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Extended film theory for transpiration boundary layer flow at high mass transfer rates

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Title:Extended film theory for transpiration boundary layer flow at high mass transfer rates
Authors:Nakamura, Fuminori
Contributors:Coimbra, Carlos F M (advisor)
Mechanical Engineering (department)
Date Issued:May 2003
Publisher:University of Hawaii at Manoa
Abstract:Mass transfer is of interest to understand a wide variety of applications ranging from natural systems to technological processes, from biological metabolic rates to mass exchanger and catalytic converters, from pollution control to transpiration cooling, etc. Moreover, mass transfer processes playa critical role in the regulation of climate at both local and global levels. For example, in Oahu, trade winds pick up moisture as they blow from the ocean to the windward coast of the island. As the moist air reaches the mountain range and is forced to move up (and cool off), water vapor is condensed. The inertia of the flow is sufficient to make the condensing vapors pass the mountain ridge, delivering high rates of precipitation to the Manoa valley. The main mechanism in the rain formation in this case is a mass transfer-controlled process. The evaporation rate of water vapor from the surface of the ocean and the amount of condensation formed during the cool-off process directly impact the yearly levels of precipitation in the Manoa valley. Despite its relevance to natural and technological processes, there are still much not known in the process of evaporation and the combined effects of convective flow, heat and mass transfer. In order to estimate mass transfer rates in boundary layer flows, two approaches are currently available: 1. To solve numerically the boundary layer equations. 2. To use appropriate graphs in textbooks to estimate the mass transfer rate, based on solutions given by the methods described in item (1). Both methods described above have shortcomings. The first is not practical because it requires a considerable amount of effort and time to yield a comprehensive understanding of the phenomena involved for each case under study. The second is limited in accuracy and leaves the mass transfer analyst with little flexibility beyond the results available in the literature. Ideally one would like to have reliable correlations that are valid for a wide range of parameters such as blowing factors, Schmidt numbers, Reynolds numbers, etc. The goal of the present study is to provide one such correlation based on a detailed analysis of the boundary layer equations and results of film theory applied to a porous plate. To pursue our goal for mass transfer rates in the boundary layer flow, in the present study, we will consider an inert binary mixture where one of the species is transferred (evaporated) through a porous (or wet) flat plate. A laminar boundary layer is formed over the plate, and we will focus on high mass transfer in the blowing (evaporation) regime, such as water evaporating at high temperatures (when the vapor pressure at the liquid-vapor interface is relatively high and therefore the mass fraction at the interface is not negligibly small). We will develop the functional form for a correlation that gives the mass transfer rate as a function of the relevant parameters. As it is usual in heat and mass transfer problems, a correlation is formed by collapsing the information contained in the boundary value problem (the combination of differential governing equations and boundary conditions) into an algebraic expression that involves only the boundary conditions and the properties of the medium. In our case, the Schmidt number (the ratio of momentum to mass diffusion coefficients), the flow conditions (free stream velocity, viscosity and length scale, or the Reynolds number), and vapor concentrations at the liquid-vapor interface and at the free-stream conditions are the dependent variables. The mass transfer (or evaporation) rate is therefore correlated in terms of the Reynolds and Schmidt numbers and the boundary conditions for mass concentrations. The boundary conditions are lumped into a dimensionless number referred to as the mass transfer potential, which is given by Bm =(m1,s -m1,e)/(1-m1.s), where 'm1' is the mass fraction of species 1 and the subscripts 's' and 'e' referred to "surface" and "external".
Description:vi, 45 leaves
Rights:All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
Appears in Collections: M.S. - Mechanical Engineering

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