulation frequencies. These effects intensify and become dominant under rewetting conditions. The new interface equation provides an advanced tool for further studies of hydrodynamic mechanisms that govern the motion of thin liquid films on hot solid surfaces, that involve high temperature gradients and intense evaporation. This furnishes a hydrodynamic foundation for analysis of rewetting phenomena, and the definition of rewetting temperature and quench velocity, that are presented in a subsequent paper.

Bubble growth predictions by the hyperbolic and parabolic heat conduction equations

A model for bubble growth in a uniformly superheated liquid is presented which is valid for both inertia and heat diffusion controlled growth. Two different heat transfer equations are considered: The Fourier (parabolic) equation and the hyperbolic heat conduction equation. It is shown that for short times, bubble growth prediction based on the Fourier equation, differs considerably from that based on the hyperbolic heat conduction equation. For long times, both predictions coincide. Using the hyperbolic heat conduction equation is important for bubble growth prediction in fluids like Helium II, in which thermal disturbances have a low speed of propagation. In such liquids the second sound effects must be considered long after the inertia and dynamic effects become unimportant.The validity of using a semi-infinite approximation to the heat conduction problem during the bubble growth period is investigated. An analytical solution in spherical coordinates reveals that the ratio between the spherical and semi-infinite solutions is a function of the Jakob number. Results of the present model, using the Fourier equation, are shown to be in better agreement with data for bubble growth in water, than other published solutions.ZusammenfassungEs wird ein Modell für Blasenwachstum in überhitzter Flüssigkeit vorgestellt, das sowohl bei durch Trägheit als auch bei durch Wärmediffusion kontrolliertem Blasenwachstum verwendbar ist. Zwei unterschiedliche Wärmeübertragungsbeziehungen werden in Betracht gezogen: Die Fourier-Gleichung (parabolisch) und eine Wärmeleitungs-Gleichung in hyperbolischer Form.Es wird gezeigt, daß die Modellergebnisse basierend auf der Fourier-Gleichung für schnelle Blasenwachstumszeiten signifikant von vergleichbaren Ergebnissen basierend auf der hyperbolischen Gleichung abweichen, während sie für langsames Wachstum mehr oder weniger identisch sind. Die Verwendung der hyperbolischen Wärmeleitungsgleichung in Blasenwachstumsmodellen ist vor allem in Fluiden wie Helium II von Bedeutung, wo thermische Störungen eine geringe Ausbreitungsgeschwindigkeit haben. Hier müssen die ‚second sound‘-Effekte noch berücksichtigt werden, wenn die dynamischen und die Einflüsse der Trägheit schon vernachlässigbar sind.Es wurde untersucht, ob die Benutzung einer semi-unendlichen Approximation des Wärmeleitungsproblems während des Blasenwachstums zulässig ist. Eine analytische Lösung in Kugelkoordinaten zeigt, daß das Verhältnis zwischen letzteren und semi-unendlichen Ergebnissen eine Funktion der Jakob-Zahl ist.Schließlich wird gezeigt, daß die Resultate des vorgestellten Modells bei Benutzung der Fourier-Gleichung experimentelle Ergebnisse von Blasenwachstum in Wasser besser wiedergeben als andere bekannte Lösungen.

Two dimensional analysis of transient flow and heat transfer in a natural circulation loop

The transient heat transfer, fluid flow and pressure in a natural circulation loop have been studied under laminar flow conditions. Most studies of these systems have utilized a onedimensional approach which requires a priori specifications of the friction and the heat-transfer coefficients. In the present work the variation of the friction and heat-transfer coefficients are determined. Detailed pressure, temperature and velocity distributions are presented.ZusammenfassungInstationärer Wärmeübergang, Strömungs- und Druckverlauf wurden in einem laminaren Naturkonvektionskreislauf untersucht. Die meisten Arbeiten auf diesem Gebiet basieren auf einer eindimensionalen Näherungslösung, die Kenntnis des Reibungs- und Wärmeübergangskoeffizienten voraussetzt. Die vorliegende Arbeit beschreibt die Änderung des Reibungs- und Wärmeübergangskoeffizienten. Sie zeigt die einzelnen Druck-, Temperatur- und Geschwindigkeitsverläufe auf.