V. Dharma Rao

A Theoretical Study on Convective Condensation of Water Vapor From Humid Air in Turbulent Flow in a Vertical Duct

The problem of condensation of water vapor from humid air flowing in a duct in turbulent flow is formulated theoretically. Vapor condensing at the dew-point temperature of the vapor-air mixture diffuses to the wall of the duct through an air film. The flow of the condensate is laminar. The condensing vapor releases both convection and latent heats to the wall of the duct. Thus, it is treated as a combined heat and mass transfer problem. The mass, momentum, and energy balance equations for the vapor-air mixture flowing in the duct and the diffusion equation for the vapor species are considered. T i , the temperature at gas-to-liquid interface, at which condensation takes place, is estimated with the help of the heat balance and mass balance equations at interface. The local and average values of the condensation Nusselt number, condensate Reynolds number, gas-liquid interface temperature, and pressure drop are estimated from the numerical results for different values of the system parameters, such as relative humidity and temperature of air at inlet, gas phase Reynolds number, and total pressure at inlet. The gas phase convection Nusselt and Sherwood numbers are also computed. A comparison of the present work with experimental data, for the case of in-tube condensation of vapor from humid air, shows satisfactory agreement.

Turbulent film boiling on a horizontal cylinder : Effect of temperature dependent properties

The turbulent film boiling from a horizontal cylinder is theoretically investigated considering the properties of the vapor as temperature dependent. In addition the effect of the thermal radiation from the surface of the cylinder on the film boiling heat transfer coefficients is studied. Some of the two-phase boundary layer characteristics are established. Comparison of the results from the present theory with relevant experimental data revealed very satisfactory agreement. An equation is proposed from the computational results with the aid of regression.

Convective Condensation of Vapor in Laminar Flow in a Vertical Parallel Plate Channel in the Presence of a High-Concentration Noncondensable Gas

The problem of laminar film condensation of a vapor from vapor-gas mixture in laminar flow in a vertical parallel plate channel is formulated theoretically. The flowing gas-vapor mixture contains a noncondensable gas in high concentration. An example of this case is the flow of humid air, in which air is present in high concentration. Vapor condenses at the dew point temperature corresponding to mass fraction of vapor in the gas-vapor mixture and the total pressure. The rate of condensation is controlled by the diffusion of the vapor through the noncondensable gas film. Thus the problem of convective condensation is treated as a combined problem of heat and mass transfer. The problem is governed by the mass, momentum and energy balance equations for the vapor-gas mixture flowing in a channel, and the diffusion equation for the vapor species. The flow of the falling film of condensate is governed by the momentum and energy balance equations for the condensate film. The boundary conditions for the gas phase and the condensate film are considered. The temperature at the gas-to-liquid interface is estimated by making use of the equations of heat and mass balance at the interface. The local condensation Nusselt number, condensation Reynolds number, and temperature at the gas-to-liquid interface are estimated from the numerical results for different values of the system parameters at the channel inlet, such as relative humidity, temperature of vapor-gas mixture, gas phase Reynolds number, and total pressure. The condensation heat transfer coefficients computed from the present theory are compared with the experimental data available in literature, and the agreement is found to be good. The present work is an extension of the earlier work, in which the problem of in-duct condensation of humid air in turbulent flow was solved theoretically. Humid air is considered as the gas-vapor mixture, since various physical and thermal properties have to be specified during the analysis.

Effect of thermo-physical properties on turbulent film boiling

Turbulent film boiling from a vertical surface is theoretically investigated considering the properties as functions of the temperature. The proposed analytical model is tested making use of the experimental data available in the literature for liquid nitrogen. It is observed that a satisfactory agreement is found between the theory and the experimental data. A new correlation for the prediction of heat transfer coefficients under film boiling conditions is presented.ZusammenfassungDas turbulente Filmsieden an einer senkrechten Fläche wird unter Berücksichtigung temperaturabhängiger Stoffwerte theoretisch untersucht. Eine Überprüfung des vorgeschlagenen analytischen Modells erfolgt mit Hilfe von in der Literatur greifbaren experimentellen Daten für flüssigen Stickstoff, wobei befriedigende Übereinstimmung zwischen Theorie und Versuchsdaten festgestellt werden konnte. Ferner wird eine neue Korrelationsbeziehung für die Vorausberechnung der Wärmeübergangskoeffizienten unter Filmsiedebedingungen angegeben.

