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Convective Heat and Mass Transfer in Porous Media NATO ASI Series Advanced ScIence Institutes SerIes A Series presenting the results of activities sponsored by the NATO Science Committee, which aims at the dissemination of advanced scientific and technological know/edge, with a view to strengthening Unks between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A LHe ScIences Plenum Publishing Corporation B Physics London and New York C Mathematical K1uwer Academic Publishers and Physical Sciences Dordrecht, Boston and London o Behavioural and Social ScIences E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological ScIences Berlin, Heidelberg, New York, London, H Cell Biology Paris and Tokyo I Global environmental Change NATo-PCO-DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords and/or abstracts) to more than 30000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NATO-PCO-DATA BASE is possible in two ways: - via online FILE 128 (NATO-PCO-DATA BASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, Italy. - via CD-ROM -NATO-PCO-DATA BASE-with user-friendly retrieval software in English, French and German (@wrv GmbH and DATAWARE Technologies Inc. 1989). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-Poo, Overijse, Belgium. SerIes E: Applied Sciences -Vol. 196 Convective Heat and Mass Transfer in Porous Media edited by Sadik Kaka~ Department of Mechanical Engineering, University of Miami, Coral Gables, Aorida, U.S.A. Biral Kilkiş Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey Frank A. Kulacki Colorado State University, College of Engineering, Ft. Collins, Colorado, U.S.A. and Faruk Arin~ Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey Springer-Science+Business Media, B.V. Proceedings of Ihe NATO Advancod Study Institute O" Convective Heat and Mass Transfer in Porous Media Qeşme.lzmir. Turkey 6-17 August 1990 ISBN 978-94-010-5419-5 ISBN 978-94-011-3220-6 (eBook) DOI 10.1007/978-94-011-3220-6 Printed on ackJ.free psper AlI Rlghts Rese!Ved <O 1991 Springer Science+Business Media Dordrechl Originally published by Kluwer Academic Publishers in 1991 Softcover raprint of the hardcover 1st edition 1991 No part of the material protected by this copyright notice may be reproduced ar utilized in any fa"" or by any means. electronic Dr mechanical. including photo c:opying. recording Of by any information storage and retrieval system, without writ1en permission from the copyright owner. CONTENTS Preface ix Opening Lecture : Transport Processes in a Rapidly Changing World A.E. Dergles PART I -FUNDAMENTALS Modelling of Transport Phenomena in Porous Media LD~ 7 Fundamentals of Mechanics of Saturated Porous Media: Basic Equations and Waves R.I. Nigmatulin and A.A. Gubaidullin 71 The Stability of Convective Flows in Porous Media D.A. Nield 79 Free Convection Heat and Mass Transfer in a Porous Medium H.S. Takhar and V.M. Soundalgekar 123 Natural Convection in a Vertical Porous Annulus G. Lauriat and V. Prasad 143 Non-Darcy Natural Convection in Saturated Porous Media V. Prasad and N. Kladias 173 Mixed Convection in Saturated Porous Media F.C. Lai, F.A. Kulacki and V. Prasad 225 Forced Convective Flow and Heat Transfer Through a Porous Medium Exposed to a Flat Plate or a Olannel G. Lauriat and K. Vafai 289 Forced Convection Heat Transfer in a Porous Medium H.S. Takhar and V.M. Soundalgekar 329 Radiation Transport in Porous or Fibrous Media Y. Kurosaki and J. Yamada 347 Fundamentals of Drying of Capillary -Porous Bodies S.A. Dories 391 Heat Transfer During Unsaturated Flow in Porous Media O.A. Plumb 435 PART I -FUNDAMENTALS (continued) Buoyancy-Induced Flow and Heat Transfer in Saturated Fissured Media F.A. Kulacki and G. Rajen 465 Effect of Randomness on Heat and Mass Transfer in Porous Media J.G. Georgiadis 499 Analytical Solutions to Transient Convective Mass Transfer Within Porous Media R.M. Cotta, C. Baohua and P.F.L.H. Filho 525 PART II -SPECIAL TOPICS Natural Convection in Porous Media with Variable Porosity and Thermal Dispersion Effects P. Cheng, S.W. Hsiao and C.K. Chen 543 Convective Flow Interaction and Heat Transfer Between Fluid and