Principle

The velocity profile in the laminar flow of a fluid through a cylindrical tube is employed to disperse an injected solute. The radial diffusion of the solute in the tube, arising from the radial concentration gradients so created, opposes this dispersion. The combined effect is to produce a solute distribution in the longitudinal direction within the tube that is Gaussian and whose second central moment is related to the mutual diffusion coefficient of the fluid system.

Object

The object of the experiment is the measurement of the mutual diffusion coefficient of a binary liquid mixture. The experiment illustrates how an understanding of fluid mechanics and transport processes can be employed to develop a powerful and simple measurement technique. The aim of the present simple experiment to be described is to determine the diffusion coefficient of the system n-hexane/n-heptane for almost pure n-heptane at 25 °C.

Background

The process of diffusion is the name applied to the relative motion of molecular species in a fluid mixture under the influence of a gradient of concentration, or more completely, of chemical potential. The simplest possible realization of the process is illustrated in Fig. 21.1, where at time t = 0 a concentration difference is established in a binary fluid mixture across an interface at z = 0.

This book represents a collection of the favorite experiments in heat transfer and thermodynamics of some of the world's eminent scholars in the field. It was my intent to include experiments that they had used in their lectures which had a proven track record in regard to students' reaction and understanding. Experiments that were too complicated, even bordering on research, or too esoteric were rejected.

Some of the experiments are well known, some of them are relatively new; and for all of them I have tried to devise the presentation that appears to be best from a consistent point of view. The book has been prepared as a connected account; each experiment is intended to be used as a whole rather than in parts. The readers were envisioned as both engineering and physics students; however, the appeal will probably lie with engineering students from all disciplines.

A brief word is necessary about the selection of topics to be found in this book as well as the order in which they were placed. The experiments selected were varied, representative, new, old, fascinating, and challenging. I selected those I thought my students would enjoy as well as students in Japan, Germany, Brazil, and other countries with different backgrounds and methodologies.

Principle

One method of measuring thermal diffusivities of different solids is to immerse a sphere of the material in a hot (or cold) water bath, and to measure the temperature response at different points within the solid.

Objective

To provide a simple undergraduate experiment illustrating Fourier's Law for unsteady heat conduction.

Apparatus

A 5–8-cm-diameter sphere is used of the material whose thermal conductivity it is desired to measure. Plexiglas is good because one can see the placement of the thermocouples. Other possible choices include wood, rubber, sponge rubber, or even such familiar objects as an apple or an orange. For soft materials sheathed, hypodermic-type thermocouples are preferable. For hard materials small radial holes are drilled to the center and to the midradius. Thermocouples are inserted into the bottom of these holes, and good thermal contact is ensured by using conductive heat transfer paste. The holes are sealed against water entry by silicone or other sealant. A constant-temperature water bath with a stirrer is required, together with a frame to hold the sphere. In the simplest version the thermocouples are read manually from a potentiometer with a thermocouple switch, or from two potentiometers. A preferable arrangement uses amplifiers for the two inserted thermocouples, with digital or analog readout. A multichannel temperature scanner may be used, or the instructor may wish to write a simple program for sampling the data and storing in a PC.

Principle

An image of an electrically heated wire boiling under water is projected on a screen. Boiling in real time is easily observed.

Object

This experiment provides a greatly enlarged, easily controlled demonstration of boiling. The image is so clear the audience leaves with an unforgettable picture of the processes that constitute boiling.

Apparatus

Power is brought into the projector through the posts that are fastened to the lid of the slide. (The lid is shown in profile in Fig. 19.1.) The posts are fastened to leads that are made of springy copper strips with clips on the ends which hold the wire from which the boiling occurs. When the whole device is assembled it looks like Fig. 19.1.

The wire is the only part of the assembly that is critical. We have found that Chromel A wire 0.010 inches in diameter is appropriate. This wire passes through critical heat flux (CHF, burnout, boiling transition, etc.) when an AC current of 6.4 amps passes through it. Very little more current than this also causes the wire to physically burn out.

The power for this wire is provided by a Variac which has a maximum output of 10 amps. An ammeter in the line passing the Variac output is needed to insure that the maximum allowable current is not exceeded.

Principle

At the ice–water interface in a steady-state condition, the heat flux transferred from water to the ice–water interface is equal to that conducted from the ice–water interface to ice. By measuring the coordinates of the ice–water interface, the heat flux from the interface to ice is calculated by the boundaryelement method. The local heat-transfer coefficient on the ice–water interface is, then, estimated by Newton's law of cooling.

