Transport Phenomena in Heat and Mass Transfer (eBook)

J.A. Reizes (Herausgeber)

eBook Download: PDF | EPUB

2012 | 1. Auflage
650 Seiten
Elsevier Science (Verlag)
978-0-444-59979-7 (ISBN)

Infos

Theoretical, numerical and experimental studies of transport phenomena in heat and mass transfer are reported in depth in this volume. Papers are presented which review and discuss the most recent developments in areas such as: Mass transfer; Cooling of electronic components; Phase change processes; Instrumentation techniques; Numerical methods; Heat transfer in rotating machinery; Hypersonic flows; and Industrial applications. Bringing together the experience of specialists in these fields, the volume will be of interest to researchers and practising engineers who wish to enhance their knowledge in these rapidly developing areas.

Textauszug

APPLICATION OF THE ELECTROCHEMICAL MASS TRANSFER TECHNIQUE TO THE STUDY OF BUOYANCY-DRIVEN FLOWS

H.D. Chiang and R.J. Goldstein,     Energy and Resources Laboratories, Industrial Technology Research Institute, Taiwan, ROC; Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455 USA

ABSTRACT

The applicability of an electrochemical mass transfer technique in studying buoyancy-driven convection is examined. Emphasis is placed on the copper deposition system. A detailed description of the system, the physical properties of the solutions used, and the related methodology are summarized. Justification of the analogy between the electrochemical technique and comparable heat transfer studies is presented.

1 INTRODUCTION

The mass transfer process involved in an electrochemical system was initially studied almost exclusively by electrochemists and chemical engineers. Their interests lay in understanding the physics and chemistry involved and applying mass transfer to electrochemical processing. The analogy between electrochemical systems and the corresponding heat transfer systems expanded the scope of the technique to a wide range of applications.

The electrochemical system employs a diffusion-controlled electrolytic reaction (or pair of reactions) to study the desired transport phenomena. With an externally applied potential difference across two electrodes in the electrolytic solution, a current will flow from the anode to the cathode, generating a mass transfer process within the solution. This mass transfer could be by migration, diffusion, and, perhaps after exceeding a critical threshold, by convection. The study of the mass transfer coefficient at the cathode surface can be used to increase understanding of the mass transfer process in its own right or to infer corresponding heat transfer phenomena through analogy.

Advantages of an electrochemical system over a conventional heat transfer system in the study of buoyancy-driven convection include: (1) high precision and local measurements are more easily made, (2) large Rayleigh numbers (Ra) can be achieved in a moderate-sized apparatus, (3) boundary conditions can be controlled better, and (4) sidewall conduction and radiation effects are eliminated. The electrochemical systems normally used operate with high Schmidt number (Sc) fluids limiting the analogy to high-Prandtl-number (Pr) fluids. Even so, for researchers in the heat and mass transfer communities the electrochemical technique provides a promising alternative as a measurement tool.

A wealth of information on electrochemical systems is available. For readers interested in the fundamentals, books by Levich (1962) and Newman (1973) provide extensive coverage of the theoretical aspects of electrochemical mass transfer. On the application side, reviews by Mizushina (1971) and Wragg (1977) give in-depth surveys of the literature. These, however, do not provide the novice with sufficient information on the subtle know-how required to apply the technique properly. A detailed review paper by Selman and Tobias (1978) covers the various operating conditions and their constraints in a systematic fashion. Due to its broad scope, however, the paper left open some questions concerning the use of the technique, especially for those in the heat transfer field who are interested in the analogy between electrochemical systems and their heat transfer counterparts. In the following sections, a simplified description of the electrochemical systems used for the study of natural convection is given, along with property correlations and procedures for concentration measurement.

2 THE ELECTROCHEMICAL METHOD

A typical electrochemical system consists of an electrolytic solution as the working fluid and two electrodes, anode and cathode (there could be more than one cathode). Mass transfer is induced in the solution by applying an external electric potential difference across the anode and cathode(s). Positive ions (cations) of the electrolyte move toward the cathode while negative ions (anions) move toward the anode. The movement of the ions is controlled by: (1) electric migration due to the electric field, (2) diffusion because of ion-density gradient, and (3) convection, if the fluid is in motion. Migration is the movement of ions under the influence of an electric field. Fluid motion can be driven by pressure drop in forced flows or by density gradients in buoyancy-driven flow.