Porous Layers V. Prasad 563 Temperature Distribution in a Porous Slab with Random Therrnophysical Characteristic L. Carlomusto, A. Pian ese, L.M. de Socio, P. Kotsiopoulos and T. Calderon 617 Forced Convection in Packed Tubes and Channels with Variable Porosity and Thermal Dispersion Effects P. Cheng, A. Chowdhury and C.T. Hsu 625 Transient Double Diffusive Convection in a Horizontal Fluid Layer Situated on top of a Porous Substrate M. Kazmierczak and D. Poulikakos 655 Drying of Wood Residues in a Fixed Bed R. Sheikholeslami and A.P. Watkinson 673 Heat and Mass Transfer in Adsorbent Beds S. Ulkii 695 Solidification of a Binary Mixture Samrating a Bed of Glass Spheres W.Z. Cao and D. Poulikakos 725 Melting in the Presence of Natural Convection in a Saturated Porous Medium A. Bejan 739 Air-Water Two-Phase Flow Pressure Drop in Large Scale Porous Media Lj.B. Vujisic, I. Catton and N.H. Afgan 773 Boiling and Dryout in Unconsolidated Porous Media A.K. Stubos and J.M. Ruchlin 791 Heat Transfer from a Surface Covered with Hair A. Bejan and J.L. Lage 823 PART ill -EXPERIMENTAL METHODS Measurements of Thermal Conductivity in Porous Media E. Hahne, Y.W. Song and U. Gross 849 Determination of Velocity Vectors in Porous Media with Fluorescent Particle Image Velocimetry (FPIV) M.A. Northrup, T.J. Kulp, S.M. Angel and G.F. Pinder 867 Non Invasive Measurement Techniques in Porous Media S.A. Bories, M.C. Charrier-Mojtabi, D. Houi and P.G. Raynaud 883 Flash Method of Measuring Thermal Diffusivity and Conductivity 1. Tavman 923 PART IV -APPLICATIONS Mechanics, Heat and Mass Transfer in Saturated Porous Media. Application to Petroleum Technology R.I. Nigmatulin, K.M. Federov, Z.N. Hai and A.A. Kislitcin 939 Drying Complex Porous Materials -Modelling and Experiments O.A. Plumb 963 Some Geophysical Problems Involving Convection in Porous Media D.A. Nield 985 Porous Surface Boiling and Its Application to Cooling Microelectronic Chips W. Nakayama 1007 Heat and Mass Transfer in Spouted Beds B. Kdkl§ and S. Kaka~ 1031 Liquid Seeping into Porous Ground M.N. Aybers 1061 PART V -FUTURE RESEARCH NEEDS Future Research Needs in Convective Heat and Mass Transport in Porous Media J.G. Georgiadis 1073 Index 1089 PREFACE The rapid growth of literature on convective heat and mass transfer through porous media has brought both engineering and fundamental knowledge to a new state of completeness and depth. Additionally, several new questions of fundamental merit have arisen in several areas which bear direct relation to further advancement of basic knowledge and applications in this field. For example, the growth of fundamental heat transfer data and correlations for engineering use for saturated media has now reached the point where the relations for heat transfer coefficients and flow parameters are known well enough for design purposes. Multiple flow field regimes in natural convection have been identified in several important enclosure geometries. New questions have arisen on the nature of equations being used in theoretical studies, i.e., the Validity of Darcy assumption is being brought into question; Wall effects in high and low velocity flow fields have been found to play a role in predicting transport coefficients; The formulation of transport problems in fractured media are being investigated as both an extension of those in a homogeneous medium and for application in engineering systems in geologic media and problems on saturated media are being addressed to determine their proper formulation and solution. The long standing problem of how to adequately formulate and solve problems of multi-phase heat and mass transfer in heterogeneous media is important in the technologies of chemical reactor engineering and enhanced oil recovery. This NATO ASI provides in-depth information to heat transfer and fluid mechanics researchers regarding up-to-date results and areas of future research in the field of heat and mass transfer in porous media. The subject is treated in considerable depth by lecturers eminent in their field. The other participants, included scientists, engineers, and senior graduate students who themselves are involved in similar research