Object

Ice formation around tubes in a water flow relates to many practical problems such as lowering thermal efficiency or increasing pressure drop in a water-cooled heat exchanger in a refrigeration system. It also relates to many other applications such as the ice-bank method in a low-temperature heatstorage system. In those cases, the local heat-transfer coefficient on the ice surface is an important factor in predicting the ice amount around the tubes and also the thermal efficiency of the heat exchanger. The measurement of the local heat-transfer coefficient, therefore, presents essential information for practical designs.

Apparatus

The experimental apparatus consists of a calming section, a test section, a flow meter, a refrigeration unit, and two circulation systems of water and a coolant as shown in Fig. 13.1. In Fig. 13.2, a schematic illustration of the test section is shown. The test section has a 0.15-m × 0.04-m cross-sectional area and has a 1.0-m length. The walls are made of transparent acrylic resin plates in order to observe the growth of the ice layer, and are installed in the vertical position to minimize the effect of the natural convection of water.

Thermodynamics is one of the major branches of physics. It is concerned with the behavior of energy as affected by changes of temperature. In particular, thermodynamics explains the observed properties of matter at any temperature. In this connection, we might consider heat capacities, magnetic and electrical effects, phase transitions, and higher-order transitions (such as the Ehrenfest third-order transition) as principle topics.

Classical thermodynamics on the other hand treats the many observable properties of solids and fluids in such a manner that they can all be viewed as a consequence of a few. The four laws of thermodynamics are the result of observation: thus the importance of experimentation in this science. The development of the four laws is elegant. The laws contain an aesthetic spirit that once grasped and understood by the student will stand as the undercurrent for all the other physical sciences.

To tickle the student's imagination consider the application of thermodynamics to one aspect of the study of black holes. It is known a black hole has entropy. For example, the area of the event horizon of a black hole is entropy. Adding mass to a black hole increases the event horizon since it has added entropy. If the black hole has entropy it has temperature, which means black holes can radiate energy. The question arises how can black holes (possessing temperature) emit particles of radiant energy if nothing can escape past the event horizon?

Principle

The temperature response of the unsteady inlet temperature varying with time is an essential parameter in the thermal design of the heat exchanger and other heat transport equipment. The temperature amplitude variation along the general passage decays exponentially and can usually be determined by experiment. This variation will affect the entire heat transport process within the heat exchanger and other heat-transport equipment.

Objective

The objective of this experiment is to determine the decay of the temperature oscillation along the channel for a timewise oscillation of inlet temperature. In practical applications, the heat transfer within the channel may be exposed to some planned or unplanned transients or start-ups and shutdowns during the operation. Thus, such a knowledge is critically necessary for those devices which never attain steady-state operation because of their nature of periodical operation in time.

Apparatus

The experimental apparatus consists of a rectangular duct with different sections of filter, calming, inlet, test, and convergence. The geometry of the test section is a rectangular duct with a cross section of 254 × 25.4 mm2 (10 × 1 in.2). The instrumentation includes a wave generator, a power supply, a heater, an inclined manometer, voltmeters, thermocouples, an orifice plate, and a fan, as shown in Fig. 14.1.

Air flows from the calming section to the inlet section (2770 mm in length) wherein the velocity becomes fully developed.

The following list of experiments and demonstrations is presented to supplement those given in Part I of the book. The experiments have varying degrees of difficulty and should offer additional variety to illustrate the fundamentals of heat transfer.

Background

Engineering students are unique. They are usually uninterested in a problem unless they can visualize it. There are two ways visualization can be accomplished. One can create a mathematical model where mathematical symbols simulate properties, devices, and behaviors, or one can create the engineering problem in the laboratory. The former is usually faster and easier for the teacher, and the latter appears to be disappearing from educational institutions due to the ease and familiarity with the computer.

Motivation

The motivation behind this book is based on three quotations:

Surely excellence in instruction is at the very root of education, and of necessity demands the maintenance of good academic standards. In that light, it follows that performing experiments is the grist of engineering. Nothing can be more significant than the marriage of excellent instruction incorporating well-defined academic standards with student involvement in the laboratory, that is, having the student put that instruction to practical use.

Principle

Transfer of electricity out of a storage battery is much more efficient (closer to reversibility) when it is very fast rather than very slow.

Object

It is often argued that reversible processes take an infinite time to complete and, therefore, are of questionable usefulness. Although there is truth in this argument for certain processes, such as transfer of energy across a finite temperature difference, the argument is neither universally valid nor representative of some practical phenomena. A simple and very important counterexample is provided by a storage battery. If discharged quickly, the battery does work almost equal to the stored energy. If discharged more slowly than the rate of its internal discharge (let alone infinitely more slowly), the battery does practically no work, that is, all its availability is dissipated. The availability is dissipated because the internal discharge generates entropy spontaneously or, said differently, the internal discharge is irreversible.

