Heat Transfer and Fluid Flow in Minichannels and Microchannels

Satish Kandlikar, Srinivas Garimella, Dongqing Li, Stephane Colin, Michael R. King

• Publisher: Butterworth-Heinemann
• Year: 2013
• Print ISBN: 9780080983462
• eBook ISBN: 9780080983516
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Fluid Mechanics

Heat exchangers with minichannel and microchannel flow passages are becoming increasingly popular due to their ability to remove large heat fluxes under single-phase and two-phase applications. Heat Transfer and Fluid Flow in Minichannels and Microchannels methodically covers gas, liquid, and electrokinetic flows, as well as flow boiling and condensation, in minichannel and microchannel applications. Examining biomedical applications as well, the book is an ideal reference for anyone involved in the design processes of microchannel flow passages in a heat exchanger. - Each chapter is accompanied by a real-life case study - New edition of the first book that solely deals with heat and fluid flow in minichannels and microchannels - Presents findings that are directly useful to designers; researchers can use the information in developing new models or identifying research needs

Chapter 1

Introduction

Satish G. Kandlikar^a and Michael R. King^b, ^aMechanical Engineering Department, Rochester Institute of Technology, Rochester, NY, USA, ^bDepartment of Biomedical Engineering, Cornell University, Ithaca, NY, USA

Microchannel and minichannel flow occurs in the natural world, and also forms the basis of many engineering applications. Different physical mechanisms govern convection, heat, and mass transport as one moves from the macroscale to the microscale. In this introductory chapter, we describe a practical flow channel classification scheme. The common dimensionless parameters that arise in modeling microchannel flow and heat transfer are introduced. Some unique considerations in biological microchannel applications are discussed, such as the challenge of transporting and growing biological cells on a chip.

Keywords

Biomedical; classification; dimensional analysis; heat transfer; microchannel

1.1 Need for smaller flow passages

Fluid flow inside channels is at the heart of many natural and man-made systems. Heat and mass transfer is accomplished across channel walls in biological systems, such as the brain, lungs, kidneys, intestines, and blood vessels, as well as in many man-made systems, such as heat exchangers, nuclear reactors, desalination units, and air separation units. In general, transport processes occur across the channel walls, whereas bulk flow takes place through the cross-sectional area of the channel. The channel cross-section thus serves as a conduit to transport fluid to and away from the channel walls.

A channel serves to accomplish two objectives: (i) to bring a fluid into intimate contact with the channel walls, and (ii) to bring fresh fluid to the walls and remove fluid away from the walls as the transport process is accomplished. The rate of the transport process depends on the surface area, which varies with the diameter D for a circular tube, whereas the flow rate depends on the cross-sectional area, which varies linearly with D². Thus, the tube surface area to volume ratio varies as 1/D. Clearly, as the diameter decreases, the surface area to volume ratio increases. In the human body, two of the most efficient heat and mass transfer processes occur inside the lungs and the kidneys, with the flow channels approaching capillary dimensions of around 4 μm.

Figure 1.1 shows the ranges of channel dimensions employed in various systems. Interestingly, biological systems with mass transport processes employ much smaller dimensions, whereas larger channels are used for fluid transportation. From an engineering standpoint, there has been a steady shift from larger diameters, on the order of 10–20 mm, to smaller-diameter channels. Since the dimensions of interest are in the range of a few tens or hundreds of micrometers, use of the term “microscale” has become an accepted classifier for science and engineering associated with processes at this scale.

Figure 1.1 Ranges of channel diameters employed in various applications (Kandlikar and Steinke, 2003).

As the channel size becomes smaller, some of the conventional theories for (bulk) fluid, energy, and mass transport need to be revisited for validation. There are two fundamental elements responsible for departure from “conventional” theories at the microscale. For example, differences in modeling fluid flow in small-diameter channels may arise as a result of

1. a change in the fundamental process, such as a deviation from the continuum assumption for gas flow, or an increased influence of some additional forces, such as electrokinetic forces;

2. uncertainty regarding the applicability of empirical factors derived from experiments conducted at larger scales, such as entrance and exit loss coefficients for fluid flow in pipes; or

3. uncertainty in measurements at microscale, including geometrical dimensions and operating parameters.

In this book, the potential changes in fundamental processes are discussed in detail, and the needs for experimental validation of empirical constants and correlations are identified if they are not available for small-diameter channels.