and who wish to learn more about current developments, as well as scientists from other areas who are planning to begin research on porous media. The lectures are supplemented by informal discussions designed to encourage the free and critical exchange of ideas. A limited number of contributions from the participants are also included to the ten-working-day programme. The material in the volume is arranged in five parts which cover the fundamentals, special topics, experimental methods, applications and the future research needs in convective heat and mass transport in porous media. We hope that this volume will achieve the major objective of the Institute - to provide an international forum for the dissamination of information on the fundamentals and applications of convective heat and mass transport in porous media -by serving as a reference for engineers and for specialized courses on the subject. The sponsorship of the NATO Scientific Affairs Division ,Turkish Technical and Scientific Council, and Middle East Technical University are greatfully acknowledged. Our gratitude goes to Drs. Weigong Li and H. Yiincii for his valuable efforts in making the Institute a success and to Mrs. A. Schaerli and Mrs. G. Beyaz for their efficient secreterial work. The editors wish to extend a word of appreciation to the Turkish industrial fIrmS Selnikel, MNG, Gama, for their financial support. A word of appreciation is also due to the members of the Organizing Committee, Session Chairmen for their efforts in programming, organizing and expediting the technical sessions. ix Much of the planning of this NATO ASI was carried out at the University of Miami, Coral Gables and the Middle East Technical University. The editing of this volume was finalized during Dr. K~'s stay at the Lehrstuhl A flir Thennodynamik, Techniche Universitiit Munchen, FRG, as the recipient of the U.S. Senior Scientist Award from the Alexander von Humboldt Stifrung. Dr. Kaka~ is thankful to Prof. F. Mayinger for providing the facilities of his Chair. Finally, our heartfelt thanks to all invited lecturers and authors who provided the substance of the Institute, and the participants for their attendance, questions, and comments. S. Kaka~ B. Killa§ F. A. Kulacki F.Ann~ Arthur E. Bergles Rensselaer Polyt.ec::mU.c Institute Troy, New York 12180-3590 I am very pleased to be with yoo for the ~ of this i:aport:ant ASI. '!his is the 5th t.ime I have been privileged to participate in an ASI in TUrkey, ani each one has provided faxI JllellDries of good times, renewed acquaintances, and new friemships. '!he NMO Internatiooal. scientific Exdlar¥Je Pl::og:tanues for 1990 include 71 Advarx:led stuiy Institutes and 59 Advarx:led Research WO'rkshq:lS. '!he Pl::og:tames seem. to qat strorger every year, as evideooed by the aqeOOa for this Institute. My remarks will be light fran the starxlpoint of technical detail. I ~'t even menticm Darcy's equation. However, I will discuss sane broader aspects of transport processes that, for the most part, defy mathematical mdel.lin;J. yet they have profound inplicaticms for us all. As we awroadl the 21st century, there is a tedmological cptim:ism stirred by the o Olallerqe to develop large scale use of energy resource alternatives (bianass, solar thermal, wirrl, new tedmology nuclear plants, fusicm reactors) o Olallerqe of autaoobiles with even greater fuel efficierx:y ani integraticm with electronic highways o Possibility of substantial awlication of magnetically levitated rail transport o Aerospace plane o Space station o Olallerqe of interplanetary exploraticm o Developoent of micranechani.cal devices o IDplementation of intelliqent machines and expert systems o Widespread use of the latest oamamicaticm tedmologies. 'Dlere is also enthusiasm aboot the develq:ment of a qlobal ec:x:x1CDY and the qlobalizaticm of en;Jineerin;J. Naisbett ani A1:mdene in Megat.rerps 2000 predict a boan.in:j qlobal econany in the 1990's, integrated to the point where the 160 c:x::All'1tries of the world functicm as a sirqle econany, one marketplace. s. Kakaf et al. (etis.), Convective Heat and Mass Transfer in Porous Media, 1-4. e 1991 KlllM'er Academic Publishers.