With heat transfer, convection and diffusion processes are present, but there is no equivalent to migration. In order to use ionic transport as an analog to the heat transfer process, the ionic migration has to be made negligible. This is achieved by introducing a second electrolyte–the so-called “supporting electrolyte”. This is normally an acid or base with a concentration many times that of the active electrolyte, and which is selected such that its ions do not react at the electrodes over the range of potential difference used in the experiment. The excess of supporting electrolyte will sharply reduce the electric field in the bulk of the solution, and the migration effect on the charge carrier will only be a minor correction.

Among the more commonly used electrolytic solutions are:

A Cupric Sulphate-Sulphuric Acid solution (CuSO4-H2SO4-H2O)

B Potassium Ferrocyanide-Potassium Ferricyanide-Sodium Hydroxide solution (K3]Fe(CN)6[-K4]Fe(CN)6[-NaOH-H2O)

With a cupric-sulphate solution, copper is dissolved from the anode and deposited on the cathode (metal-deposition reaction). For the other system (also known as redox-couple system), only charge transfer occurs at the electrodes. The respective reactions at the cathode surface are:

(1a)

and

(1b)

The copper deposition system is usually employed for natural convection studies. Hence, emphasis will be placed on the copper system here, but the general principles apply to both systems.

The mass transfer coefficient for species “i” is,

(2)

where is the transfer flux of species “i” due to diffusion and convection, and ΔCi is the concentration difference of the species across the region of interest.

The total flux at the cathode surface can be determined from Faraday’s Law

(3)

where I is the current density at the cathode surface, ni is the valence of the transferred ion, and F is Faraday’s constant.

As mentioned above, the migration effect on the active electrolyte is negligible after the addition of the supporting electrolyte (H2SO4 when using CuSO4). This is, strictly speaking, valid only for the limiting case,

Otherwise, some migration effect will exist. The migration flux can be related to the current density by the introduction of the transference number ti. The transference number, a function of the solution concentrations (see Section 6), is proportional to the migration flux:

(4)

Combining Eq. 4 with Eqs. 2 and 3 gives

(5)

Usually, the concentration difference is determined from the bulk and surface concentrations. The bulk concentration is usually assumed to be constant and can be measured by chemical analysis; however, the surface concentration is an unknown. In a heat transfer study, the temperature is usually continuous across a solid-fluid interface. Thus, the interface temperature can be determined from measurement on the solid side. Measurement of surface concentration is not that direct. This is resolved by using the “limiting current” condition. As the externally applied potential across the electrodes is increased, the current increases monotonically until a plateau - on a graph of current vs. voltage – occurs (cf. Fig. 1). For the cupric sulphate system, the concentration of copper ions at the cathode surface will be negligible at the limiting current. For the redox-couple system (ferri-ferro-cyanide), the concentration of [Fe(CN)6]3- at the cathode will be negligible at the limiting current.

FIGURE 1 The limiting current potential

The limiting current density is the maximum current density attainable at the cathode by the transport of the reacting ions. To understand the cause of this limit and its resulting plateau in the current-potential plot, the various components of the cell potential should be introduced.

In an electrolytic solution, the driving force for the passage of current between the anode and cathode is the electric potential difference across them. This potential difference can be separated into three distinct parts: (1) ohmic potential, ΔΦohm, (2) concentration overpotential, η, and (3) surface overpotential, ζ. The overall cell potential difference can be written as

(6)

where subscripts a and c refer to anode and cathode conditions, respectively.

The ohmic potential has its usual meaning here. It is due to the electrical resistance of the bulk solution. The addition of supporting electrolyte drastically reduces this resistance, and, thus, the ohmic potential difference is...

Produkt-Details

• Erscheint lt. Verlag: 2.12.2012
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-444-59979-7 / 0444599797
• ISBN-13: 978-0-444-59979-7 / 9780444599797