Apparatus

As shown schematically in Fig. 29.1, the apparatus consists of a cell with two electrodes (1), a temperature bath (2), a glass thermometer and an electric heating plate (3), a galvanostat (4), a resistance box (5), an ammeter (6), and a voltmeter (7). Another schematic of the apparatus is shown in Fig. 29.2.

Principle

Existence of two different characteristic regions in nucleate boiling, that is, the region of isolated bubbles at low heat fluxes and the region of interference at high heat fluxes, can be demonstrated by measuring the resultant force acting on a compact heater that is suspended in a pool of liquid with boiling on its upper surface.

Object

As the surface temperature of a heater submerged in a pool of saturated liquid is raised above the saturation temperature, nucleate boiling appears after the incipience of boiling, and then continues up to the point of critical heat flux. In this nucleate-boiling regime, the heat flux from the heated surface to the liquid increases with increasing surface temperature, and the relationship between the heat flux and the surface temperature (the so-called boiling curve) is of a monotonic nature, in most cases exhibiting no noticeable change of character throughout the aforementioned regime. Visual observations by means of a high-speed cine camera, however, reveal that nucleate boiling is divided into two regions. Namely, when the heat flux is low, small isolated bubbles repeat the growth and departure process at a comparatively small number of active nucleation sites on the heated surface, but at high heat fluxes, the heated surface is covered with a thin liquid sublayer (which is generally called the macrolayer) holding numerous tiny vapor jets rooted to nucleation sites, and the vapor fed continuously from these vapor jets accumulates to develop massive vapor slugs successively on the foregoing liquid sublayer.

Principle

A linear heat source placed in a material of semi-infinite nature causes temperature changes due to heat conduction. The relationship between temperature at a given distance from the heat source and time in the coordinate system (T - To, log t) is linear after some time.

Object

The experiment demonstrates heat conduction in semi-infinite space. It allows one also to obtain experimentally both the thermal conductivity and the thermal diffusivity of the material. An object used for the experiment can be any material in the form of powder, granules, or paste in bulk.

Apparatus

The apparatus consists of a glass beaker (diameter 0.1 m, height 0.2 m) which is filled with a selected material. At the center of the beaker a linear heat source 0.1 m long is placed and there is a temperature sensor parallel to the heater at a distance of 10 mm from the heater (Fig. 4.1). Both of them are in the form of a capillary metal tube 0.2–0.5 mm in diameter. The heat source is connected to a stabilized power supply (approximately 1.5 W) and the temperature sensor to a display and/or to a recorder.

Procedure

The experiment is carried out at ambient temperature. Switch on the power and register temperature in 2 minute intervals for 20 minutes. After completing the experiment remove the heat source and the temperature sensor to cool them to ambient temperature.

We talk of heat as energy in the process of being transferred. Note, heat is not stored within matter, but rather heat is either “done on” or “done by” matter. Heat is a way of transferring energy across the boundaries of a system. It should be noted that heat is not a conserved substance, as was thought in the past (a remnant of the caloric theory of heat). Also, it is not a fluid as one might envision when the phrase heat flow is used, nor is heat a property of matter. Thus terms such as “heat of a substance” are meaningless. Since heat is neither a property of a system nor contained in a system, we speak of heat as a mode of energy transfer accompanied by a net amount of entropy transfer uniquely specified by the energy transfer as well as the temperature at which it occurs.

We may transfer heat by three different modes: conduction, convection, and radiation. Since each mode is subject to different laws, experiments such as those contained herein are necessary in order to understand the physical aspects involved in a heat-transfer problem.

Object

In the design of continuous-flow combustion systems, an important performance requirement is that combustion must be sustained over a wide range of operating conditions. For the combustors employed in aircraft gas turbines, this poses special problems because they are often called upon to operate at very low inlet temperatures and pressures and at fuel/air ratios that lie well outside the normal burning limits of hydrocarbon–air mixtures.

The stability performance of a continuous-flow combustor is usually expressed in the form of a stability plot that separates the regions of stable and unstable combustion. The traditional plot has equivalence ratio or fuel/air ratio as the ordinate, and some loading parameter, such as air velocity or air mass flow rate through the combustor, as the abscissa. A plot of this type is often called a stability loop, owing to its shape, as illustrated in Fig. 32.1.

Background

Stability loops provide two basic kinds of information. First, for any given fuel/air ratio, they indicate the blowout velocity UBO, which is the gas velocity at which flame extinction occurs. Attention is usually focused on the maximum blowout velocity, which tends to coincide with mixture strengths that lie close to the stoichiometric value. Second, for any given combustor loading, they show the range of fuel/air ratios over which stable combustion can be achieved.