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About this book

This book is a synthesis of emerging topics in heat and mass transfer in porous media. It brings together some of the world leaders in research on transport p- nomena in porous media to present the state of the art of its theory as well as the applicationofthetheoryinemerging?eldssuchasbioengineering,microelectronics and nanotechnology. The well renowned scientists presenting their ?ndings in the review chapters presented are not only among the best world leaders in their ?eld, they also capture the research that is undertaken in all the parts of the globe, from the Far East (Hong-Kong), the Southern Hemisphere (New Zealand and South Africa) to Europe and America. The book is separated into two parts. The ?rst presents the state of the art of the theory of heat and mass transfer in porous media and can be used in both the traditional (underground ?ow, ?ltering and reservoir engineering) as well as in the more recent emerging applications. The second part deals with emerging topics and applications of the theory to bioengineering, microelectronics, and nanotechnology. Traditionally,thetopicoftransportphenomenainporousmediawasalmostexc- sivelyreservedtothe?eldofunderground?ow(water,oil,gas,etc.)and?ltering.With some singular exceptions on applications to drying processes of fabric, the devel- ment of the theory of transport phenomena in porous media was historically driven by the needs of technologies linked to reservoir engineering or civil engineering. A turningpointinthisdevelopmentwasreachedintheearlypartofthesecondhalfinthe twentycenturywhenspecialattentiontoheattransferinporousmediayieldedan- ceedingexpansionofinterest.Thisdevelopmentcontinuedinthetwenty?rstcentury and reached recently such an impressive use in a diverse collection of technological applications that created the motivation behind the preparation of this book.

Table of Contents

Frontmatter

Dual-Phase-Lagging and Porous-Medium Heat Conduction Processes

Abstract
We review some major progresses on dual-phase-lagging heat conduction and its intrinsic application in porous-medium heat conduction. The topics include well-posedness, solution structure, thermal wave and resonance, and intrinsic equivalence between the dual-phase-lagging heat conduction and the Fourier heat conduction in porous media subject to lack of local thermal equilibrium.
Liqiu Wang, Mingtian Xu, Xiaohao Wei

Heat Transfer Analysis Under Local Thermal Non-equilibrium Conditions

Without Abstract
A. Haji-Sheikh, W.J. Minkowycz

General Heterogeneity Effects on the Onset of Convection in a Porous Medium

Without Abstract
D.A. Nield

The Instability of Unsteady Boundary Layers in Porous Media

Without Abstract
D.A.S. Rees, A. Selim, J.P. Ennis-King

Analytical Transition to Weak Turbulence and Chaotic Natural Convection in Porous Media

Abstract
A review on the transition to weak turbulence and chaotic natural convection in porous media is presented in this chapter. In particular, the question on how can one obtain the transition point analytically is emphasized and topics such as the hysteresis phenomenon linked to this transition is discussed. Fractal types of results obtained by comparing solutions at different accuracy levels are finally presented to conclude the chapter.
Peter Vadász

Natural Convection in Gravity-Modulated Porous Layers

Abstract
We analyze natural convection in porous layers subjected to gravity modulation. In particular a linear stability analysis and weak non-linear analysis is presented for both synchronous and subharmonic solutions and the exact point for the transition from synchronous to subharmonic solutions is computed. It is demonstrated that increasing the excitation frequency rapidly stabilizes the convection up to the transition point from synchronous to subharmonic convection. Beyond the transition point, the effect of increasing the frequency is to slowly destabilize the convection. The weak-non-linear results show that increasing the excitation frequency rapidly decays the convection amplitude. An analogy between the inverted pendulum with an oscillating pivot point and the gravity modulated porous layer is developed and it is shown that the convection cell wavelength is related to the length of the pendulum.
Saneshan Govender

Thermal Vibrational Convection in a Porous Medium Saturated by a Pure or Binary Fluid

