N o n - N e w to n ia n F l u i d H e a t T r a n s f e r in P o r o u s M e d ia ...... C. E. Hickox, D. K. Gartling, D. F. McVey, and A. J. Russo, Analysis of heat and mass.
ADVANCES IN HEAT TRANSFER, VOLUME 24
Non-Newtonian Fluid Heat Transfer in Porous Media
A. y . SHENOY D epartm ent o f Energy and M echanical Engineering Shizuoka University H am am atsu, Japan
I. I n t r o d u c t i o n .........................................................................................................................102 II. Basic Definitions and E q u a t i o n s ...................................................................................... 106 A . Non-N ew tonian F l u i d s ................................................................................................. 106 B. Governing E q u a t i o n s ..................................................................................................110 C. Dimensionless G r o u p s ..................................................................................................119 D. Flow Regime M a p ....................................................................................................... 120 III. Steady-State Forced Convection: D arcy-Forchheim er Regime Boundary-Layer F l o w ..........................................................................................................................................121 A. Isotherm al Sem i-Infinite P l a t e ................................................................................ 122 B. Nonisotherm al Smooth Surface o f A rbitrary S h a p e .............................................. 124 IV. Steady-State N atural Convection: D arcy-Forchheim er Regime Boundary-Layer F l o w ..........................................................................................................................................127 A. Inelastic O stw ald-de Waele Power-Law F l u i d s ....................................................127 B. Inelastic Herschel-Bulkley Power-Law Fluids with Yield S tr e s s ....................... 139 C. Elastic Boger Fluids o f C onstant V i s c o s i t y ..........................................................142 V. Steady-State Mixed Convection: P ure Darcy Regime Boundary-Layer Flow . . 144 A. Inelastic O stw ald-de Waele Pow er-Law F l u i d s ....................................................144 B. Elastic Boger Fluids o f C onstant V i s c o s i t y ..........................................................151 VI. Steady-State Convection: Some A dditonal T o p i c s ....................................................155 A. C onfined Forced Flow in Highly P orous M e d i a ....................................................155 B. Free Convective Flow from a Point H eat Source in Low-Porosity M edia . . 160 C. Free Convective Flow from a Line H eat Source in Low -Porosity M edia . . 163 VII. Nonsteady-State Convection: P ure Darcy R e g im e ..........................................................167 A . T ransient N atural Convection Past an Isotherm al Vertical Flat Plate . . . 167 B. Oscillatory Convection in Densely Packed H orizontal Porous Layer . . . 174 VIII. Concluding R e m a rk s ............................................................................................................. 178 N o m e n c la tu r e .........................................................................................................................179 R e f e r e n c e s .............................................................................................................................. 184
101 Copyright © 1994 by A cadem ic Press, Inc. AH rights o f reproduction in any form reserved. ISBN 0-12-020024-4
102
A. V.
Shenoy
N o n - N e w to n ia n F lu id H e a t T r a n s f e r in P o r o u s M e d ia
I. Introduction
TABLE I— continued
Various topics relating to heat transfer in non-Newtonian fluid systems have been dealt with in earlier volumes of this series by Metzner [1], Dimant and Poreh [2], Cho and Hartnett [3], Shenoy and Mashelkar [4], and Hartnett and Kostic [5], But none have considered the presence of a porous medium in non-Newtonian fluid heat transfer. The articles of Shenoy [6 , 7] as well as Irvine and Karni [8 ], which comprehensively review the work on heat transfer in non-Newtonian fluids, make no mention of this subject. However, there has been a sudden surge of interest in heat transfer in nonNewtonian fluid-saturated porous medium, due to the realization that a number of fluids exhibiting non-Newtonian behavior come in contact with porous media, particularly in ceramic processing, enhanced oil recovery, and filtration. Heat transfer in porous media, in general, is of great pragmatic importance in a wide variety of scientific and engineering applications, as can be seen from some of the applications summarized in Table I. Hence,
S cientific an d engineering discipline
Scientific and engineering discipline Biomechanics
in
K ulkarni and Dorais wamy [16] W hitaker [17]
Food technology
C ertain foods rot due to diffusion o f heat and mass transfer through a porous mass. Im provem ents in m ethods o f food preservation require knowledge o f transport processes through porous m edia. Similarly, drying o f foods, especially in dehydration o f fruits and vegetables, involves changing porosity accom panied by sim ultaneous heat and mass transfer.
Singh and M edina [18]
Geophysics
(a) In exploration o f geopressurized reservoirs, an understanding o f flow and heat transfer through the e arth ’s porous m antle is of im portance, as the trapped w ater in these reservoirs is at high tem peratures and pressures due to the massive weight o f overlying rock. It is also under the influence of the E arth ’s magnetic field which affects the stability o f convection. (b) E xtraction o f geotherm al energy for use by industrial plants is an area where porous media studies attain prim e im portance. In geothermal regions, high underground tem perature induces upw ard convective drift whose mechanistic behavior m ust be understood for the purpose o f harnessing geotherm al energy.
Com barnous and Bories [19]
G roundw ater hydrology
In the study o f seepage o f water through river beds and in investigations o f potential underground w ater resources, various form s of convection through porous m edia are encountered. The use o f aquifiers for hot w ater storage is an area where therm al gradients affect perform ance and m ust be understood. It is also necessary to describe the porous m edium with which the groundw ater is in contact.
Com barnous and Bories [19] Tsang et al. [23, 24]
Industrial engineering
In filtration studies, the m ain concern is to determine how fluid moves through the porous structure leaving behind unw anted m aterial. The porosity o f the system is continually changing and altering the pressure drop characteristics o f the system.
Kozicki [25]
References
Fluids flowing through lungs and arteries are bounded by two layers held together by regularly spaced tissues that are often idealized as porous m edia. Instabilities in the m ovement o f these fluids give a good indication o f the associated pathological condition.
Fung and Tang [9, 10]
Ceramic engineering
Drying a n d /o r burnout o f binder system from green compacts during colloidal processing o f advanced ceramics involves simultaneous m om entum heat and mass transfer in disordered porous media.
Stangle and Aksay [11]
Chemical engineering
(a) During tem porary storage and eventual disposal o f nuclear waste, there is always a concern about risk assessment and this requires a thorough knowledge o f the heat transfer characteristics o f the porous system. (b) In the case o f packed bed reactors, transport processes through porous m edia have to be well understood.
Hickock et al. [12] F arr et al. [13]
W akao and Kaguei [14] Lem coff