1.2 Flow channel classification

Channel classification based on hydraulic diameter is intended to serve as a simple guide for conveying the dimensional range under consideration. Channel size reduction has different effects on different processes. Deriving specific criteria based on the process parameters may seem to be an attractive option, but considering the number of processes and parameters that govern transitions from regular to microscale phenomena (if present), a simple dimensional classification is generally adopted in the literature. The classification proposed by Mehendale et al. (2000) described the range from 1 to 100 μm as microchannels, 100 μm to 1 mm as mesochannels, 1–6 mm as compact passages, and greater than 6 mm as conventional passages.

Kandlikar and Grande (2003) considered the rarefaction effect of common gases at atmospheric pressure. Table 1.1 shows the ranges of channel dimensions that would fall under different flow types.

Table 1.1

Channel Dimensions for Different Types of Flow for Gases at 1 atm (Kandlikar and Grande, 2003)

In biological systems, the flow in capillaries occurs at very low Reynolds numbers. A different modeling approach is needed in such cases. Also, the influence of electrokinetic forces begins to play an important role. Two-phase flow in channels below 10 μm remains unexplored. In a slight modification of the earlier channel classification scheme of Kandlikar and Grande (2003), a more general scheme based on the smallest channel dimension is presented in Table 1.2. Although one may be able to classify the channels depending on the relevant physical phenomena, such as single-phase flow, boiling, condensation, or cell transport, the scheme given in Table 1.2 is recommended for wider application.

Table 1.2

Channel Classification Scheme (Kandlikar and Grande, 2003)

Conventional channels	>3 mm
Minichannels	3 mm≥D>200 μm
Microchannels	200 μm≥D>10 μm
Transitional microchannels	10 μm≥D>1 μm
Transitional nanochannels	1 μm≥D>0.1 μm
Nanochannels	0.1 μm≥D

D: smallest channel dimension.

In Table 1.2, D is the channel diameter. In the case of noncircular channels, it is recommended that the minimum channel dimension (e.g., the short side of a rectangular cross-section) should be used in place of the diameter D. We will use the above classification scheme for defining minichannels and microchannels. This classification scheme is employed for simplicity in terminology; the applicability of continuum theory or slip flow conditions for gas flow needs to be checked for the actual operating conditions in any channel.

1.3 Basic heat transfer and pressure drop considerations

The effect of hydraulic diameter on heat transfer and pressure drop is illustrated in Figures 1.2 and 1.3 for water and air flowing in a square channel under constant heat flux and fully developed laminar flow conditions. The heat transfer coefficient h is unaffected by the flow Reynolds number (Re) in the fully developed laminar region. It is given by:

(1.1)

where k is the thermal conductivity of the fluid and D_h is the hydraulic diameter of the channel. The Nusselt number (Nu) for fully developed laminar flow in a square channel under constant heat flux conditions is 3.61. Figure 1.2 shows the variation of h for flow of water and air with channel hydraulic diameter under these conditions. The dramatic enhancement in h with a reduction in channel size is clearly demonstrated.

Figure 1.2 Variation of the heat transfer coefficient with channel size for fully developed laminar flow of air and water.

Figure 1.3 Variation of pressure gradient with channel size for fully developed laminar flow of air and water.

On the other hand, the friction factor f varies inversely with Re, since the product f·Re remains constant during fully developed laminar flow. The frictional pressure drop per unit length for the flow of an incompressible fluid is given by:

(1.2)

where Δp_f/L is the frictional pressure gradient, f is the Fanning friction factor, G is the mass flux, and ρ is the fluid density. For fully developed laminar flow, we can write:

(1.3)

where Re is the Reynolds number, Re=GD_h/μ, and C is a constant, C=14...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• About the Authors
• Preface
• Nomenclature
• Chapter 1. Introduction
• Chapter 2. Single-Phase Gas Flow in Microchannels
• Chapter 3. Single-Phase Liquid Flow in Minichannels and Microchannels
• Chapter 4. Single-Phase Electrokinetic Flow in Microchannels
• Chapter 5. Flow Boiling in Minichannels and Microchannels
• Chapter 6. Condensation in Minichannels and Microchannels
• Chapter 7. Biomedical Applications of Microchannel Flows
• Index