Without Abstract
Yazdan Pedramrazi, Marie-Catherine Charrier-Mojtabi, Abdelkader Mojtabi

New Developments in Bioconvection in Porous Media: Bioconvection Plumes, Bio-Thermal Convection, and Effects of Vertical Vibration

abstract
This chapter reviews new developments in bioconvection in a fluid saturated porous medium caused by either gyrotactic or oxytactic microorganisms. Bioconvection arises as a result of an unstable density stratification caused by upswimming microorganisms. This unstable density stratification occurs when the microorganisms, heavier than water, accumulate in the upper regions of the fluid. This hydrodynamic instability may lead to the development of bioconvection plumes, which in case of oxytactic microorganisms transport cells and oxygen from the upper fluid region to the lower fluid regions. The presented modeling is limited to the situation when the average pore size is much larger than the size of a microorganism; therefore, local vorticity generated by flow through the pores does not affect the ability of microorganisms to reorient.
The chapter introduces bio-thermal convection, which, contrary to traditional bioconvection, has two destabilizing mechanisms that contribute to creating the unstable density stratification. The utilization of the Galerkin method to solve a linear stability problem leads to a correlation between the critical value of the bioconvection Rayleigh number and the traditional “thermal” Rayleigh number. The chapter also investigates the potential of utilizing the vertical vibration for controlling bioconvection. The linear stability analysis indicates that vertical vibration has a stabilizing effect on the suspension.
A.V. Kuznetsov

Macromolecular Transport in Arterial Walls: Current and Future Directions

abstract
Relevant mathematical models associated with the transport of macromolecules in the blood stream and in the arterial walls are reviewed in this work. A robust four-layer model (endothelium, intima, internal elastic lamina and media) based on porous media concept and accounting for selective permeability of each porous layer to certain solutes is presented to describe the transport of macromolecules in the arterial wall coupled with the transport in the lumen. The variances in the current models are analyzed and discussed. Future direction in developing a rigorous mathematical model for transport in arterial walls using porous media theory and fluid-structure interaction approach is outlined in this study.
K. Khanafer, K. Vafai

Flow and Heat Transfer in Biological Tissues: Application of Porous Media Theory

The transport phenomena in porous media have generated increasing interest over the past several decades owing to the importance of porous media in diverse fields such as biotechnology, living structures, chemical and environmental engineering, etc. Particularly, significant advances have been achieved in applying porous media theory in modeling biomedical applications. Examples include computational biology, tissue replacement production, drug delivery, advanced medical imaging, porous scaffolds for tissue engineering and effective tissue replacement to alleviate organ shortages, and transport in biological tissues. Another important application of porous media includes diffusion process in the extracellular space (ECS) which is crucial for investigating central nervous system physiology. In this chapter, three applications namely brain aneurysm, flow and heat transfer in biological tissues, and porous scaffolds for tissue engineering are analyzed as related to the advances in porous media theory in biological applications.
Khalil Khanafer, Abdalla AlAmiri, Ioan Pop, Joseph L. Bull

Metal Foams as Passive Thermal Control Systems

Without Abstract
Shankar Krishnan, Jayathi Y. Murthy, Suresh V. Garimella

Nanofluid Suspensions and Bi-composite Media as Derivatives of Interface Heat Transfer Modeling in Porous Media

Abstract
Spectacular heat transfer enhancement has been measured in nanofluid suspensions. Attempts in explaining these experimental results did not yield yet a definite answer. Modelling the heat conduction process in nanofluid suspensions is being shown to be a special case of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq). Similarly, the modelling of heat conduction in bi-composite systems is also equivalent to the applicable process in porous media. The chapter reviews the topic of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq), introduces one of the most accurate methods of measuring the thermal conductivity, the transient hot wire method, and discusses its possible application to dual-phase systems. Maxwell’s concept of effective thermal conductivity is then introduced and theoretical results applicable for nanofluid suspensions are compared with published experimental data.
Peter Vadász

Backmatter

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