Correlation for Heat Transfer in Nucleate Boiling on Horizontal Cylindrical Surface

This experimental investigation deals with nucleate boiling studies on horizontal cylindrical heating elements made out of copper in the medium of Forane around atmospheric conditions. The data could be successfully correlated with the system of criteria employed by the authors in their earlier study of nucleate boiling process on cylindrical heating elements. Inclusion of the data from the present experimental study on Forane and that of other investigators yielded a comprehensive correlation with an average deviation of 20% and standard deviation of 25% over a wide range of system pressures.

Laminar film boiling on a vertical fin

Laminar film boiling on a vertical fin is formulated as a conjugate phenomenon and investigated for no slip and zero shear conditions at the vapor-liquid interface. The results indicate that the combined effects of thermal leakage at the ends of the fin and radiation from its lateral face have profound influence on the average Nusselt number. Further, from the formulation it can be shown that the isothermal condition can be deduced by suitably changing the boundary conditions of the fin at its extremities. The results of the investigation are rendered into dimensionless functional relationships between the average Nusselt numberNum, fin parameterM, radiation parameterNR and temperature ratio term Ψ. The proposed equation can be made use of in design calculations.ZusammenfassungLaminares Filmsieden an einer vertikalen Rippe wird als ein konjugiert-komplexes Problem formuliert und für den Fall untersucht, daß entweder kein Schlupf oder keine Schubspannungen ander Flüssigkeits-Dampf-Grenzfläche auftreten. Die Ergebnisse zeigen, daß die zusammengefaßten Effekte von thermischen Verlusten an den Enden der Rippe, sowie Strahlung von der Seitenfläche, die mittleren Nusselt-Zahlen beeinflussen. Weiterhin kann gezeigt werden, daß bei zweckmäßiger Änderung der Randbedingungen an den Enden der Rippe die isotherme Randbedingung abgeleitet werden kann. Für die Ergebnisse der Untersuchung werden dimensionslose funktionelle Beziehungen zwischen der mittleren Nusselt-ZahlNum, dem RippenparameterM, dem Strahlungs-parameterNR und dem Temperaturverhältnis Ψ aufgestellt. Die aufgestellte Gleichung kann für Konstruktionsberechnungen benutzt werden.

NATURAL CONVECTION FROM A RADIATING FIN IN AIR—A CONJUGATE PROBLEM

The problem of natural convection from a thermally radiating fin to air is solved as a conjugate phenomenon, coupling the relevant consititutive equations. Integral method of analysis is employed to solve the non-linear thermal problem. From the results, it is observed that the process of heat dissipation from the lateral face of the fin is dependent on three dimensionless parameters viz., the temperature ratio term ΨT’, the conduction-convection-radiation parameter ΨT’ and the fin parameter At. Results are discussed to bring out the influence of these parameters. The efficiency characteristics presented in the analysis can be employed in the design of a fin taking into consideration the actual working conditions. Explicit expression is provided to calculate the average Nusselt number

LAMINAR FILM BOILING ON A VERTICAL SURFACE WITH THERMAL LEAKAGE AT ITS ENDS

The analysis presented is for laminar film boiling on a vertical surface treating the test section as a fin with the heat leakage from its ends. The formulation of the problem is accomplished as a conjugate between the thermal conduction in the test section and the phenomenon of film boiling on its lateral face. This approach revealed that the film boiling heat transfer coefficients, both local and average values, are profoundly influenced by the fin parameter. An explicit form of the equation is provided from the computer results to evaluate the film boiling heat transfer coefficient.